What more could be learned from a rare astronomical event if we knew precisely when it would occur? This is actually related to a question I recently asked on Worldbuilding, but seemed more appropriately asked here.

To keep this from being too broad in scope, let's assume that someone figured out the exact moment that Eta Carinae will go supernova (I wouldn't hold it against anyone if they suggested a more scientifically interesting event).

Due to this foreknowledge, we could point every telescope we have in its direction for the main event.  Is there any science we know we could do/learn from this event that we wouldn't get by reacting to it after the fact?  I know such an event would generate data for a century or more to come, but I'm interest in the moment of the explosion.

Somewhat related, is there anything we would/could do now to prepare for it if this event were going to happen today?

I would argue that simply knowing that a star was about to undergo a supernova could be information enough.

It's not always easy to figure out what type of star a given supernova progenitor was. Sometimes, there were no observations of the relevant region of sky prior to the supernova, and so we can't simply look back at prior observations and extrapolate from that. We can definitely look at certain spectral lines and other information from the remnant, but it's rarely as sure as actually observing the progenitor.

There are some classes of stars which have yet to be conclusively identified as supernova progenitors, though there may be evidence suggesting that they should evolve as such. Red supergiants are one group, leading to the so-called "red supergiant problem" (see Smartt et al. (2009) and this question). If we knew that a red supergiant was a supernova progenitor, that would possibly solve the problem.

Wolf-Rayet stars, thought to produce Type Ib/c supernovae, are another group (see Yoon et al. (2012). Evolutionary models and indirect observational evidence predict that they should lead to these supernovae, but no observations of Wolf-Rayet supernova progenitors have been observed.

Eta Carinae A - which I assume is the star you're referring to - appears to be a luminous blue variable (LBV). We do know that LBVs lead to supernovae (see for instance the case of SN 2006jc, which underwent a major outburst two days prior). However, it can be harder to distinguish between supernovae and certain supernova imposter events, caused by LBVs. I'd speculate that we could try to observe Eta Carinae A in the period leading up to the supernovae, to try to observe the differences between outbursts and the actual supernova, which could give us better information on the nature of the evolution of these stars. Additionally, there is neutrino emission in the periods leading up to supernovae (see this question); perhaps detectors on Earth could monitor the progenitor and see if they can find anything.

We could also, given enough warning time, attempt to study the progenitor in the final phases of stellar evolution. This page gives a table for the time periods of various fusion phases in the life of a $25M_\odot$ star:
$$\begin{array}{|c|c|}
\hline \text{Fusion phase}&\text{Length of phase}\\
\hline \text{Hydrogen} & \text{7 million years}\\
\hline \text{Helium} & \text{500,000 years}\\
\hline \text{Carbon} & \text{600 years}\\
\hline \text{Neon} & \text{1 year}\\
\hline \text{Oxygen} & \text{6 months}\\
\hline \text{Silicon} & \text{1 day}\\
\hline
\end{array}$$
This would let us figure out where the star is in its life and figure out what effects different fusion pathways could be having, if any.

Finally, I'm assuming that your question means that we know when the light from the supernova reaches Earth, and that this would happen in the near future.


Would a spacecraft just go "through" a gas giant? From my understanding of the word gas giant, it is a planet composed of entirely a gaseous atmosphere, and so planets Jupiter and onwards fall in this category.

That being said, what would stop a spacecraft from just going right through any of these planets?

For earth, a spacecraft would firstly rapidly disintegrate approaching the surface of earth, and if it happens to still have part of itself, it will collide with the surface.

For gas giants like Uranus, if a spacecraft is able to counter the gravitational forces and slow down, could it actually "go through" Uranus?

In short, No.

Side detail:
Uranus and Neptune consist likely of 20% gas and 80% rock, coming from simple density considerations. They have large inner cores with masses around $\rm 12-14 \; m_{earth} $, and something like $\rm 2-3 \; m_{earth} $ of gas on top of them.
Jupiter and Saturn are true gas giants. They both have $\rm 5-20 \; m_{earth} $ of solids in them  and the rest of the $\rm 320 \; m_{earth} $ (=Jupiter) and $\rm 95 \; m_{earth} $ (=Saturn) are gas.

However even if Jupiter and Saturn were 100% gas, you couldn't fly through them.

The main reasons for this is

Enormous density, pressure and temperature. A gas mass of several tens of Earth masses will collapse under its own gravity to enormous central densities, temperatures and thus static pressures.
The densities that this gas will be compressed to, can have densities comparable and exceeding that of water, which is a good rule-of-thumb for the center of Jupiter (typical calculations show gas densities around $\rm 20 g/cm^3$, source).
The static pressure will crush your spacecraft, the high density will near instantly slow you down to zero due to strong friction, and the high temperatures will just melt or evaporate your spacecraft.

Just because something is gaseous, doesn't mean you can soar through it, as you would on a calm day with a glider on a light breeze.

There are other factors that complicate even getting there:

Re-entry heat. The cold upper atmospheres of the gas giants increase the mach numbers $v / c_{sound}$ at re-entry by up to a factor of two. As recently discussed on space exploration the re-entry heating that a spacecraft experiences scales as the 8th power of the re-entry speed or more. So a spacecraft would experience around $2^8 = 256$ times more heat load. The engineering challenge to survive this already would be considerable.
I bring this up, because as @uhoh pointed out, it is unclear whether you want to just slice the atmosphere or fly through the $r=0$ coordinate of the planet.
Core erosion. Funny enough, the solid core is probably not even there anymore. Recent work has shown, that under the enormous pressures given at the center of a gas giant a phenomenon called 'core erosion' will take place. In this, typical rock-composing elements prefer to exist in a gaseous phase rather than in a solid phase at those high pressure, thus the solid core will dissolve into the surrounding gas.
This will further increase friction when trying to fly through the gas.


Does a meteor's direction change between country or latitude? So here is the question me and a friend of mine from Norway we saw a meteor but que said he saw it in the opposite direction as me and I was looking from spain, does that make any sense? Or we should see it going the same direction? Thanks in advance

If you see the same meteor, it of course only has one path - even while the apparent movement differs for different observers. What you basically do in that case is triangulation - which you could use with your known geographic location (and time for the observations, and the direction horizontally and vertically) reconstruct the flight path. That's a method which actually is used to identify meteors and and tracking them, e.g. via the fireball network.

Is it possible that you saw the meteor given your geographic separation?
(note 11 March: This paragraph is heavily revised and comes to the opposite conclusion with the right trigonometry)
Given the mentioned separation between Norway and Spain, we talk of a few thousand kilometres. The typical height at which you see a meteor is between 50 and 100km. The curvature of Earth then makes sure you don't see the same meteor when you are too far apart - but it might be still just right here:
Madrid and Oslo are about 2000km apart, the Earth's circumference is about 40000km. The earth's radius is $r_E = 6371$km which allows us to calculate the angle $\alpha$ between those as seen from Earth's centre: $\alpha = 0.31$ (radians). With that angle we can calculate the height an object must be at when we look horizontally and just see it at the horizon (laying on the floor makes it easy to calculate), given it's separated by the angle $\alpha$:

$$
d_s = r_E\cdot tan\alpha
$$
and
$$
\frac{h+r_e}{\sin 90°} = \frac{d_s}{\sin\alpha} = \frac{r_e\tan\alpha}{\sin\alpha} = \frac{r_E}{\cos\alpha} = r_E \sec\alpha
$$
so that
$$
h = \frac{r_E}{\cos\alpha}-r_E
$$
Now if you enter the angle between Oslo and Madrid you get a height of about 79km for an object passing half-way (thus at half the angle to each). So it might have been that very same meteor if it was very close to the local horizon. Given that this estimation is pessimistic as it ignores observer height, things get a bit better if you assume that you stand on your feet, on a building or even a mountain. Either way, the meteor will have been close to the horizon for both of you, and very likely for one travelling left to right, for the other observer right to left.


Can a planet in our system eclipse the sun as seen from another one? When the Sun, Earth and Moon get properly aligned, we get eclipses, where the Sun is partially or totally hidden by the Moon when seen from Earth.
Is it possible for one planet of the solar system to produce an eclipse on another one?
There are two underlying questions in this:

are alignments of the Sun and two planets actually possible (and if so, how frequent)? Given the slightly different orbital planes of the planets, this seems difficult?

even though planets are much smaller than the Sun, with appropriate distances between the three bodies considered, is it actually possible for one planet to partially or completely hide the Sun like we see in the Sun-Moon-Earth case, or does it only happen for planet-satellite combinations given the relative distances (i.e. in all other cases if would just be a tiny point transiting across the Sun)?

I understand that the Earth would not be able to project a shadow far enough to get such a phenomenon on other planets, but are there other combinations where it’s possible/did happen?

In our solar system, it is possible for one planet to partially eclipse the sun, but it is not possible for any planet to cause a full solar eclipse as seen from another planet.
The sun is too big and the planets are too small and too far apart.  Transits occur, and can occur for any pair of planets, but they are very rare.  As seen from earth, Mercury only transits a dozen or so times per century, and before 2004, the last time Venus had transited the sun was 1882. http://www.eclipsewise.com/transit/transit.html Orbital periods increase for the planets further away from the sun, so transits across the sun by the outer planets (while possible since no planets are in orbital resonance since Pluto got kicked out) are increasingly rare. Michael Seifert dug up these treasures, documenting transits of the outer planets: Jupiter, Saturn, Uranus.  As expected, the transit of Uranus from Neptune is the rarest, occurring next in October, 38172 CE.
Proof that no planets could fully eclipse the sun from another planet:
To rule out the possibility that any eclipses are possible, We only have to verify orbits pairwise in order of increasing distance from the sun. Since, if the $nth$ planet can't fully eclipse the sun from the $n+1_{th}$ planet than it certainly won't be able to do so from any other planet.  For example, if Jupiter can't eclipse the sun from Saturn, it certainly won't be able to from Neptune.
As seen from a planet, if the apparent size of the sun in the sky is smaller than the apparent size of the next inner planet, then a full eclipse is possible.  The largest an inner planet can appear from an outer planet is when the inner planet is at aphelion and the outer planet is at perihelion and the pass is directly overhead of the observer.
The formula for angular radius of a sphere is $\delta = \arcsin (d/2D)$ where d is the diameter of the sphere and D is the distance between the observer and the center of the sphere.
I ran these calculations using matlab and data from NASA. https://nssdc.gsfc.nasa.gov/planetary/factsheet/
For my input data, the rows are planets, and the columns are diameter (km), perihelion (e6km), and aphelion (e6km).
Here are my results.  Since the values in the second column are smaller than the first for each row, no inter-planetary solar eclipse is possible. As an example of how to read this table, an observer on Venus will see an angular radius of 6.48e-3 radians for the sun in the sky, but an angular radius of only 6.47e-5 radians for the next inner planet, which is Mercury.

Here is my matlab code for posterity:
sunDiameter = 1.3927e6;
planetVals = [4879,12104,12756,6792,142984,120536,51118,49528;...
46.0,107.5,147.1,206.6,740.5,1352.6,2741.3,4444.5;...
69.8,108.9,152.1,249.2,816.6,1514.5,3003.6,4545.7];
results = zeros(2,7);
for i=1:7
  innerPlanetDiam = planetVals(1,i);
  innerPlanetApogee = planetVals(3,i)*1e6;
  outerPlanetPerigee = planetVals(2,i+1)*1e6;
  outerPlanetDiam = planetVals(1,i+1);
  sunApparentSize =
    asin(sunDiameter/(2*(outerPlanetPerigee-outerPlanetDiam/2)));
  innerPlanetApparentSize =
    asin(innerPlanetDiam/(2*(outerPlanetPerigee-outerPlanetDiam/2-innerPlanetApogee)));
  results(1,i) = sunApparentSize;
  results(2,i) = innerPlanetApparentSize;
end
results'


Universe’s Glow Shows There Are Fewer/More Galaxies Than We Thought, Say Scientists There are several articles like this:
Universe’s Glow Shows There Are Fewer Galaxies Than We Thought, Say Scientists

NASA’s New Horizons spacecraft beyond Pluto has made a groundbreaking measurement of the Universe’s background glow—with astonishing results. It turns out that there are many fewer galaxies out there than previously thought.

But then they seem to say the opposite:

“The Universe is dark, but not as dark as we thought,” said Lauer. Having measured the Universe’s glow, Lauer and his colleagues subtracted known sources such as the stars in the Milky Way and reflections from interstellar dust only to find that some light remained unaccounted for.
So what’s the source? Options include:
...
There are many more faint, distant galaxies than theories suggest.

Is it more or fewer? Or am I misunderstanding something?

This is a tricky science result to explain and, as often turns out to be the case, not quite as secure or solid as the press release recyclers report.
The original paper is by Lauer et al. (2021) and measures the cosmic optical background (COB) using images taken with New Horizons, which is way beyond the orbit of Pluto. The advantage over things like HST is that the images are not contaminated by light scattering from zodiacal dust. Most of the paper deals with how they remove various instrumental signatures, get a figure for the dark sky brightness (about 27 mag per square arcsec in the V-band) and then attempt to explain this by examining the "light budget" from various known sources.
There are 4 main known sources. Faint stars below the detection limit of New Horizons (which is only about $V\sim 19$); ditto for galaxies; there is scattered light from bright stars out side the field of view; and there is a diffuse scattered light from dust in the Galaxy. The genuine COB is their measured sky brightness minus the contribution from stars and scattered light from our Galaxy.
They make an estimate of these 4 components and the sum comes to less than their dark sky brightness, but only by around 2 error bars; so a weakly significant result.
Now it gets confusing. In the text they say that the integrated light from faint galaxies (IGL) accounts for 50% of the COB, and may be consistent with it at the 2 error bar level. See Fig 18 in the paper.
Previous studies, based on HST data, suggested that if you extrapolated galaxy counts down to galaxies of about $10^6 M_\odot$, then there would be ten times as many unseen galaxies as you could count in the Hubble deep fields, mainly at $V>30$. However, if you work out how much IGL these would contribute it turns out to be larger than the COB that Lauer et al. have measured. Hence the headline that there may be fewer galaxies in the universe than previously claimed. I say may, because this claim is not one of the main conclusions of the paper, and in the text they say there may not be a significant discrepancy once the uncertainties are considered. This aspect of the work has been highly exaggerated in the press releases.
Lauer et al.'s estimate of the IGL is based on adding up the galaxies that have been observed down to $V\sim 30$. So you do need some extra faint galaxies to boost the IGL enough to fully explain the COB, but just hiding these at magnitudes $V>30$ may not be sufficient. The suggestion is that galaxies with $V<30$ are being undercounted. This is the origin of the second part of your report. It is that there may be more galaxies at brightnesses that ought to have been seen in the deep HST images. The implications of that are not explored.
Personally, I would like to take a look at how they have treated faint Galactic stars. Extrapolating from local luminosity functions may not be appropriate for estimating the contribution of stars down to $V=30$ in the halo of our Galaxy. If there are more lower mass objects in the halo than locally then this might have a bearing on the (2 sigma) discrepancy between the (apparent) COB and the IGL.


Why do brighter stars/planets appear physically larger? Look at Sirius and then some 2nd magnitude star. Sirius appears physically larger despite both stars subtending approximately the same angular diameter.
Callisto is far enough from Jupiter at its greatest elongation to be seen with the naked-eye, but a common reason it still isn't visible is because Jupiter's glare hides it.
To be clear, I'm not talking about Jupiter's additional reflected light making it harder to spot dim Callisto the same way the Moon makes nearby stars harder to see. Jupiter literally appears larger in the sky because of how bright it is. Why is that?

It is an optical illusion. Our brains associate brighter with bigger.  This is how software like stellarium are able to make convincing views of the night sky: they play this in reverse and use larger "stars" for brighter ones.  Your brain sees them the same.
Your brain is not tuned as a scientific device, there are lots of tricks that we can play on our visual system.


Celestial navigation from scratch Is it possible to establish one's longitude and latitude by observing the stars? Can you use observations of the stars to find the relative distance between two locations, which would be useful in map-making? What kind of crude tools would help (a sextant is too complex, but maybe a backstaff?)

What difference would there be if you were doing this on a planet that was not the Earth, and had a different location in the galaxy, a different day and year length?

To expand a little on James's answer: The pole angle method doesn't care what time of year it is, the celestial pole isn't going anywhere. ;) However, if you're in the tropics, the altitude of the celestial pole is rather low, which can make accurate observation difficult.

Of course, if you're doing this on another planet, (or even in Earth's southern hemisphere) you may not have a convenient pole star, and doing this sort of thing without decent equipment isn't going to be particularly accurate.

To determine longitude you need to have a good way of determining the time relative to a fixed reference, like the Greenwich meridian. The Earth makes one rotation on its axis (relative to the stars) in a (sidereal) day, so one day is equivalent to 360° of longitude, one hour corresponds to 15°, and one minute of time corresponds to 15 minutes of longitude, which is 15 nautical miles at the equator, and around 11.5 nautical miles at 40° latitude. In other words, if your time calculations are off by one minute, your position calculations can be off by 10 to 15 miles.

Newton described a method of determining the time from the moon, you can read about it in Wikipedia's Lunar distance (navigation) article. From the Earth, the Moon's angular diameter is roughly 0.5°, and it takes roughly an hour for it to travel through that distance relative to the stars. So if you want time measurements accurate to the minute you need very good observations. However, that's the easy part.

You also need very accurate calculations that tell you where the Moon's supposed to be at that point in time. And that's not easy to do - the Moon's motion is tricky! I won't go into the details here, but Wikipedia has a good introduction to lunar theory. If you're curious about the kind of formulas that get used, take a look at the links in this question.

So it wasn't just the difficulty of making sufficiently accurate shipboard observations that prevented Newton's method from being adopted, it was also the difficulty of preparing sufficiently accurate lunar tables. Actually, Newton's method of lunar distances was used, principally from 1763 (when the necessary tables and method were first published) until about 1850, when it was superseded by the marine chronometer. However, as Wikipedia mentions,

  The method saw usage all the way up to the beginning of the 20th
  century on smaller vessels that could not afford a chronometer or had
  to rely on the this technique for correction of the chronometer.
  [...]
  Captain Joshua Slocum, in making the first solo circumnavigation in
  1895–1898, somewhat anachronistically used the lunar method along with
  dead reckoning in his navigation.

To quote Captain Slocum:

  Even expert lunarians are considered as doing clever work when they
  average within eight miles of the truth.

Of course, on another planet you may have a better-behaved moon, or no moon at all. Or, as James mentioned, you may be very lucky and have a nearby large planet with fast-moving moons that are visible to the naked eye.


Why we define Stellar motions with respect to sun? We take observations from earth but to define radial velocity, transverse velocity and the proper motion of stars, why we consider them with respect to the sun? and then we do some corrections due to both rotational and orbital motion of the earth.

Why can't we directly consider these motions with respect to earth instead of Sun?

And what is the whole procedure of correction?

The Earth is a moving (actually, accelerating) platform from which we make our observations. If you want to describe the motion of a distant celestial body, then it does not make much sense to provide a geocentric velocity, because this will depend on exactly when the observations were taken (because the Earth orbits with a speed of about 30 km/s, but the velocity changes throughout the year), the position on the Earth that the measurement was taken (because the Earth's equator revolves at around 0.5 km/s, but this is different at different latitudes) and the position of the star in the sky (because the previous two effects have to be resolved in the direction of the star).

Given that, then it is far easier to quote a velocity in a frame of reference that does not depend on these things. One can use the heliocentric frame in most circumstances - that is the frame of reference in which the Sun is stationary. To do this, one has to remove the components of the Earth's orbital and rotational velocity. However, if very precise measurements are being done then it is better to use the barycentric reference frame, which is with respect to the centre of mass of the solar system (since the Sun orbits this with a speed of around 0.1 m/s).


Einstein General relativity and bending of space As Einstein's General relativity suggests that the space
time curves in the presence of matter, which is experimentally
proven too, this phenomenon also explains orbits. My question
is if the presence of mass curves space-time, in which direction
does it bend, if we assume that it bends in one of all possible
directions then what makes the body to choose that particular
direction. Does all the bodies bend the space-time in the same
direction ?

We cannot say that it bends in a particular direction because space-time in relativity is 4-dimensional. The space-time diagram which we see frequently is just a simple way of explaining it in two dimensions because 4-dimensional space is hard to visualize.


How to derive Kepler's 1st Law? I was going through the derivation of Kepler's 1st Law in the textbook "An Introduction to Modern Astrophysics" by Carroll and Ostlie. From there, I got stuck in a few places in their derivation as I found it confusing. In total, I have 2 questions.

Q1: In the second sentence that I highlighted, it is mentioned that when equation 29 is translated into a physical standpoint, it implies that "both objects in a binary orbit move about the centre of mass in ellipses, with the centre of mass occupying one focus of each ellipse" however I don't see how the physical implications of equation 29 will translate into this that they claim. This equation clearly only describes the position vector of the reduced mass, so how can it be extrapolated to talk about the motion of a binary system when there are 2 masses rather than 1 reduced mass. (Clarification: I am aware that reduced mass is a way to model binary systems, but in this case I don't see the link between the motion of the reduced mass and the motion of 2 bodies)
Q2: On the very last line, it is mentioned that "L is at minimum as eccentricity approaches unity, as expected". However I don't see the qualitative reasoning as to why this would be "expected". Is there a physical or physics explanation as to why we expect an orbit with a large eccentricity to have a lower angular momentum than one with a low eccentricity?

I must say that I agree with you, this way of derivate the Kepler law is not the most intuitive, it's maybe for this reason they specify: "revisited".
R1: The reason is stated at the very begin of the chapter, where you derive the relation between $r$ and the angle to the perihelion $\theta$ for the general case of an ellipse (Eq 3 in your book in Cap 2.1 Elliptical orbit, but I can see I have an older version than yours), where:
$$ r = \frac{a(1-e^2)}{1+e\,cos(\theta)}$$
here, the eccentricity of a ellipse is then define as:
$$ e = \sqrt{1- \frac{b^2}{a^2}}$$
in the case of Kepler's law you can define the eccentricity as $e = D/\mu G M$ and  $a$ as:
$$ a = \frac{L^2 G\, M}{\mu^2\,G^2\,M^2 - D^2}$$
and you can work out in equation (29), obtaining the equation in the same form as for an elliptical orbit.
The reason to derive $r$ is because it indicates the distance of the object from the focal point (centre of mass of the system), which in the case of the solar system, is the distance of the planet to the Sun (actually the focal point of the solar system, or better to say of the Sun-Jupiter system, is a few kilometre above the solar surface).
R2: the eccentricity $e$ quantify the shape of a cone cross-section Eccentricity (math) Wikipedia.
For example, in the case of the an ellipse you have $0 < e < 1$, and it indicates how much the ellipse is "squashed". Another example, if you have $e=0$ than you have a circle.
In the case of $e=1$ you have a parabola, from the equation of $e$ above it means that $a\gg b$. In a more physics sense, it means that the system is not in a gravitationally bounded state, and the less massive object $m_1 \ll m_2$ is on a parabolic trajectory, deviated by the gravitational pull of $m_2$, and will not stay in orbit.


Can you simulate artificial gravity by using an electromagnetic field? If you create a electromagnetic field under a surface could you then create artificial gravity effect by wearing magnetized clothing and shoes?

Or could you bombard objects that you want to experience gravitational forces with artificial gravitons or graviolis? Or inject or drink a ferrofluid (non-toxic) like that used in rocket fuel?

  A ferrofluid (portmanteau of ferromagnetic and fluid) is a liquid that
  becomes strongly magnetized in the presence of a magnetic field. A
  grinding process for ferrofluid was invented in 1963 by NASA's Steve
  Papell as a liquid rocket fuel that could be drawn toward a pump inlet
  in a weightless environment by applying a magnetic field.

  https://en.wikipedia.org/wiki/Ferrofluid

What I mean is create the forces of attraction and then make the objects you want to attract attractive, obviously.

This is as opposed to using other methods such as acceleration or centrifugal or centripetal force (or in addition to it).

There are two aspects to this question: first, creating a field that can exert a force and second, having a body that is coupled to that field and "feels" the acceleration.

Electric field: You probably want a uniform field of acceleration, like on earth, where the same amount of gravity is present everywhere in our daily life (close to the surface of earth).  This can be achieved by putting sources into floor and ceiling of your ... space station.  With various setups this could create a homogeneous electric field (like a parallel plate capacitor).

Now, use the field by putting charged bodies into it.  I could imagine a space suit with an eletrically charged layer, insulated on both sides.  I don't have an idea for a suit in the magnetic field though, because there are no magnetic charges.

Quick calculation: Assume a spherical human with a radius $r$ of half a meter.  The suit is a charged conducting sphere and charging it with $V_\text{suit}=1\mathrm{MV}$, which is a lot, even for Marx generators, then the charge stored in the suit is

$$Q = V_\text{suit} 4\pi \epsilon_0 r = 6\cdot10^{-5}\,\mathrm{C}\,.$$

This doesn't look like a lot in the exponent, but Coulomb is an insanely large unit.  Now charging up the capacitor formed by floor and ceiling to some voltage $V_\text{deck}$, the total force on the suit is

$$F = E \cdot Q = \frac{V_\text{deck}}{d}\, Q$$

And the acceleration of the body should be one g:

$$F = m a = m g$$

At a mass of lets say $m=70\,\mathrm{kg}$ this requires a voltage of:

$$V_\text{deck} = \frac{m g d}{Q} = 2\cdot10^7\,\mathrm{V}$$

Good luck with that :-)  The typical dielectric strength of air is $3\mathrm{MV}/\mathrm{m}$ so you would instantly get an electrical arc between floor and ceiling.

Magnetic field:  Magnetic fields behave a bit differently and the best option is probably a linearly varying magnetic field $\mathbf{B}$ from floor to ceiling (use Helmholtz coils).  If you manage to build a suit with some magnetic dipole moment $\mathbf{m}$ (for example using a permanent magnet, or running a current through the suit), the force is

$$\mathbf{F} = \nabla (\mathbf{m} \cdot \mathbf{B})$$

The dipole moment of a normal neodymium magnet is given to be about $1\,\mathrm{Am}^2$ here.  For the same $m=70\,\mathrm{kg}$ body the magnetic field has to have a gradient of 7 Tesla per centimeter ...  or a difference of whopping 1400 Tesla from floor to ceiling (give or take one magnitude for not scaling the magnet to human weight).  As a comparison, the magnets at LHC generate fields of about 10 Tesla.

Bottom line: Earth is big, therefore gravity at earth's surface is strong, because of that it's hard to reproduce it using electric or magnetic fields.

Graviton: The graviton is still a hypothetical particle.  Even if we confirm its existence, its behaviour should be (for the large part) very similar to gravity as we know it.  "Bombarding" something with gravitons is then equivalent to having a large mass nearby.  Understanding the theory will most probably not enable us to build graviton guns that work analogous to lamps producing photons.  Speaking of large masses, how about lining the floor with neutron star matter?

Ferrofluid: A paramagnetic material can be used to couple to the magnetic field, but I believe you need active stabilisation (circuits in the floor and ceiling).  There actually seems to be a theorem about that: Earnshaw's theorem.  There are other implications to drinking ferrofluids, besides the chemical toxicity, because it might accumulate in some spots of your body and more of the artificial gravity will attack at that spot.

I guess, we are still better off with gravity-like acceleration by rotation or propulsion ...


Are there accurate equinox and solstice predictions for the distant past? I am trying to find information on the equinox/solstice dates before 1600, more exactly referring up to 10,000 BCE so as to create a sort of calculator on an Excel spreadsheet.

I have read about the SOLEX, but it is not available anymore. Is there any other software that can accurately (as possible, of course) predict the equinoxes and solstices keeping in mind the perihelion/aphelion effects on the period between equinoxes/solstices?

If you believe it is possible to try a formula on excel to calculate these dates for me (instead of just copying down the dates into a database), please keep in mind that my mathematical/programming knowledge is limited.

I wrote
https://github.com/barrycarter/bcapps/blob/master/STACK/bc-solve-astro-13008.c
to find historical solstices and equinoxes. The full results are at:

https://github.com/barrycarter/bcapps/blob/master/ASTRO/solstices-and-equinoxes.txt.bz2

Accuracy:

I'm using the EARTH_IAU_1976 precession model and the
EARTH_IAU_1980 nutation and obliquity models, which are
the only models supported by the CSPICE library I'm
using:

http://hesperia.gsfc.nasa.gov/ssw/stereo/gen/exe/icy64/doc/frames.req

This is the same library and the same models NASA uses to
do its own calculations, but the models are known to have
limited accuracy. Quoting "http://aa.usno.navy.mil/faq/docs/SpringPhenom.php":

The times given in the tables are accurate to within two or
three hours for 25 to 5 BCE, and one or two hours for 4 BCE
to 38 CE. The uncertainty in these times arises from the
stochastic, that is unpredictable, change in the Earth's
rotation rate.

The accuracy gets worse the further back OR the further
forward you go: not only don't we know precisely about the
Earth's rotation in the past, but we can't even predict the
Earth's rotation precisely for the future.

Sample output:

EQU 511720269.432607 A.D.   2016-03-20 04:30:01
SOL 519734120.174820 A.D.   2016-06-20 22:34:11
EQU 527826138.004142 A.D.   2016-09-22 14:21:09
SOL 535589116.137776 A.D.   2016-12-21 10:44:07

Format:

The first column indicates whether this is a solstice or an equinox.
The second column is the ephemeris time of the
solstice/equinox. If you're doing serious astronomical
work, this is the column you should use. The approximate definition is the number of seconds since the J2000 epoch. The precise definition as used in CSPICE is: https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/FORTRAN/req/time.html#Ephemeris%20Time%20(ET)
The remaining columns indicate the UTC time of the
solstice/equinox in a more human-readable format:

The CSPICE libraries assume that the Gregorian
calendar reformation occurred on 4 October 1582
(meaning the day after 4 October 1582 was 15 October
1582). Looking at these lines:

SOL -13191695511.794357 A.D.   1581-12-11 20:07:27
EQU -13183992131.003845 A.D.   1582-03-10 23:57:07
SOL -13175951250.170158 A.D.   1582-06-12 01:31:48
EQU -13167875920.223862 A.D.   1582-09-13 12:40:38
SOL -13160138634.917915 A.D.   1582-12-22 01:55:23
EQU -13152434815.793312 A.D.   1583-03-21 05:52:23
SOL -13144394485.035870 A.D.   1583-06-22 07:17:53
EQU -13136319216.460808 A.D.   1583-09-23 18:25:42

you can see that the dates of the solstices/equinoxes jump
ahead 10 days per the reformation.

The CSPICE libraries use the Julian calendar prior to
4 October 1582. In reality, the Julian calendar was
introduced in 46 BCE:
https://en.wikipedia.org/wiki/Julian_calendar
Prior to 46 BCE, there were other calendar systems in
use, but the CSPICE libraries assume the Julian
calendar goes back indefinitely:

https://en.wikipedia.org/wiki/Proleptic_Julian_calendar

My calculations go back to 13201 BCE (the limits of DE431,
the ephemeris I'm using), and it's possible human beings
weren't even using calendars regularly at the time: quoting
"https://en.wikipedia.org/wiki/History_of_calendars#Prehistory":

A mesolithic arrangement of twelve pits and an arc found in
Warren Field, Aberdeenshire, Scotland, dated to roughly
10,000 years ago, has been described as a lunar calendar
and dubbed the "world's oldest known calendar" in 2013.

Notes:

It takes the Earth 365.256363004 days to revolve around
the Sun with respect to the fixed stars, but the time
between vernal equinoxes is slightly less (365.242190402
days) because the position of the vernal equinox moves
(precesses) with respect to the stars. Source:
http://hpiers.obspm.fr/eop-pc/models/constants.html
The Gregorian calendar's average day length of 365.2425
is much closer to 365.242190402 days than the Julian
calendar's 365.25 average day length, but it's still not
perfect. As noted in
Do solstices and equinoxes shift over time?
if we continue using the Gregorian calendar in the far
future, the equinoxes and solstices will drift
backwards. By 17090 (the limit of DE431), they will look
like this:

EQU 476198945887.238159 A.D.  17090-02-22 08:56:59
SOL 476207018540.040894 A.D.  17090-05-26 19:21:11
EQU 476214808218.146362 A.D.  17090-08-24 23:09:09
SOL 476222655067.609985 A.D.  17090-11-23 18:49:59

about a month behind their "regular" times.

MY EARLIER PARTIAL ANSWER FOR REFERENCE:

Since HORIZONS (http://ssd.jpl.nasa.gov/?horizons) and SPICE (http://naif.jpl.nasa.gov/naif/tutorials.html) can compute the ecliptic and solar position back that far, it should be possible to compute equinoxes and solstices with reasonable accuracy. However, I haven't been able to find a site that actually lists these dates (I'm pretty sure USNO did this at one point, but I can't find their list). Other possibly helpful sources/questions:

How did Meeus calculate equinox and solstice dates?
http://ns1763.ca/equinox/eqindex.html
http://data.giss.nasa.gov/ar5/srvernal.html
http://www.usno.navy.mil/USNO/astronomical-applications/data-services/spring-phenom (appears to be down at the moment)


How to disentangle a very distant star's relative velocity vs. redshift distance We measure a star's relative velocity towards or away from us via its Doppler-shifted spectrum. This is also how we measure the distance of very distant stars: measuring the shifts in the spectrum tells us its relative velocity, which we interpret as a distance via Hubble's Law.

Suppose we knew the star's relative velocity and distance exactly. It seems to me that if the star were moving away from us slightly less than would be expected from expansion alone, it would be because it was moving towards us more than the matter surrounding it: it would have some additional velocity component towards us. If we were to try to infer that star's distance from expansion alone, we would measure its relative velocity via the Doppler shift and would conclude that it was closer than it actually is. Conversely, if it were moving away from us faster than it should based on expansion alone, we would estimate its distance further than it actually is.

Is there any way to disentangle this degeneracy?

Conrad is almost right. It is true generally that if a Galaxy is close enough to take spectra of individual stars (e.g. luminous supergiants) then it is not far enough away to be regarded as part of the "Hubble flow" and so applying Hubble's law to this star, or its host galaxy, would not yield a reliable distance in any case, but would reflect the "peculiar motion" of that galaxy.

To put some numbers on this. Galaxy peculiar motions tend to be a few 100 km/s, as do the individual velocities of stars with respect to their galaxies. Taking a Hubble constant of 70 km/s per Mpc, we see that we need to be at distances of 15 Mpc before Hubble recession velocities ($v = H_0 d$) become large compared with peculiar motions. At these distances we cannot observe individual stars - they are too faint and unresolved from the bulk of the Galactic light.

The exceptions are supernovae. The redshifts of individual supernovae, that briefly outshine their galaxies, can be measured right across the universe. Here you are correct that the measured redshift is a combination of cosmological redshift due to the expansion of the universe and a velocity of the star relative to the Hubble flow at that distance. There is no way to distinguish between these two unless velocity measurements could be obtained for other objects in the same galaxy. Given the rarity of supernovae, we might wait a long time for this.

But does it matter? Even if we look at a "low redshift" supernova at $z=0.1$, its Hubble recession velocity is 30,000 km/s and far in excess of any peculiar velocity contribution at the level of $\sim 1$%.


Cosmic Microwave Background Map When a satellite takes measurements of the radiation from different patches of the sky to construct a map of the thermal radiation of the universe on the surface of a sphere, it would also contain radiation from the Milky Way, for one.
A big patch of the map will have noise due to the objects in the Milky Way or from other sources.

How does one know where and how much noise to remove while constructing the map?

Above I have plotted few Planck's radiation contribution:
The violet is due to CMBR, Green is due to Milky way Galaxy, and Blue is due to contribution from both.

One way to resolve out CMBR is by modeling milky way from higher frequency of the graph since CMBR contribution is negligible at higher frequency. At particular direction one can associate temperature due to Milky way by setting a high pass frequency. Then one can subtract this temperature contribution at lower frequencies where CMBR contribution is significant. This is the one of the way probably not the best, but doable.

Note1: The graph is not from actual data. It is just for explaining how to go about it.

Note2: What should be high pass frequency will be a good question. With good arguments one can decide what should be the high pass frequency. And there's always way about it.


Lunar orbit distance Can anyone calculate the distance the moon travels in a single year? I can calculate it as it is close to 2.4 million km, but I need adjustments as the earth is moving and so is the Sun. So, I need the absolute distance rather than distance from earth's perspective.

It depends on where we observe it from. There is no absolute velocity reference.

For example, the most distant quasars are moving away from us at nearly the speed of the light. They "see" our Moon going away from them at nearly light speed. So, for them, the Moon travels around a light year each year (its other movements are negligible, compared to that).

If we observe it from the Earth, then we see a Moon on a circular orbit around us. Consider the following well-known facts:

Its orbital radius is $\approx$ 385000 km,
Its orbital time is $\approx$ 29 days,
A year is $\approx$ 365.25 days,

, then we can easily calculate the distance: $385000km \cdot \pi \cdot \frac{365.25}{29} \approx \underline{\underline{3\cdot 10^7 km}}$.

If we observe it from the point of view of the Sun: as we can see detailed in this answer, the orbit of the Moon around the Sun is practically circular: the 400000km orbital radius around the Earth is just a minor perturbation on its $\approx$ 150million km orbit around the Sun. Thus, we can calculate the length of the orbit of the Earth, which is $2 \cdot \pi \cdot 150 000 000 km \approx \underline{\underline{9.4245\cdot 10^8 km}}$.

Well... it is not entirely true that there is no absolute velocity reference: the WMAP probe, measuring the minor perturbations of the cosmic microwave background radiation, found also a relativistic Doppler effect, from which you can read more here. In essence, this is what it measured:

However, the results actually measured were these:

The deviation is due to our galaxy's movement of around 160km/s in the direction of the constellation Hercules, in an reference frame of the Cosmic Microwave Background, that is the closest thing there is to an absolute reference frame.

The answer of your question in this frame: all other movements (of the Sun, the orbit of the Earth around the Sun, and the orbit of the Moon around the Earth) are negligible or cancel themselves out. The result can be gotten by multiplying:

the speed in the frame of the CMB (160km/s)
the seconds of a year ($\approx$ 31.5million)

It is $\approx 160\frac{km}{s} * 31.5\cdot 10^7 s = \underline{\underline{5\cdot 10^{10} km}}$.


How wary should I be of old cosmology books? Recently I bought a couple of books on cosmology from a second-hand bookshop. One was published in 1993 and the other is from the 1970.

I know, from a recent book, that the inflaton theory is probably newer than both books and that the Higgs Boson has been discovered, but that is all that I know has changed recently in the field of cosmology. Has anything else changed since then?

Which topics of the books should I understand are considered outdated?

The two books are Modern Cosmology by Jagjit Singh (published 1961 and rereleased in 1970) and Afterglow of Creation by Marcus Chown (published in 1993)

How wary should I be of old cosmology books?

It's a sliding scale. Generally the older the book, the more the chance of something being wrong. But it depends what books you're talking about. Are they text books? Or are they popscience books? Some books, even newish books, have a habit of presenting speculation as established fact. There's been a lot of trouble about inflation and the multiverse recently. Peter Woit talks about it on his Not Even Wrong blog. He says “the political campaign for the multiverse continues today with a piece by Amanda Gefter at Nautilus. It’s a full-throated salvo from the Linde-Guth side of the multiverse propaganda war they are now waging”.

  I know, from a recent book, that the inflaton theory is probably newer than both books

Inflation started in circa 1980. Guth coined the phrase and generally gets the credit, but it arguably goes back to Erast Gliner in 1965 and his paper algebraic properties of the energy-momentum tensor and vacuum like states of matter. It didn’t get much attention.

  and that the Higgs Boson has been discovered

When inflation was first mooted Alan Guth talked about the Higgs field and GUTs, saying magnetic monopoles were "topologically stable knots in the Higgs field expectation value”. But that was old inflation, which was replaced by new inflation, which was replaced by eternal inflation. As far as I know the Higgs field is not thought to be linked to the inflaton field.

  Has anything else changed since then?

Yes, like pela said, before 1998 people thought the expanding universe was slowing down. There are other changes too. Some people used to say the universe was once the size of a grapefruit. Now since WMAP some people say the observable universe was once the size of a grapefruit, and the universe is infinite. For myself I cannot see how that fits with big bang cosmology, which I think is largely correct.

  Which topics of the books should I understand are considered outdated?

It's hard to say. Dark matter, dark energy, cosmological constant, flatness of the universe, size of the universe, age of the universe. If you could name the books maybe I could look at the chapters.


Why are black holes that massive? Today known most massive star, R136a1  weighs approximately 256 times the mass of our sun, how did supermassive black holes, with a mass of 10 billion times the sun form?

I understand, that when a star becomes black hole, its density increases, but does its mass also grow?

The mass of a object does not increase when it collapses into a black hole. So a supermassive black hole must have started off quite small, and then grown.

The formation and growth of supermassive black hole is not settled science. Supermassive black holes probably started as large stellar mass black holes (The very earliest stars could have been very large, and were almost entirely free of any heavier elements, and could have collapsed to form black holes with a mass of about 100 suns) The black holes then grew as more matter fell into them.

There is a strong correlation between the size of a SMBH and its galaxy. Its not clear why this is, but it suggests that the environment that drove galaxy growth, also contributed to the growth of the black hole.

This article on the Growth of supermassive black holes across cosmic time may interest you.


Is it possible for the year to have 11 full moons (i.e. the opposite of a blue moon) A blue moon is so called for when we have 13 full moons in a year.

https://en.wikipedia.org/wiki/Blue_moon

Is it possible to have 11 fun moons in a year? (Maybe if we included calendar changes, for example the start of the Gregorian calendar, this would be more likely)

If this is possible, what is this phenomenon called, and how rare are these years?

Since a full moon happens once every 29 days (and that's not exact, but close enough), the longest period of time where you can have 11 full moons but not 12 is 11 x 29 + 28, or 347 days, so in a normal year, it's not possible.  There are slight variations in the time between full moons but not nearly enough to make up the extra 18 days needed.

So you'd need a special circumstance.   Great Brittan's short year in 1752 wasn't sufficiently short, it had 11 days removed.

There is a phenomenon where not everywhere on Earth gets a full moon every 29 days.   In the North and South poles for example, where during summer they get 24 hours of sun and winter, no sun, a somewhat similar effect happens with the moon.   The Moon orbits the Earth at 5 degrees off the ecliptic or basically, the plane between the Earth and the Sun and that makes the Moon's apparent movement across the sky a little more complicated than the Sun's, but because full moons only happen when the moon is roughly opposite the sun, it's not hard to see that when the sun is in the sky for 24 hours during the Polar summer, they don't get a full moon for several months because the full moon is below the horizon when the sun is in the sky 24 hours.   You might only see 6-9 full moons a year at the poles (if I was to guess), and there's probably a range of latitudes close to the poles where 11 full moons might be about the yearly average.

If you want to split hairs even further, the Moon only takes an instant to pass the 180 degree point in relation to the Earth and Sun, so in a sense, a perfect 180 degree full moon is only visible to half the earth and by the time the other half of the earth turns to make that moon visible, the moon has already gone past 180 degrees and from a certain perspective, it's no longer full.   But, a full moon is generally regarded as a roughly 24 hour period, not an instantaneous moment, so I don't like that argument personally.


How do we know which elements are in a galaxy spectra? I know that each element has it's own distinct spectra (this is a good site that lists them: Periodic Table) but when looking at a spectra of a galaxy (or even a star) how do we match those elements to their distinct spectra? Looking at this image from Spectra in the Lab :

Some of the lines in the spectra overlap. The galaxies are also moving away, so it makes it more difficult to figure out the elements producing the emission/absprtion lines, right?

Also, each element usually has more than one absorption/emission line, so how can we say that just one line is the H-alpha line, or the K and H calcium lines, for example, as in this spectra:

(image from: http://spiff.rit.edu/classes/phys301/lectures/doppler/doppler.html)

Because the wavelength ratio of the lines remains constant despite any cosmological red shift.

For example, if the redshift is $z$, all the lines are shifted redward in wavelength by a factor $(1+z)$. This means that a pattern of lines can still be recognisable.

We also have a pretty good idea of what the spectra should look like, which chemical elements will produce visible absorption features with what relative strengths and so on (see below). This usually makes identification of line features straightforward.

Of course if there were just a single line visible in the spectrum (it does happen, usually in high redshift quasars) it can be difficult to pinpoint the redshift.

In terms of analysing what's in a Galaxy, well usually the light is dominated by the mixed spectrum of billions of stars. This spectrum is interpreted and modelled using galaxy evolution models and population synthesis models that predict a spectrum from a given ensemble.

If a Galaxy is near enough, the chemical abundances of its interstellar medium can be estimated from resolved spectra of emission nebulae.

In comparison, interpreting spectra from an individual star is trivial. Hundreds if not thousands of absorption lines can easily be identified and matched with the predictions of very detailed stellar atmosphere models to estimate chemical abundances. These models contain up to millions of possible radiative transitions as well as the various line strengths and broadening processes that affect the spectrum.


Question about $3p/c^2$ in Friedmann equation The Friedmann Equation:

$$\frac{\ddot{a}}{a} = -\frac{4\pi G}{3}\left(\rho + \frac{3p}{c^2}\right) + \frac{\Lambda c^2}{3}$$

I want to know, where does the $3p/c^2$ come from. I know it is something like density of energy or something like that but I don't know where it comes from.

There are two Friedman equations.

One related to the energy-density component in the Einstein field equations.
One related to the pressure component in the Einstein field equations.

The Einstein field equations are the following ten equations (16 equations for 4x4 tensor components but only ten of them are independent due to symmetry)

$$G_{\mu\nu} + \Lambda g_{\mu\nu} = \kappa T_{\mu\nu} = \frac{8 \pi G}{c^4} T_{\mu\nu}$$

where $G_{\mu\nu} = R_{\mu\nu} - \frac{1}{2} g_{\mu\nu}R$ is the Einstein tensor, $g_{\mu\nu}$ the metric tensor, $\Lambda$ is the cosmological constant, $\kappa = \frac{8 \pi G}{c^4}$ is the Einstein constant, $T_{\mu\nu}$ is the energy-momentum tensor

Friedman was actually assuming that only the matter/energy density component is non-zero $T_{44}= \epsilon = \rho c^2$. He assumed "Die Materie ist inkohärent" (ie non interacting dust with $p=0$) by which the components $T_{ii}$ are non-zero for $i \neq 4$. The other components (energy flux and momentum) are set equal to zero based on the assumption that the motion of energy and matter is considered to be negligibly small.

LeMaître kept the pressure in place arguing that the pressure associated with the kinetic energy of matter might be negligible but this may not be the case for radiation pressure. So he used also $T_{11} = T_{22} = T_{33} = -p$

Using the Robertson Walker metric metric $d s^2 =  dt^2 - a(t)^2 \left[ \frac{dr^2}{1-k r^2}+r^2d\Omega^2\right]$ the equations become expressions in terms or the scale factor $a(t)$:

$$\begin{array}{rcrcl} G_{00} &=& c^{-2}\frac{3k}{a^2} + 3c^{-2} \frac{\dot a^2}{a^2} &=& \frac{8 \pi G}{c^4} \rho c^2 - \Lambda  \\ -G_{11} = -G_{22} = -G_{33} &=& c^{-2}\frac{k}{a^2} + c^{-2}\frac{\dot a^2}{a^2} + 2 c^{-2} \frac{\ddot a}{a} &=& -\frac{8 \pi G}{c^4} p + \Lambda \end{array} $$

If you subtract the second equations from the first equations

$$G_{00}+G_{11}+G_{22}+G_{33} = -6 c^{-2} \frac{\ddot a}{a} =
  \frac{8 \pi G}{c^4} (3p+ \rho c^2) + 2\Lambda   $$

and rearrange some terms, then you could also write

$$
 \frac{\ddot a}{a} = -\frac{4 \pi G}{3}  \left( \rho + \frac{3p}{c^2} \right) + \frac{ \Lambda c^2}{3}   $$


Milky Way, view outward or inward? I have a question about the view of the Milky Way that we can see from earth with the naked eye.  I believe this to be light from the stars contained in one of the "arms" of the galaxy.  I had always assumed that, from our vantage point, I was looking outward through one of the arms.  This was based on the appearance of the apparent curvature over the sky above.

However, it occurred to me that this could also be looking in towards the center of the galaxy.  And the fact that it appears to curve around us over the night sky is just an illusion.

Or, perhaps at different times in the year we are alternatively looking inward and then later looking outward.

Can any shed some, errr, light on this?

An image of the whole sky (360 degrees) centred on Sagittarius and rotated so the galaxy is in the middle:

This image from the "2MASS infrared survey" actually uses infra-red light, as it penetrates the interstellar dust better than visible light. It shows that any apparent curvature is an illusion. The milky way goes straight across the sky.

It also shows that when we look towards Sagittarius we look towards the galactic centre, and when we look away from it (towards Auriga) we are looking through to stars in the outer spiral arms. The night side of the Earth faces the galactic centre during July, and faces outwards in January.

Also visible in the image are the two Magellanic clouds (small but nearby galaxies outside the milky way), the clear bulge around the centre of the galaxy and the dark bands of dust along the milky way. The central bulge is much brighter in infrared than the spiral arms. Using infrared makes these features more visible.


Does the Moon capture radiation pressure from the sun causing momentum from photon propulsion? Could a planet's main use for natural satellites be that of a photon sail?

If we assume the 15 CM per year is accurate (which I'm not 100% sure it is), then it's possible to answer this.  In a loose sense, yes, the pressure should move the moon away from the sun faster, but more accurately and the real answer is that doesn't happen because there are 3 bodies in play and when you have 3 body gravitation, things get a lot more complicated.

First, just for fun, a source for the 15 CM.

  The moon away each year by photon momentum.The moon is the perfect
  color,size and The moon has a mass of 7.35 x 10²² kilograms. It is
  only about 60 percent as dense as Earth so it should be effected by
  the photons from the sun causing movement.And that movement should be
  combined with earths 15cm giving a new total distance a year right

If we only look at equal force per surface area, which is what you're describing, it's not density, it's the ratio surface area to mass.  The Moon's surface area is about 7.4% of Earth's (about 1/13.5) and it's mass about 1/81st of Earths.  Source.  81/13.5 = about 6.  That means given equal pressure, the moon should accelerate 6 times as much which corresponds over small distances to 6 times the distance or 90 CM per year - BUT, that's if you ONLY take into account the pressure.

The effect of the sun losing mass has equal effect on both the Earth and the smaller Moon.

And a 3rd factor to consider is the tidal bulge on the sun caused by the Earth-Moon system, which is very small but all these effects are small.   The Earth-Moon system creates a tiny bulge on the surface of the Sun and because the Sun rotates ahead of the Earth-Moon, that tiny tidal bulge has a tiny pull on the Earth-Moon system that slowly accelerates them and pushes them slowly away from the sun.  That effect is equal for both the Moon and Earth too.

All 3 of those are factors in the 15 CM per year estimate and only one of them has 6 times the effect on the Moon than the Earth.   The planets Venus and Jupiter might also be factors in that 15 CM per year estimate too, but lets leave that alone for now.

If we consider the 3 body problem it gets very mathy, but I'll just talk about how it applies to solar pressure.   Lets start with a picture.

When the Moon is waning its moving towards the sun and any pressure from the sun slows the moon down, (a tiny bit) and that slow-down moves the Moon closer to the Earth which speeds it up even more - funny how that works, pushing to slow something down in orbit and it goes faster - but that's how it works, cause potential energy converts to kinetic as the orbit drops, kinda like how falling makes things go faster.

When the Moon is waxing, it's moving away from the sun and any pressure from the sun speeds it up which moves it away from the earth and that in turn, slows it down.  So that's your answer in a nutshell.  The solar pressure doesn't push the moon away from the sun so much as it pushes the moon into a lower and then higher orbit around the Earth depending on where the Moon is in it's orbit around the Earth and the various positions in both the Moon's and Earth's elliptical orbits.  The overall effect is very difficult to calculate and I suspect it could go either way depending in part on the timing of large coronal mass ejections hitting the moon and in part on any possible resonance between the eccentricity of the Moon around the Earth and the Earth around the sun, er, I think.

What is safe to say is that the Earth-Moon system obeys the same surface area to mass ratio the Earth alone because that's simple momentum which needs to be conserved.    The Earth-Moon system has a combined surface area of 1.074 Earths and a combined mass of 1.012 Earths, so the Moon being in the Earth-Moon system makes the Earth move away due to solar pressure about 6% faster.  15 CM to 15.9 CM.  Not a very big change, and it's possible that the 15 CM estimate is based on the Earth-Moon barycenter not the Earth itself.

So, the effect is more of a wobble in the Moon's orbit around the earth than an actual force that pushes the Moon away from the sun faster than it pushes the Earth away.

All this, is, of-course, unimportant compared to the much bigger solar tidal force on the Earth-Moon system.   As the Moon gets closer to the sun (new moon in the picture above) The sun effectively pulls the Moon a little bit away from the Earth and when it's further from the sun (full moon), The Moon is effectively pulled towards the earth.  The net effect of this solar tide is a measurable wobble in the Moon's orbit around the earth.  The effect on the Moon's orbit around the earth due to photon pressure and coronal mass ejection pressure - basically insignificant.

Hope that's clear.


Why are only some of the geologic features in Mars' Noctis Labyrinthus region named? I found this page Names Approved for Six Cavi and a Tholus on Mars which lists seven features on Mars. I'm curious about the decisions to name only these features: Dalu Cavus, Layl Cavus, Malam Cavus, Nat Cavus, Noc Cavus, Usiku Cavus, and Noctis Tholus in Noctis Labyrinthus. Why only some of the canyon, graben and/or valley locations are named?  Does it have to do with the depth of the features?

Doing a search for the area of Noctis Labyrinthus, Northernmost Latitude: -3.0, Southernmost Latitude: -13.0, Westernmost Longitude: 259.0, Easternmost Longitude: 268.0, I found only this,

Nomenclature on planetary bodies is meant to ease and standardize communication.  If an object is referred to often, or if it is important for someone's research, then the scientist(s) involved can submit a name request to the International Astronomical Union (IAU), or through some other body that submits names to the IAU (such as the United States Geologic Survey's Astrogeology branch in Flagstaff, AZ).  After checking for various criteria*, the name may or may not be approved.  If it is approved, then the feature is named.  If it is not approved, then the scientist(s) can resubmit that name or a different name.

I am not sure if it is a full list, but the USGS's Gazetteer of Planetary Nomenclature lists a lot of the themes on different bodies.  Based on that, cavi and tholi would be named based on nearby albedo (brightness) features or craters.

*Criteria for naming are extensive.  Almost every type of feature (such as an impact crater) on many bodies has a theme, and that theme must be followed.  If the name does not meet that theme, then it will be rejected.  Other criteria are that the name cannot be offensive or induce a strong negative response (such as naming something "Satan" could induce a negative response in many people); the name cannot be used elsewhere in the solar system already (though some historic exceptions exist); the feature must be well defined (a vague region on a surface would not, therefore, qualify); the feature cannot be named after someone who is alive or has died less than three years ago; and there cannot be a preponderance of names that are biased towards or against gender, nationality, region of the world, etc.


What planets and moons have we seeded with life (if any)? Which planets and moons have we accidentally (or purposely) seeded with life?  I would expect this to be any planet or moon we have sent an unsterilized (or not fully sterilized) lander to, or crashed anything into.

I am speaking largely of bacteria and other microorganisms that might have hitched a ride on our spacecraft, or any life that was deliberately taken to and left on another world (which I am not aware).  I know we went to the moon, we at the very least "seeded the moon" temporarily with life (humans) and probably bacteria on the space suits / lander / equipment we sent.

I wondering where we have "seeded" / brought life (even if it doesn't / didn't survive there).

This would seem to be constrained to planets and moons earth has landed on or impacted at all, as we have no way of telling after the fact whether a lander was perfectly sterilized. That list is as follows:

Planets:

Mercury: USA's MESSENGER in 2015 de-orbited and crashed upon completion of mission. Contamination is unlikely because of high impact and temperatures.
Venus: 13 missions by the USSR and 1 by the USA (1966-1985). Contamination unlikely due to harsh environment.
Mars: 12 missions, multi-national origins. Contamination plausible.
Jupiter: The Galileo missions (2), by the USA Contamination unlikely, because of pressure.

Moons:

Earth's moon: Far too many to count, myriad landings. Contamination plausible.
Saturn's moon Titan: Huygens probe, landed by the ESA (2005) Contamination Plausible.

Asteroids/Comets:

Eros: 2001 landing by USA. Contamination possible.
Itokawa: 2005 landing by Japan. Contamination possible.
Comet 9P/Tempel 1: 2005 landing by USA. Contamination is unlikely because of high impact speeds.
Comet 67P/Churyumov–Gerasimenko: 2014 landing by ESA. Contamination possible.


What factors makes a star big in size(Physically)?Is the size of the nebula a relevant factor? (Our sun compared to some of the known stars)

I know that the star is born in a nebula.Do only a extremely gigantic nebula give rise to large-radius star or is there any other factors related?

The size of the nebula doesn't matter at all, what matters to the size of a star is the mass and age of that star.  Even the mass of the nebula doesn't really matter, because giant molecular clouds fragment dramatically as they make many many stars.  It's a very complicated and detailed process that controls how they fragment, so usually one merely assumes a statistical distribution of stellar masses, called the "initial mass function," which applies more or less universally to any sized nebula.

Once the mass of the star is determined (statistically), the star contracts with age, so very young stars have all kinds of different sizes while they contract.  Eventually fusion initiates in the core (which is sometimes considered the "birth" of the star, though it was pretty much already a star before that), and then the size of the star is determined by its mass because a higher mass star doesn't need to contract as small to reach fusion temperatures.  Later, when core fuel runs out, stellar envelopes expand dramatically into giants or supergiants, which to a point reverses the process for the envelope as what happened in the original contraction of the star.  The size varies a lot after that.


Why doesn't the night sky keep on getting brighter and brighter every day? I think this should happen because of the below logic.

Consider Day 0 of planet earth. There is no light coming from any surrounding star that has reached our planet and hence its pitch dark.
On Day 1, the light of 1 star reaches us. And once it reaches us it will keep on coming continuously as it's not a pulse, it's just a continuous stream. Let us think that it's a 'string' or 'thread' say which starts from that star and reaches our planet and so we now have this connection.
On Day 2, light from another star reaches us. Again there is 1 more 'thread' which has now connected that star with our planet.
On subsequent days (and in between) more and more such threads get connected with our planet. And unless earlier stars that made this connection with our planet dies, the connections will only grow in number.
And so I would think that the night sky should become brighter and brighter every day.

Why doesn't this happen?

This assumes that the stars formed at the same time as the Earth.  This is not the case.  Stars had been forming for billions of years since the Earth formed.
The Earth didn't form in a single day, but for convenience let's pick one Early day in the Earth's formation as "day 0".
On day 0 light from many stars that had been travelling for years reaches Earth. The night sky is full of stars.
On day 1 light from those same stars that was emitted one day later reaches Earth, the sky brightness doesn't change.
On day 2 the same and so on.
Over time some stars will have moved nearer, some will have moved away, some stars will have reached the end of their life and some will have been born. But, on average there is no change.


Why do PMS stars on the Hayashi track remain at a constant temperature while they contract? Why do pre-main-sequence stars on the Hayashi track remain at a constant temperature while they contract?

I've read the Wikipedia article, so no need to repeat the derivation.

What I took away from that is that the extra heat generated by contraction is given off almost exactly because the whole star is convective and the atmosphere is very capable of radiating that heat away if the opacity is mainly caused by hydrogen ions, which is the case in the cooler of the pre-main-sequence stars.

Is that correct?

The surface temperature of fully convective stars is set by their opacity mechanism, often emission when the H minus ion is created.  The rate the star emits light is not set by the contraction rate, it is the other way around-- the star loses heat at a rate set by its structure, and that's what sets the contraction rate.  (As said, the rate of gravitational energy release is always double the rate the star loses heat to starlight.)  The reason the surface temperature always has to be something like 3000 K is pretty complicated, but it seems to be due to the fact that this temperature is a kind of peak in the surface's ability to emit light.  Convection sets the temperature structure, but there are a range of possible solutions with different internal energy, so the history of heat loss picks out whichever solution has the right internal energy.  But just why the surface is always about the same T is still the trickiest part to understand, I am hoping to get a better handle on that eventually.  Ignore anything you see in introductory textbooks, they never get it right.


Would being ejected from the Milky Way Galaxy have any major impact on life on Earth? I was reading about the impending collision of our galaxy with the Andromeda galaxy, and learned that there is a small possibility that our solar system could be ejected during the collision.

Assuming that orbits within our solar system remain unchanged (it is ejected as a whole), would floating in intergalactic space cause any significant changes in the living conditions on earth?

I can think of two ways this benefits life.

Less chance of a passing star disrupting our Oort Cloud and sending
deadly comets crashing into the Earth.
Less chance of nearby supernova destroying our ozone layer.

On the other hand, if our Solar System passes near a relativistic jet emanating from the central black hole of a galaxy, Earth will get hit with high speed particles that will disrupt the magnetosphere and ozone layer. Definitely not good for any life on Earth at that time.

Getting ejected from the galaxy also means there is less chance of future humans exploring the galaxy by hopping to nearby stars. We'd only have our solar system to explore and colonize. There would not be another star system within a hundred thousand light years.


Why is detecting brown dwarfs difficult? Why is detecting brown dwarf stars tedious and not always successful? They emit light in the infrared region, and given that we're surrounded by state-of-the-art technology in space today, why haven't the success rate grown? Why aren't all of the infrared-capable telescopes able to see them?

Brown dwarfs have historically been difficult to detect (directly) simply because of how faint they are. Typical luminosities may range from $10^{-3}L_{\odot}$ to $10^{-5}L_{\odot}$ depending on spectral type. Any object that dim will be tough to find, regardless of spectral type or what sort of telescope you're using - you can have the largest, highest-resolution telescope in the world, but it can't make the source intrinsically brighter.
This can be mitigated in part by looking for brown dwarfs in young stellar clusters, when they're at the most luminous point in their lives - old brown dwarfs are quite difficult to detect directly. The downside to this is that young, high-mass brown dwarfs are not easy to differentiate from young, low-mass stars; there's much less of a distinction early in life. The development of the lithium test in the 1990s helped make strides in this area, but in many cases it's not conclusive.
Another reason that brown dwarfs weren't confirmed observationally until a couple decades ago was simply inadequate equipment; adaptive optics wouldn't come into use until the 1990s, even though we may take it for granted today. Additionally, we've since made advances in indirect detection techniques, such as the radial velocity method and (to, I think, a lesser extent) changes in astrometric measurements. The radial velocity method has been used widely to detect massive exoplanets, and as brown dwarfs are more massive than exoplanets, they should produce stronger signals (assuming the same semi-major axis).
The bottom line, though, is simply that brown dwarfs are extremely faint. At the same time, WISE, 2MASS and other surveys have discovered hundreds (thousands?) of candidate and confirmed brown dwarfs. Granted, given the expected brown dwarf population of the galaxy, that's not a lot, but it's not nothing.


Why does matter stay collapsed in the core, following a supernova explosion? Following a supernova explosion a star may turn into a white dwarf, neutron star, black hole, or just a stellar dust & gas leftover.

Excluding the latter case, why and how does the star's core matter stays collapsed, after such an event where matter is burst and scattered in space?

In order to "blow something up" you need to release more energy than its binding energy and have a way of trapping that energy so it can't escape in another way.

At the centre of a core collapse supernovae is a 10 km radius, $1.4 M_{\odot}$ ball of (almost) neutrons.
Its gravitational binding energy is $\sim GM^2/R = 5\times 10^{46}$ J.

This is almost exactly how much energy is released by the collapse of the core from a much larger size (i.e. the energy of the supernova is gravitational to begin with) and since some of that energy goes into dissociating iron nuclei and making neutrons (both endothermic processes) and most of the rest escapes in the form of neutrinos, then there can't be enough energy to unbind the core. Only a tiny fraction (1%) of this energy is transferred to the envelope of the original star, which since it has a much larger radius (by at least 5 orders of magnitude), is enough to overcome its gravitational binding energy and blast it into space.

The case of a type Ia supernova (an exploding white dwarf) is quite different. Here the energy source is not gravitational collapse, but from a thermonuclear detonation of all the carbon and oxygen that make up the white dwarf, to form iron peak elements. This exothermic process rapidly releases enough energy to unbind the original star (e.g. see here) and it is completely destroyed.


what is the highest throughput astronomy project in pixels? I was having a discussing about big scientific projects with colleagues, and I postulated that astronomy is still one of the scientific fields with biggest projects per amount of data dealt with, after the high-energy physics.

I would like to know what is the highest throughput astronomy project as defined by the number of pixels in the images analysed in the project.

Something like "project XYZ" with an estimated "1.2 trillion pixels" worth of pictures taked and analysed over 5 years.

If you refer to "data volume" instead of real image pixels, it would be the Millenium Run (25TB of data):

http://www.mpa-garching.mpg.de/galform/virgo/millennium/

  The Millennium Run used more than 10 billion particles to trace the
  evolution of the matter distribution in a cubic region of the Universe
  over 2 billion light-years on a side.


Periodic behavior of Venus After a couple months of watching a very bright Venus appear at dusk and set soon after the Sun, I've noticed that it seems to have temporarily disappeared to the naked eye. I used a virtual sky simulator (Stellarium) to confirm that the Evening Star has indeed transitioned to being the Morning Star (though due to obstacles blocking my view of the horizon in my backyard, Venus is still too close to the Sun for me to witness it at dawn before sunrise renders it invisible).

What is the period of Venus's alternation between morning and evening visibility? I gather this isn't a simple seasonal period as its visibility should depend on the Sun-Earth-Venus angle rather than just Earth's yearly orbit.

Assumed a Venus year is 0.615 198 Earth years.

0.615 198 yr / (1 - 0.615 198) = 1.598739 yr = 583 days 11 hours 24 minutes for one period in mean, or roughly 19.5 months.

That's 1.598739 periods for Earth and 2.598739 periods for Venus:
1.598739 * 365.256 days = 583.95 days = 2.598739 * 224.705 days

The relative accuracy should be somewhere near 1e-5.

Since both orbits are elliptical the actual period oscillates around that mean value.


Anecdote of an astronomer looking for correlations in antipodal pairings of stars; what am I remembering? The question Are the stars distributed in uniform distribution, on the celestial dome, with respect to brightness? brings to mind a different study that I vaguely remember hearing about a while ago, perhaps several decades. This is a summary of how I recall it, it may not be 100% accurate:

An astronomer was stuck in a situation for an extended length of time and in order to keep busy and do science used a small personal computer to do an analysis of star positions, focusing on pairs that were diametrically opposed; at nearly antipodal points, in order to see if there was a deviation from other pairs of points that were not antipodal.

One possible effect that might cause such an anomaly was that the universe was small and closed and light from a star might reach us from both the "short" and "long" part of a great circle drawn on a 4-sphere (or torus?), thereby appearing to us at antipodal points of the celestial sphere, a bit like how amateur radio operators with directional antennas with good rejection ratios can sometimes receive the same signal from both directions along the great circle containing both sites.

Does this sound familliar to anyone? Was it ever published? I've tried googling several ways but lack the proper search terms.

This is a partial answer because while I'm quite sure that

Fang Lizhi is the astronomer I'm thinking of
The paper Periodicity of Redshift Distribution in a T-3 Universe (FERMILAB-Pub-90/26-A
January 1990) is a description of the research I'm remembering

I can not understand the paper well enough to connect it to how I remember the author describing his computational experience working on the small Apple computer while trapped in an embassy, and what this paper has (if anything) to do with comparing antipodal points.

Hopefully this is enough information for someone to go further and post a proper answer.

There is also the book The Most Wanted Man in China: My Journey from Scientist to Enemy of the State by the same person. On Page 294:

  What I needed was a computer. Again I was fortunate, because one of the diplomats, who originally had been a student of mathematics, was being transferred back home and was ready to part with his first generation Apple computer.


Where to obtain Tycho Brahe's data? I would like to obtain Tycho Brahe's data on Mars. What would be an authoritative source? One source I could find is this page (the data is given as an Excel file) but I have no idea can that be trusted. Does some astronomical organization or university keep the data public? I suppose Tycho wrote his data into a book. Where is that book located at the moment?

This must be what you are looking for, "Tabulae Rudolphinae". Tycho Brahe's star catalogue and planetary data published by Kepler in 1627 .


Problem regarding the absorption lines of the sun Some of the wavelengths of light that are emitted from the sun will be absorbed by atoms in the outer layer of the sun and also the atmosphere of the sun, and we see this as absorption lines in the spectrum. Now, this absorbed radiation will indeed be re-emitted again, so one might think that these emission lines should "cancel out" the absorption lines. The usual explanation for why this doesn't happen is that the re-emitted light is radiated in all directions, not just towards us, meaning that to us these wavelengths will be much fainter than the other wavelengths.
But the problem I have is that this happens all around the sun (since the atmosphere is completely surrounding it), and intuitively it seems then that all of this re-emitted light should combine such that far away it would appear that the sun is radiating these wavelengths just as it is radiating all the other wavelengths. And if that is true, then we shouldn't see absorption lines in the spectrum. So what is it that I am missing?

Possibly you are labouring under the misapprehension that the number of photons is somehow a conserved quantity? That isn't true, there are more photons at any given wavelength when you are deeper into the star, because there is a temperature gradient. Cooler material further out is less emissive because fewer atoms are in excited states.
The temperature gradient is responsible for the formation of absorption lines. If the photosphere of the Sun were at a single temperature then we would see a perfect blackbody spectrum, for the reasons you outline.
The filling in of absorption by scattering would only take place if the radiation field that the atoms were in were isotropic. But it isn't isotropic because of the temperature gradient.
A much better way to think about the spectrum of a star is to imagine that you can see to a wavelength-dependent depth into the star. Where there is a strong atomic absorption feature, you cannot see very far into the star at that wavelength.
Since the star gets hotter the deeper you go into it, and the emissivity scales as $T^4$, then the deeper we can see into the star, the brighter it will appear at that wavelength (and vice-versa).
EDIT:
More formally. The radiative transfer equation, if you want to consider the absorption and remission as some sort of scattering process, would be
$$\frac{dI_{\nu}}{ds} = -\sigma_\nu I_{\nu} + \sigma_\nu J_\nu\ ,$$
where $I$ is the specific intensity in the solar photosphere (in this case, directed towards the Earth), $J$ is the mean specific intensity at a point in the solar photosphere averaged over all directions (i.e. $J = \int I d\Omega/4\pi$, where $\Omega$ is solid angle), $\sigma$ is the scattering coefficient (assumed to be isotropic) and $ds$ is a piece of pathlength towards the observer. The $\nu$ subscript just indicates everything is wavelength/frequency dependent.
To avoid creating an absorption or emission line then $dI_\nu/ds$ must equal zero (i.e. nothing is added or subtracted from the beam of light).
This will only happen if $I_\nu = J_\nu$, which would require that the  specific intensity averaged over all directions is equal to the specific intensity emerging from the Sun and heading towards the observer. This will only be true if the radiation field is isotropic and equal to $I_\nu$ in all directions.
Whilst this would be true for a blackbody radiation field at a set temperature,
it isn't true in the solar photosphere. The specific intensity heading towards us (generally outwards) is always larger than the specific intensity heading away (generally inwards and true regardless of which portion of the visible solar disc is considered) because of the temperature gradient in the photosphere, which means it is hotter further into the interior. That means that $I_\nu$ is always greater than $J_\nu$ and hence $dI_\nu/ds < 0$ and we have net absorption.


Are there any known low-inclination trans-Neptunian objects? All the trans-Neptunian object's orbits I know are very inclined compared to those of the eight recognized planets, and Centaur's orbits are highly inclined as well.
Are there any known Centaurs and/or trans-Neptunian objects or TNOs whose orbit isn't significantly inclined to the ecliptic or to the invariable plane, but is on about the same plane as the eight main planets?
And to double check, the hypothetical planet Nine also has a high orbital inclination, doesn't it?

Queries to the JPL Small Body Database or the ESA Asteroids Dynamic Site for such bodies return several results.
Some of the bigger ones are:
Centaurs with H < 10 and i < 4°

386968 (2012 BR61), q = 11.7 au, Q = 31.6 au
527328 (2007 TK422), q = 17.0 au, Q = 25.2 au

TNOs with H < 5 and i < 2°

119951 (2002 KX14), q = 37.3 au, Q = 40.9 au
42301 (2001 UR163), q = 36.8 au, Q = 66.4 au
48639 (1995 TL8), q = 39.9 au, Q = 65.0 au


Minimum Mass Solar Nebulae Scaling Factors I'm attempting to build a MMSN, I've been trying for about... a week to get an intuition on the scaling factors for calculating the mass of the disks, I'm not entirely sure how to think about it. I feel as if the concept is extremely simple but that I'm thinking of it incorrectly. Can someone explain what exactly these scaling factors account for and how one would calculate them? I'm not looking for a solution, I'm looking for intuition on how these scaling factors are found.

My understand is that you pick an element, (Fe), and compare that to the solar abundance (does this mean the abundance of Fe in the sun? From there I would look at the abundance of Fe in the cores of the planet and compare them somehow to get some sort of scaling factor. From what I understand Fe makes .14% of the suns mass, so if I know lets say that neptune has a mass of 17m(earth) how would I start finding the scaling factor.

Thanks!

Attempt to do an intuitive explanation:

The Sun was formed from a cloud of matter. A small amount of that matter remained around the Sun, and had a similar composition. This was the solar nebulae.

But the composition of the planets are now not the same as the Sun. This is explained by that some of the matter was collected by the Sun, and some of it was blown out of the system.

That was only the light stuff! like hydrogen and helium. Most iron and other metals are conjectured to have remained in orbit, forming the planets.

As the Sun is representative for the original composition (partly at least, stellar fusion has skewed the hydrogen/helium ratio). So if iron is 0.14% of the Sun, that is also the original abundance in the nebulae. So all the iron in the planetary bodies is 0.14% of the original nebulae mass.

From that you can calculate the original mass. It is a 'minimum' because some of the iron may have escaped as well.


How can I calculate the uncertainties in magnitude like the CDS does? When you check an entry of the Gaia DR2 stellar catalogue in Vizier, for example this one, you can see that there is a value for the G magnitude (in our case 18.0733 mag) and a value for the uncertainty on that (in our case 0.0023 mag). The thing is that the G value is part of Gaia DR2 but the uncertainty is not, it was calculated by the CDS for Vizier (using the values presented for the flux as far as I can understand). I have two small related questions:

How does the CDS calculate the value from the uncertainty exactly? at least so that the one given by the CDS and the calculated one agree to the fourth decimal.

Is there a way in astropy or astroquery to retrieve the photometric uncertainty value from the catalog? Or do I have to calculate it as in the first question?

Thank you in advance.

That is because what is measured is a flux and the flux errors are in the DR2 catalogue.
Since magnitudes are based on the logarithm of the flux, then there is no straightforward correspondence (although it matters little if the error bars are less than a few hundredths if a magnitude).
Simple error propagation formulae give
$$|\Delta G| \simeq \frac{2.5}{\ln 10} \left(\frac{\Delta f}{f}\right),$$
where $f$ is the flux in the G band.
This gives $\Delta G= 0.0023(1)$ for your example. Other algorithms give almost the same result, e.g. taking the average of the $\pm \Delta G$ from using $\pm \Delta f$ to calculate the magnitude.
If the difference between the algorithms (they do give differing results when the flux error exceeds $\sim 10$%), or the fact that the true error is asymmetric in magnitude are important, then you shouldn't be using the symmetric magnitude error bar from CDS.


Is the universe considered to be flat? I've read various articles and books (like this one) stating that we are not certain about the geometry of the universe, but there were experiments on-going or planned that would help us find out.

Recently though, I've watched a lecture by cosmologist Lawrence Krauss where he seems to categorically assert that the universe has been proven to be flat by the BOOMERanG experiment. Here's the relevant portion of the talk.

I've looked around and there are still articles stating that we still don't know the answer to this question, like this one.

So, my question is two-fold:

Am I mixing concepts and talking about different things?
If not then is this evidence not widely accepted by some reason? What reason would that be?

I think the reason you're suffering from conflicting sources is that you're mixing both new and old, out-of-date pieces of information. First off, the book you cited was published in 2001 - 15 years ago - and the other article you cite was published in 1999 - 17 years ago. There's been a lot of work done in the past 15 years, often under the term "precision cosmology", in an attempt to really nail down the precise content, shape, size, etc. of our Universe. By the early 2000's we pretty much knew the science behind everything (we knew about dark matter, dark energy, had well-developed theories on the Big Bang, etc.) but what we didn't have, were good, solid, believable numbers to put into these theories, explaining why the flatness of the universe was still contested in your sources.

I'll direct you to two incredibly important observatories which have been paramount in achieving our goal of having "good numbers". The first is the Wilkinson Microwave Anistropy Probe (WMAP), launched in 2001, and the second is the Planck satellite, launched in 2009. Both missions were designed to stare intently at the Cosmic Microwave Background (CMB) radiation and try to sort out the treasure trove of information which can be gleaned from it. In this vein, you might also come upon the Cosmic Background Explorer (COBE), launched in 1989. This satellite had a similar purpose as the other two, but was not nearly as precise as the later two missions as to provide us with good numbers and definitive statements by the early 2000's. For that reason I'll mostly focus on what WMAP and Planck have told us.

WMAP was a hugely successful mission which stared at the CMB for 9 years and created the most detailed and comprehensive map of its day. With 9 years of data, scientists were really able to reduce the observational errors on various cosmological quantities, including the flatness of the universe. You can see a table of their final cosmological parameters here. For the flatness, what you want to do is add up $\Omega_b$ (the baryonic matter density), $\Omega_d$ (the dark matter density), and $\Omega_\Lambda$ (the dark energy density). This will give you the overall density parameter, $\Omega_0$, which tells you the flatness of our universe. As I'm sure you know from your sources, if $\Omega_0 < 1$ we have a hyperbolic universe, if $\Omega_0 = 1$ our universe is flat, and $\Omega_0 > 1$ implies a spherical universe. From the results of WMAP, we have that $\Omega_0 = 1.000 \pm 0.049$ (someone can check my math) which is very close to one, indicating a flat universe. As far as I know, WMAP was the first instrument to give a truly precise measurement of $\Omega_0$, allowing us to say definitively that our universe appears flat. As you say, the BOOMERanG experiment also provided good evidence for this, but I don't think the results were nearly as powerful as WMAP's was.

The other important satellite here is Planck. Launched in 2009, this satellite has provided us with the best high precision measurements of the CMB to-date. I'll let you dig through their results in their paper, but the punchline is that they measure the flatness of our universe to be $\Omega_0 = 0.9986 \pm 0.0314$ (calculated from this result table), again extremely close to one.

In conclusion, recent results (within the past 15 years) allow us to definitively state that our Universe appears flat. I don't think, at this time, anyone contests that or believes it is still uncertain. As it usually goes with science, answering one question has only resulted in more questions. Now that we know $\Omega_0 \simeq 1$, we have to ask why is it one? Current theory suggests it shouldn't be - that it should be either enormously small or enormously large. This is known as the Flatness Problem. That in turn delves into the Anthropic Principle as an attempted answer, but then, I'm getting out of the scope of this question.


Recently, the most distant object in the solar system was discovered. How was this accomplished? It was recently announced that the most distant object in our solar system was discovered. This object averages 132 AU from the sun. The object, initially named Farfarout, was estimated to be 400 km across. How was such a small object found and its orbit estimated by a ground-based telescope? This seems to really be pushing the limits of observable objects. Or am I wrong on this?
Ref: https://phys.org/news/2021-02-astronomers-orbit-distant-solar.html

The discovery announcement by the Minor Planet Center indicates that 2018 AG 37 ("Farfarout") was between 25.0 and 25.3 magnitude. The positions are based on observations taken with the 8 m Subaru telescope and 6.5 m Magellan-Baade telescope.
As a comparison, this ancient article by Sky & Telescope (What Is The Faintest Object Imaged By Ground-Based Telescopes?) indicates the Subaru telescope limit is around 27.7. ("Ancient" in terms of CCD cameras and computer processing. The article is from 2006.) Note that this same article indicates that a 16 inch (400 mm) amateur telescope should be able to capture images to 24th magnitude -- just 2x to 3x brighter than Farfarout!
Also, the Subaru Exposure Calculator indicates an exposure of 1 minute will capture a 25.3 magnitude object using default input (except for the Moon, which I set to New Moon).

Thus, it seems almost "easy" to capture an image of it.
Finding an unknown, faint object is another issue. I do not have any information on this aspect of the question, but I feel safe that computer searches are quite adept at finding such things. Once the first image (or pair of images that show motion) is found, other images are often found or taken to facility the calculation of the orbit. The time span of the images is only two (2) years which is short for a body with a period of 1000 years (estimate). The Wikipedia page for 2018 AG37 currently lists large uncertainties for the average distance (86 +/-68 AU) and period (798 +/-941 years). Those uncertainties will be reduced as a longer arc of the orbit is measured.


Is gravitational lensing a good way to search for negative mass? Is it possible to verify negative mass with gravitational lensing?  The following video proposes an idea that galaxies are surrounded by negative mass: https://youtu.be/MZtS7cBMIc4

Could this be proven or disproven by looking at gravitational lensing of distant galaxies, by looking at Hubble Deep Field images?  I would expect if negative mass surrounded a galaxy, it should cause the opposite effect of the positive mass galaxy.  If there is surrounding negative mass, there should be an “anti” lensing effect just outside the normal lensing effect.  Could someone perform this analysis and confirm or deny that idea?

Edit: In the following image, and others, I have looked to see if I could see such an effect out further from the source visually, and it is hard to tell.  There are so many galaxies in front that aren't affected by the lensing.  It might take a computer analysis of images surrounding the "ring" effect to see if there is a "radial effect" around the ring.  Most images probably don't show enough of the surrounding area to where the radial effect as predicted in the paper Izumi et al. (2013) would be apparent.  If this is present, I would think it indicates negative mass surrounding the positive mass, and would be a huge discovery confirming negative mass!  If absent, it would likely show that there is at least not a significant amount of negative mass clustered around the galaxies (wouldn't be a total disproof of negative mass).

Image from: Galaxies - Gravitational Lensing

One reference I found on this subject was Izumi et al. (2013), who note that the images produced by lensing around a negative mass are radially distorted while lensing by a positive mass are tangentially distorted, and that this effect can be distinguished without prior knowledge of the lens position by measuring the alignment of lens images.

I am not an expert in general relativity so I'm not able to evaluate their results, but assuming the paper is correct it does look like negative mass could indeed be detected by observations of gravitational lensing. The question of whether negative mass exists is another matter, so far it doesn't look like a likely prospect.