Why is Jupiter called so? I have read before that Jupiter is named after the great Roman god because of how bright it is. I can't help but wonder, why wasn't the name given to Venus instead? Isn't Venus much brighter than Jupiter in the night-sky, or am I mistaken?

I don't think this will be a great answer because these are just speculations. I cannot find concrete evidence or sources discussing why Jupiter (the planet) became associated with the "king of gods" and not Venus, but here's my go at citing some potential reasons.

To start, I want to point out that ultimately, we have to trace this back to the Greeks and Babylonians. Sure Jupiter (the planet) is named after the Roman god Jupiter, but really the Roman mythology traces pretty distinctly to Greek mythology and Greek mythology has strong ties to Babylonian mythology. The Greeks were the ones who associated Zeus with the planet Jupiter (and they were likely taking cues from the Babylonians) and the Romans just tagged along with that idea, but changed the god's name. So I think your question then transforms into, Why didn't the Greeks/Babylonians decide to associate the planet Venus with their chief god (being that it is the brightest) and instead chose the planet Jupiter?

Brightness of Venus and Jupiter

First, let's just confirm that Venus is indeed brighter. If you look up the Apparent Magnitude system of Wikipedia, you see a description of how astronomers measure visible brightnesses of astronomical objects (and coincidentally enough, this system was created by a Greek). In this system, smaller and more negative numbers indicate brighter objects. From the table on that page, we can see that the apparent magnitude of Venus varies from $-4.89$ at its brightest to $-3.82$ at its dimmest (this variation is caused by the different configurations of Earth, Venus, Sun positions). For Jupiter, we see that at its brightest it has an apparent magnitude of $-2.94$ and a minimum of $-1.61$. Clearly, even at its brightest, Jupiter is far outshone by Venus at its dimmest. Note that none of this takes into account light pollution or other atmospheric effects which would have been negligible to the Greeks and Babylonians anyway. So we can say emphatically yes that Venus is distinctly brighter than Jupiter, but importantly, we note that Jupiter is still brighter than every other star in the sky $-$ the brightest being Sirius with a magnitude of $-1.47$.

Confusion about Venus

Okay, the Greeks and Babylonians were sitting around looking at these planets and wondering what they were. Likely they started thinking they were big, great deities and started attributing gods to them. I can't say this is a certainty, but one possible reason Venus didn't get the top god was that initially the Greeks and Babylonians weren't even sure Venus was a planet like the rest of the planets were. Because Venus is so close to the Sun, we only ever see it at sunrise and sunset. Otherwise, it is in the sky during the day and dwarfed by the brightness of the Sun. This meant that it took the ancient peoples a long time before they even realized the bright object they saw in the evening was the same as the bright object they saw in the morning. To quote Wikipedia on this:

  Observations of Venus are not straightforward. Early Greeks thought that the evening and morning appearances of Venus represented two different objects, calling it Hesperus ("evening star") when it appeared in the western evening sky and Phosphorus ("light-bringer") when it appeared in the eastern morning sky. They eventually came to recognize that both objects were the same planet. Pythagoras is given credit for this realization.

Potentially, the ancient Greeks didn't even consider Venus to be a planet initially. The word planet is Greek and means "wandering star". The ancient Greeks identified objects in the night sky which were different and seemingly more important that the normal stars. However, initially, they don't seem to have grouped Jupiter and Mars in with the same type of object as Venus (and possibly Mercury). Jupiter's motion around the sky may have seemed more grandiose and full of purpose, hence why they attributed it to being their biggest and most important god.

Love and Beauty

As I said, the Babylonians, as well as the Greeks before they figured it out, didn't consider Venus to be a planet, but rather two separate and strange "stars". However, once they figured out the two "stars" were really one and the same and Venus was a planet just like Jupiter, they decided to attribute a proper god or goddess from the pantheon of gods to it. Jupiter was already taken so they had to pick someone else.

Despite that, I don't think the argument that Venus is brighter automatically means it should be the most important god. Note that Venus is named after the Roman goddess Venus (of course) who is also the Greek goddess Aphrodite. This is the Greek goddess of love and beauty and she herself was supposed to be exceedingly beautiful. Venus, the planet, is a beautiful sight to behold and it seems appropriate that the most radiant and beautiful planet be named after the most radiant and beautiful Goddess.


Is there a term for a horizontal moon crescent I seen the other day the moon lit directly below or towards my horizon perfectly.

My question, is there a term for when a moon's crescent is aligned with the viewer's horizon?

No formal astronomical term, but it is sometimes said to be "on its back"

Examples from "weather lore"

  When the moon lies on its back
  Then the sou-west wind will crack.

  When the moon is on its back,
  She sucks the wet into her lap.

  It's sure to be a dry moon if it lies on its back
  so you can hang your hat on its horns.


Hot and "warm" Jupiters expelling terrestrial planets? I've seen in documentaries that if a Jupiter size planet migrates close to its star then it would remove terrestrial planets along the way. This makes sense and I'm sure most models would predict this, but do we have evidence?

Indeed, the Kepler survey (taking Kepler 1-447) found 34 Planets>6 R(Earth) less than 0.1 AU from the star and the only one where another planet was found was Kepler 424 which also has a Jupiter size planet at 0.73 AU. Three "warm" Jupiters (0.1- 1.7AU) out of 47 have earth-size planets discovered in same system and all are "mini-solar systems" with the smaller planets far interior. (K68,90 and 407). If you include "super-earths" (R = 1.25-2.0 R(Earth)), then there are 7 additional stars found with "warm Jupiters" in multiple systems. The super-earths are still all inside the Jupiter's (although K18,89 and 118 have Jupiters less than 0.2 AU).

  My question is:

  Is this finding proof that migrating Jupiters have thrown out
  terrestrial planets or do their existence make the signals of
  "exterior" planets hard to discern? And what about smaller planets
  migrating in "behind" the Jupiter's?

It's not proof that they've ejected other inner planets, because there are plenty of other explanations for why we haven't observed companions. Steffen et al. (2012) analyzed Kepler data - likely some of the same examples you've looked at - and came up with several explanations besides the no-companions-because-of-planet-planet scattering hypothesis:

Inner planets never formed. It's possible that mechanisms in systems with hot Jupiters prevent inner planets from forming; the authors are unclear as to what those mechanisms might be.
The planets are too small to see during transits. This is the first explanation based on detection bias. Obviously, Kepler has its limits, and it's entirely possible that the systems have small bodies it simply can't detect.
The planets are too low-mass. It is possible that there may be planets with masses so low that transit-timing variations (TTVs) are too small for Kepler to see them.
The planets have high mutual inclinations. In other words, there might be planets with orbits highly inclined with respect to the hot Jupiters' orbits; we only detect the ones at inclinations favorable to detection from our angle.

The options the authors suggest rest mainly on experimental biases as opposed to theoretical possibilities.

Something I was confused about when I read your question was the assumption that hot Jupiters migrate mainly due to planet-planet scattering. Levison et al. argue that warm Jupiters (i.e. giant planets with semi-major axes of about 1 AU) are more likely to have migrated via planet-planet scattering, because it provides a stopping mechanism via damping, assuming the planetesimal number density scales appropriately. This happens when the energy needed to move planetesimals from their orbits is greater than the energy lost from the change in the planet's orbit. Given that planetesimals cannot survive long in orbits less than about twice the stellar radius, warm Jupiters reach semi-major axes no lower than 0.03 to 0.1 AU (see Murray et al. (1998)).

Hot Jupiters, on the other hand, may be driven largely by Type II gas disk migration, where giant planets create a gap in a protoplanetary disk that subsequently brings in material; this then brings the planet closer to the star, eventually leading to a hot Jupiter. Here's a visualization, from Planet Hunters:


Expansion of the universe and visibility of distant galaxies The universe expands at an accelerating rate, which makes me wonder if at a certain point the speed of expansion between two points will exceed the speed of light. In that case, it might eventually become impossible for two gravitationally bound clusters of the universe to exchange light. I recall reading that future civilizations born after a certain point would be unable to observe the distant galaxies that we can now, and would have no way of knowing galaxies besides their own exist.

My question: Is this possible, and if so could it have already happened; the entire observable universe is one of multiple clusters that have since sped away from each other? Or can this be ruled out by other known facts about the history of the universe?

(My answer here isn't correct, as pointed out by the first comment on this post, please refer to it.)

Yes, it certainly is possible - and it already has happened. The age of the universe is 13.8 billion years, yet it is something like 90 to 100 billion light-years in diameter. This means that we definitely can't see all of it, not because of our own observational limitations, but because the light from those parts of the universe just hasn't reached us yet - and perhaps it never will.

As for the future, yes, if cosmological expansion overpowers gravity at close range (i.e. the Milky Way and Andromeda, and the world "close" is relative here) then eventually many galaxies and clusters will disappear out of view due to light not being able to "keep up" with the expansion.


Caves traced in nine planets of solar system Are there chances of caves being found or traced on other planets of the solar system?
What's the solution?

Manufacturing special telescopes for viewing or observing caves on other planets?

or

Satellites revolving around Mars, Venus & Mercury sending images back to planet Earth for assistance?

A key requirement for caves is solid substance: while there may be rock cores inside the giant planets, the rest is liquid or gas. Metallic hydrogen may be solid or liquid in Jupiter, but presumably the pressure is high enough to prevent cave formation. So no for Jupiter, Saturn, Uranus and Neptune.
A second requirement is some factor digging cavities. On Earth water, chemical erosion and lava are factors.
The terrestrial planets have solid substance and not too extreme gravity. There are suspected "cave skylights" seen on Mars. Lava tubes are expected on Venus. Mercury volcanism was very different, but lava tubes may have existed. There are also weird hollows.
That leaves Pluto. Pluto has had cryovolcanism, so it is not implausible that "lava tubes" have been dug by molten water and ammonia.
As a bonus: smaller asteroids are often "rubble piles" of rocks loosely held together. It is not hard to imagine that there are empty spaces between big rocks that could count as caves. Same for comets, where evaporation of ice may contribute to making cave-like structures.


If we were to see the Sun with our naked eyes from the Orion belt, would all planets be encompassed inside the star? Is this calculable? When we see a star it looks much bigger in diameter to us than it really is, this picture (extracted from here) explains what I mean:

Notice that the point we see in the skynight, represented by the yellow outer circle, would actually encompass even planets orbiting the actual star, represented by the black dot in the center. In this case we see one planet inside the white circle.
My question is, can the effect of distance and brightness be measured as to know how far would we must be to watch a star that encompasses neptune?, the earth? or does it depend on different factors?

Such observations are possible, see Fomalhaut b.
It depends mainly on the diameter of the objective of the telescope (diffraction limit) and contrast. Telescopes can (at least in theory) be combined to an effective telescope of larger diameter (aperture) by interferomentry.
Masks can help to occult bright stars to overcome the contrast limitatios.

There are indirect methods to "see" faint planets, as e.g. applied in the Kepler mission, or by Gaia.

And yes, it is calculable. With naked eye we wouldn't be able to distinguish the sun from the planet orbits from a distance of about 1000 lightyears, as the orion belt stars: 1000 lightyears are about 300 parsec. This means, that the earth orbit would be about 1/300 arc second. The resolution of the human eye is about 4 arc minutes, the 72,000-fold. For Pluto it's still more than 1000-fold.


Does more ocean on an Earth analog produce a different rotation period? Would an exoplanet that has more ocean than Earth rotate at a different speed as a result of this? Would the amount of water impact the weight, gravitational pull, and/or tidal forces and cause a difference in the exoplanet's rotation period?  (For simplicity's sake, say, if it was earth-like in every respect other than having more ocean than Earth does at about 70% of the surface area.)

Would an exoplanet that has more ocean than Earth rotate at a
  different speed as a result of this?

Basically no.   Rotation speed, or angular velocity doesn't measurably change with your proposed example.

To explain this in more detail, there's two important concepts.  First, is Angular Momentum, (Short explanation or longer) and the 2nd concept is Moment of Inertia.

The basic formula is that Angular velocity (time for 1 full rotation) = Angular Momentum divided by Moment of Inertia.  Formulas and explanations are in the link(s) above, and if I was to explain it, it would get wordy, but your question seemed to be more general, less about doing the mathematical calculations, so I'll skip the formulas.

In nutshell, talking about a planet, the state of matter doesn't affect the angular momentum.   Angular momentum is conserved and that, divided by moment of inertia determines rotation speed.  Now if you get something spinning fast enough the angular rotation can overwhelm the gravity and when this happens, the planet can begin to fly apart, which happens more easily with water than a rocky surface which has some cohesion, but ignoring crazy super fast rotations, a water world, a deep ocean world, a shallow ocean world and a rocky world all obey the the angular velocity law and composition doesn't matter.  The angular momentum is conserved.  The moment of inertia of a planet can change but for the most part, doesn't change much.

The Earth's moment of Inertia, for example, changes as glaciers grow or shrink, or when there's an earthquake.   Even, every time we a tall building is built the Earth's moment of inertia increases a teeny tiny bit, similar to a skater extending their arms to slow down coming out of a spiral.

When there's an earthquake which, for the most part, settles the Earth, there's a small increases in the Earth's rotational speed.   The total angular momentum and total mass remaining the same but shifting of material changes the moment of inertia.   (Granted space dust and tidal effects change the Earth's moment of Inertia, but quite slowly).

  Would the amount of water impact the weight, gravitational pull,
  and/or tidal forces and cause a difference in the exoplanet's rotation
  period?

This is harder question to answer precisely because adding water changes the mass of the planet and changing the mass changes the moment of inertia, but sticking to the principal of your question, there's no measurable effect.

Lets take a somewhat simpler example without changing the planet's mass.  Ice ages.  When the Earth is in an ice age there's less liquid oceans and more ice at the poles but the total mass is unchanged.   More mass at the poles and less mass in the oceans decreases the Earth's moment of inertia because the bulk of the Earth's moment of inertia is around the equator,  so, as a result, the Earth rotates slightly faster during an ice age and slightly slower after an ice age.   Over time, the Earth's crust has a tendency adjust for this effect but that takes tens of thousands of years.  Parts of the Earth's crust is still rebounding from the last ice age.

Gravitational pull isn't relevant.  Neutron Stars with enormous gravitational pull can rotate very fast and the planet with the fastest rotation in our solar-system is Jupiter and the one with the slowest rotation is Mercury.   Angular velocity has no direct correlation to mass or gravity though there is an indirect correlation.   As a star, for example condenses it's rotation speeds up, because the angular momentum is conserved but as it settles the moment of inertia decreases.   That's why young stars, White Dwarfs and Neutron stars can spin very fast.

Tidal forces can create drag on rotation but the effect is slow, taking millions or hundreds of millions of years.  With enough time, tidal forces cause a planet or moon to stop rotating and become tidally locked but there's no short term affect.  (I'll say a bit more on this later).

So, a planet with large oceans wouldn't rotate any slower than a planet with no oceans because liquid or solid can have equal angular velocity, but over time, tides will slow a planet with oceans more quickly than a planet without them.

Because the Earth has oceans, the Moon's gravitation on the Earth's tidal bulge does slow down the Earth's rotation, but this has been happening for 4 billion years and the Earth still rotates every 24 hours - one of the faster planets.   If the Earth had more water the Moon's tidal tug would slow the earth down a bit faster, but it would still be very gradual.

Jupiter, which is basically a ball of gas, is the fastest rotating planet and Mercury, basically a rock, the slowest, so those are 2 examples of composition not being a factor, though Mercury's slow rotation is in large part due to the strong tidal forces it receives from the Sun.

Now, I Understand the logical approach to your question, as there's something apparent about water resisting rotation - touched on in this question, but the fact that water doesn't spin with a glass when you spin a glass is an example of conservation of angular momentum, not an argument against it.  On a planet, the oceans are rotating with the planet and the angular momentum is already there.

Hope that wasn't too long, but that's the gist of it.   I can try to clean up or clarify if needed.


What do cosmologists mean when they talk about "the running of the spectral index"? All I know is that the spectral index is related to the CMB, and that it has to be slightly less than 1 to favor inflation.

The spectral index $n_s$ describes how the clumpiness of stuff varied on various scales just after cosmic inflation. The primordial power spectrum $P(k)$ of the fluctuations (where the wave number is $k=2\pi/\lambda$ with $\lambda$ being the physical scale), is predicted by many inflationary models to be:
$$P(k) \propto k^{n_s-1}.$$
If $n_s=1$, the fluctuations are scale invariant.

If $n_s$ is not a constant, but instead changes with $k$, that is if
$$\frac{dn_s}{d \ln k} \neq 0,$$
it is called a "running spectral index". And in fact it seems that that $n_s$ does chance with $k$ (see e.g. Cherny et al. 2014).

The term "the running of the spectral index" refers to the quantity $dn_s\,/\,d\ln k$.


total energy and apparent bolometric magnitude So I have been given this question:

  A typical Type Ia Supernova emits $10^{44}\ \mathrm{J}$. All nuclear weapons
  tested by humans have released a total of about $2\times10^{6}\ \mathrm{TJ}$ of energy. Assume the Supernova energy is released at the distance of the Sun. Determine how close to your retina the nuclear weapons energy would have to be released to make both appear to have the same apparent bolometric magnitude.

The issue I'm have is normally apparent magnitudes I would have to have joules per second where this is in just total joules.

So is it that with bolometric magnitude there is an automatic assumption that when total power is mention you assume joules a second?

Could someone please advise?

I would just like to point out I am not looking for a direct answer to this question, I am just confused with why total energy has been used. I have read posts on wiki which seems to confuse me even more. I have just used the above question as an example from a book.

You have been given a terrible question and your confusion is totally justified.

The magnitude system is a measure of the brightness of objects which is a measure of the energy received per unit time interval.

Without knowing a characteristic timescale over which the energy is released in each case, then it is not answerable. Note that the timescale for energy release in the case of supernovae and bombs are different by many orders of magnitude - a type Ia supernova has a bolometric light curve (e.g. see Fig.6 of Scalzo et al. 2014) that lasts 2-3 weeks, peaking at around $10^{36}$ Watts.

Given this, we can compare with the Sun's bolometric luminosity of $3.8\times 10^{26}$ Watts and apparent bolometric magnitude of -26.8, to estimate that the peak apparent bolometric magnitude of a type Ia supernova at the distance of the Sun would be -50.3.

You cannot do the same thing with nuclear explosions. They last a fraction of a second (in terms of their light output). Or are you meant to assume that you take the average flux over the 70 years that mankind has had nuclear weapons?? The question is a nonsense unless you are given some sort of timescale over which this explosive energy is released. About the only sane things you can do are (a) use ~70 years (actually, most of the energy was released during the 1950s and early 1960s) (b) use the duration of a single nuclear explosion or (c) (and I imagine what was intended) use a similar duration as for a typical type Ia supernovae so that the question should have begun - "Imagine that X and Y amounts of total energy are emitted over a similar timescale..."


What's the minimal argument I can give to reject The Geocentric Universe? I'm new to Astrophysics, So pardon me if you find it silly to ask. I was just started reading about the basics of astrophysics. I read about the Greek Tradition, the concept of a geocentric universe. If I were asked in my childhood, to look at the sky and tell what do you think about the clockwork of the planet, I would have said that the Earth is at the center and everything moves around it as said by the greeks.
I read, How different peoples found difficulty explaining the motion through this Hypothesis. Though they were able to make some complicated models understand the wandering stars etc. And then Copernicus suggested a heliocentric model of planetary motion which is as believed, to make things simpler to make calculation simple. And So on...
It seems the things were based on more or less explaining the data by making an appropriate model and that's How science more or less works.
I want to know if there is some more basic argument that could be given to reject the Geocentric universe.
If not, Could there be some basic experiment that can be done to approve the Heliocentric Hypothesis and reject the other?

Edit: One more thing to add, Apart from the minimal argument, it would be great if the argument would remain valid at that time that is it should not contain any new information that wasn't known at that time.

Part One: Moons of other planets.
The discovery of the Galilean moons of Jupiter in 1609-1610 proved that not everything had to orbit directly around one signel object.
The discovery of the Galilean moons showed that objects could revolve around an object which revolved around another object.  There was no way for all known objects to revolve directly around each other.
Either:

The Sun, the Moon, and the planets revolved around Earth, and the 4 Galilean moons revolved around Jupiter, thus only indrectly orbiting the Earth.

or:

Earth, the Moon, and the planets orbited around the Sun, and the 4 Galilean moons revolved around Jupiter, thus only indrectly orbiting the Sun.

or:

The Sun, the Earth, the other planets, and the 4 Galilean moons, all revolved around Jupter, and the Moon revolved around Earth, thus only indrectly orbiting Jupiter.

Decades later, Titan was disvoered in 1654, and four other large moons of Saturn were discovered in 1671 to 1684.
So now there were three objects in the solar system which certainly had objects orbiting them, Earth, Jupiter, and Saturn, and there was a big astronomical question whether everything ultimately orbited the Earth or the Sun.
Part Two:  Phases of the Planets.
When telescopes were first used to observe the planets starting in 1609-1610, the phases of the planets began to be observed, phases caused by the changing angles between the Sun, the planets, and Earth.
It became noticed that the phases of Mercury and Venus went all the way from thin crescents to 100 percent full, and that their angular diameters were larger when they were thin cresents and smaller when they were full. Half the times they appeared close to the Sun they appeared small and full, and half the times they appeard close to the son they appeared large and cresent shaped. That was consistent with them orbiting around the Sun at a distance less than the distance tebween Earth and the Sun.
But the phases of Jupiter and Saturn were different.  They ranged from slightly more than half full to totally full.   Jupiter and Saturn always appeared smaller and less full the closer they were to the direcion of the Sun but were never less than half full.  They never appeared larger and less than half full when they were close to the direction of the Sun.  So they must have orbited around either the Earth or the Sun at distances greater than the distance between the Earth and the Sun.
Part Three: Parallax.

Diurnal parallax

Diurnal parallax is a parallax that varies with rotation of the Earth or with difference of location on the Earth. The Moon and to a smaller extent the terrestrial planets or asteroids seen from different viewing positions on the Earth (at one given moment) can appear differently placed against the background of fixed stars.[12][13]
The diurnal parallax has been used by John Flamsteed to measure the distance to Mars at its opposition and through that to estimate the astronomical unit and the size of the solar system.[14]

https://en.wikipedia.org/wiki/Parallax#Distance_measurement[1]
john Flamsteed lived from 1646 to 1719.

Solar parallax
After Copernicus proposed his heliocentric system, with the Earth in revolution around the Sun, it was possible to build a model of the whole Solar System without scale. To ascertain the scale, it is necessary only to measure one distance within the Solar System, e.g., the mean distance from the Earth to the Sun (now called an astronomical unit, or AU). When found by triangulation, this is referred to as the solar parallax, the difference in position of the Sun as seen from the Earth's centre and a point one Earth radius away, i. e., the angle subtended at the Sun by the Earth's mean radius. Knowing the solar parallax and the mean Earth radius allows one to calculate the AU, the first, small step on the long road of establishing the size and expansion age[20] of the visible Universe.
A primitive way to determine the distance to the Sun in terms of the distance to the Moon was already proposed by Aristarchus of Samos in his book On the Sizes and Distances of the Sun and Moon. He noted that the Sun, Moon, and Earth form a right triangle (with the right angle at the Moon) at the moment of first or last quarter moon. He then estimated that the Moon–Earth–Sun angle was 87°. Using correct geometry but inaccurate observational data, Aristarchus concluded that the Sun was slightly less than 20 times farther away than the Moon. The true value of this angle is close to 89° 50', and the Sun is actually about 390 times farther away.[18] He pointed out that the Moon and Sun have nearly equal apparent angular sizes and therefore their diameters must be in proportion to their distances from Earth. He thus concluded that the Sun was around 20 times larger than the Moon; this conclusion, although incorrect, follows logically from his incorrect data. It does suggest that the Sun is clearly larger than the Earth, which could be taken to support the heliocentric model.[21]

Although Aristarchus' results were incorrect due to observational errors, they were based on correct geometric principles of parallax, and became the basis for estimates of the size of the Solar System for almost 2000 years, until the transit of Venus was correctly observed in 1761 and 1769.[18] This method was proposed by Edmond Halley in 1716, although he did not live to see the results. The use of Venus transits was less successful than had been hoped due to the black drop effect, but the resulting estimate, 153 million kilometers, is just 2% above the currently accepted value, 149.6 million kilometers.
Much later, the Solar System was "scaled" using the parallax of asteroids, some of which, such as Eros, pass much closer to Earth than Venus. In a favourable opposition, Eros can approach the Earth to within 22 million kilometres.[22] Both the opposition of 1901 and that of 1930/1931 were used for this purpose, the calculations of the latter determination being completed by Astronomer Royal Sir Harold Spencer Jones.[23]
Also radar reflections, both off Venus (1958) and off asteroids, like Icarus, have been used for solar parallax determination. Today, use of spacecraft telemetry links has solved this old problem. The currently accepted value of solar parallax is 8".794 143.[24]

https://en.wikipedia.org/wiki/Parallax#Solar_parallax[2]
Part Four: Stellar Parallax.
The heliocentric theory implies that as the Earth orbits the Sun, the angles to stars should change. Because of the vast distances to the stars, astronomers failed to detect the parallaxes and distances to the stars for centuries.
Advances in instruments and techniques led to the first successfull measurements of stellar parallax in the 1830s, when the parallaxs and distances of Alpha centauri, 61 Cygni, and Vega were first measured.  Alpha Centauri is the closest star system to the Sun, 61 Cygni is the 15th, and there should be a few hundred star systems closer - and easier to measure their parallaxs - than Vega.
Part Five: Conclusion.
Any amateur astronomer who has telescopes, instruments, and observing technigues as good as those of professional astronomers of 17th and 18th centuries, or the 19th century up to the 1830s, can duplicate those observants which give stronger and stronger evidence that the Earth orbits the Sun instead of the Sun orbiting the Earth.


How large were the deviations of Uranus's positon from predicted which led to the discovery of Neptune? After Uranus was discovered and its orbit calculated, its future orbit was calculated, and its future positions as seen from Earth were calculated.
And observers of Uranus began to notice that Uranus was deviating from its calculated positions.  Eventually the possibility that an undiscovered planet was perturbing the orbit of Uranus was used by Adams and Le Verrier to calculate the orbit of Neptune and led to the discovery of Neptune.
So how large were the deviations in the apparent position of Uranus that were used to calculate the orbit and apparent position of Neptune?

I also asked this question at the History of Science and Mathematics Stack Exchange and got two answers so far.
The answer by Ben Crowell makes a rough calculation that the displacement should be on the order of ten arc seconds.  It also has a plot of the variation in longitude of the observed and predicted positions of Uranus over time, which seem to differ by up to a few tens of arc seconds from predicted positions.
The answer by cktai states that according to his source the deviation between the calculated and the observed orbit was 30 arc seconds in 1835 and 70 arc seconds by 1840.
An arc second is one in 1,296,000, or 0.0000007, of a full circle.
At the average distance between the Sun and Uranus, about 19.22 Astronomical units or AU, a full circle is about 120.76271 AU. Since the orbital period of Uranus is 84.01 years, Uranus travels at an orbital speed of about 1.4374801 AU per year, or about 0.0039356 AU per day, or about 0.0001639 AU per hour, or about 0.0000027 AU per minute, or about 0.000000045 AU per second.
0.000000045 AU is 6.81433 kilometers, so the average orbital speed of Uranus should be about 6.81433 kilometers per second.  The average orbital speed of Uranus is listed as 6.8 kilometers per second.
Earth is at an average distance of 1.0 Astronomical Units from the Sun, so the distance between Earth and Uranus varies between about 17.33 and 21.11 AU, and the average distance is about 19.22 AU.
So since there are 360 degrees in a full circle, at the average distance between Earth and Uranus a degree of arc would be about 0.33545 AU, and an arc minute would be about 0.00559 AU, and an arc second would be about 0.00009318 AU or 13,939.61 kilometers.
Being off position by 30 arc seconds would equal being off position by 418,188.38 kilometers, and being off position by 70 arc seconds would equal being off position by 975,772.88 kilometers.  And that would be approximately the distance traveled by Uranus in about a day.
And I guess that gives some idea of the scale of the deviations which were considered a problem and which led to the discovery of Neptune.


What might be the cause of the hot summer on Earth in 2018? I have a question relating to the hot temperature this summer. There are 3 reasons that I can come up with:

Chemical, greenhouse effect.
Increased solar activity.
Orbital Resonance. The Earth is closer to the Sun, due to gravitational pull from other planets.

Anybody know something about Orbital Resonance? The orbits are affected by one another as they line up? Particularly the larger ones like Jupiter, Neptune and Saturn?

Seen globally, the Earth is 0.75—1.0 degrees warmer than the average. This is what is modelled by warming due to raised levels of greenhouse gases.

Currently the sun is close to a solar minimum. Perturbations of the Earth's orbit by other planets do not significantly change the level of solar insolation. Also the ENSO is currently close to neutral. The hot temperatures across western Europe and East Asia are a combination of the effects of greenhouse gases, and the random influence of weather.


Is it possible that some stars are already black holes yet we see light emitted from before becoming a black hole? For stars we see that are burning fuel at a fast rate, that are very bright, (or any star for that matter sufficiently far away from us) could it be that they are already black holes (the sufficiently large ones) and we are just seeing the light emitted during it's main phase? So, if so, is it safe to say that most of the stars are already dead that we see?

Edit: I appreciate all the answers. This has been a fascinating read. I also hate having to select a "the answer" when I gleaned something from all of them.

It depends what you mean by "see".  I assume that you mean with the naked eye.  Let's do some rough calculations to estimate the odds.

The farthest single star visible to the naked eye is Deneb, estimated distance around 1550 light years. Most stars visible to the naked eye are much closer.  Since even the sort of star that forms a black hole lives a few million years, we would expect perhaps as many as one sufficiently large star in a thousand to have formed a black hole during the time their light was on the way to us.

There are about 5000 stars visible to the naked eye under good conditions, but only a hundred or so massive enough to form black holes.  So on that basis, the odds are that there is at most one such star, and probably none.

To estimate this another way, consider that there is on average one supernova in a galaxy per century.  Comparing the distance to the farthest visible star with the diameter of the galaxy I estimate we can see at most 1/2500th of the Milky Way, so we should expect only one visible star to go supernova every 250,000 years.  Dividing that by the distance in light years to the farthest visible stars, we get only about one chance in a hundred that any of the visible stars have gone supernova during the time their light was on the way to us.

One caveat is that I've gotten these figures from disparate sources, based on Google searches.  However, it seems clear that the odds are not good.  Hopefully one of the experts can provide better data.


Center of the universe Big bang is not an explosion, but an expansion of space and time. Universe had almost infinite density... wait a moment. If it had ALMOST infinite density, it had a certain volume, and thus, space already existed.
Am I commiting a mistake?

I had this question after reading this post.

Krotanix : nobody really knows the answer to this. We have good evidence that the universe is expanding, and we extrapolate this back to the big bang. Then some people say the universe was once the size of a grapefruit. See for example this. Since WMAP evidence in 2013 suggested the universe is flat, some people have started saying the observable universe was once the size of a grapefruit. And that the universe was always infinite. But this is a non-sequitur, and a non-answer.

Yes,  it looks as if 13.8 billion years space had a much higher density and started expanding. And it may have had a certain volume, so space may have already existed. But nobody knows for sure.

Re your follow-on question, nobody has discovered hollowness or emptiness anywhere in the centre of the universe. The expansion is thought to be like that of a raisin cake rising in an oven. There's no big hole in the middle.


Does the event horizon of a black hole increase or decrease by adding mass? So a black hole is a something that has enormous gravity, therefore mass accelerates faster towards it. But if the black hole double  it's mass, will it's event horizon increase in length , or will it decrease?

The radius of the event horizon ($r_\mathrm{s}$) is directly proportional to the mass of the black hole (M). More exactly:

$$r_\mathrm{s} = \frac{2 G M}{c^2}$$

The black holes whose merger was detected by LIGO would each have been about 90 km in radius, and after merger, a little less than 180km.

Read about the Schwarzchild radius


So is there nothing like satellite anymore? I just read this article. I don't know how credible it is, since I couldn't find any link to the original paper. But it says that pluto will be considered a planet again, along with more than 100 other celestial objects including our moon. So, if the definition given here is applied, then would there be anything as dwarf planet or satellite? I think even comets and asteriouds would come under this defintion. I am talking about this:

  The paper, published in Lunar and Planetary Science, declares a planet as a round body that's never undergone fusion, and has less mass than a star. That's it. This means, Pluto would be planet again-- But it would also bring along Ceres, Eris, Makemake and Haumea... as well as 97 other objects.

This is really a question of Language rather than Astronomy. The meaning of words is defined by their use. The IAU has proposed one way of using the word "planet", this group of scientists have proposed another.

Anyone can propose a definition of any word. This group proposes that a "planet" is any astronomical body which 1) Does not have, and never has had sustained nuclear fusion in its core, and 2) Is large enough for gravity to pull it into an ellipsoidal shape.

The intention of this definition is to make a planet defined entirely by "what" a body is, not by "where" it is. Under this definition the classic 8 planets, Ceres, Pluto, Charon, the Moon, the larger moons of Jupiter, Saturn Uranus and Neptune, Eris, Sedna, and the larger Kuiper belt objects would all be "planets" - about 100 known in total. The exoplanets would also be "planets"

Asteroids (except Ceres), comets and other small solar system bodies are too small, and so would not be planets.

The advantage of this definition is that the usually where something is located is not part of the definition of what it is. However, it contradicts several hundred years of use by defining the larger moons as planets.

Unlike the 8 planet definition, this does not have the support of a large international body of astronomers (the IAU). If you wish to use this definition you are free to. I doubt that without the support of the IAU this definition is ever going to be widely used. Most people will either use the 8 planet definition or the 8+Pluto definition.


How many planets are there in this solar system? So, in school (that's a long time ago) they have been teaching us there are 9 planets in our solar system.

Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto

But every now and then I keep reading stories about another "dwarf planet" (Eris, discovered in 2005) that - depending on what source tells the story - is another planet according to the astronomical definition, while other sources say that it isn't a planet. Some even say Pluto isn't a planet anymore either.
The result: I'm confused due to the contradicting stories. Even Wikipedia isn't clear about Eris and only writes (emphasis mine):

NASA initially described it as the Solar System's tenth planet.

Initially? So, is it a 10th planet or not? Fact is, there is another "something" out there and it surely seems to look like a planet. Yet, some people keep stating there are 9 planets in our solar system, while others say there are more than 9 planets, and then again there are people stating that the latest definition of "planet" has kicked out Pluto too so there are actually fewer than 9 planets in our solar system.
Trying to get a definite, official, and astronomically correct answer I can actually rely on, I'm therefore asking: How many planets are there in this solar system?
EDIT
The "Definition of planet" at Wikipedia doesn't really help either, as it states:

Many astronomers, claiming that the definition of planet was of little scientific importance, preferred to recognize Pluto's historical identity as a planet by "grandfathering" it into the planet list.*
* Dr. Bonnie Buratti (2005), "Topic — First Mission to Pluto and the Kuiper Belt; "From Darkness to Light: The Exploration of the Planet Pluto"", Jet Propulsion Laboratory. Retrieved 2007-02-22.

So, if you link somewhere to provide proof, it would be great if you could point me to a more trusted source than Wikipedia. Ideally, an astronomical trusted source and/or paper.

In addition to Undo's fine answer, I would like to explain a bit about the motivation behind the definition.

When Eris was discovered, it turned out to be really, really similar to Pluto. This posed a bit of a quandary: should Eris be accepted as a new planet? Should it not? If not, then why keep Pluto? Most importantly, this pushed to the foreground the question

  what, exactly, is a planet, anyway?

This had been ignored until then because everyone "knew" which bodies were planets and which ones were not. However, with the discovery of Eris, and the newly-realized potential of more such bodies turning up, this was no longer really an option, and some sort of hard definition had to be agreed upon.

The problem with coming up with a hard definition that decides what does make it to planethood and what doesn't is that nature very rarely presents us with clear, definite lines. Size, for example, is not a good discriminant, because solar system bodies come in a continuum of sizes from Jupiter down to meter-long asteroids. Where does one draw the line there? Any such size would be completely arbitrary.

There is, however, one characteristic that has a sharp distinction between some "planets" and some "non-planets", and it is the amount of other stuff in roughly the same orbit. This is still slightly arbitrary, because it's hard to put in numbers exactly what "roughly" means in this context, but it's more or less unambiguous.

Consider, then a quantity called the "planetary discriminant" µ, equal to the ratio of the planet's mass to the total mass of other bodies that cross its orbital radius and have non-resonant periods (so e.g. Neptune doesn't count as sharing Pluto's orbit) up to a factor of 10 longer or shorter (to rule out comets, which has little effect in practice). This is still a bit arbitrary (why 10?) but it's otherwise quite an objective quantity.

Now take this quantity and calculate it for the different bodies you might call planets, comparing it to both the objects' mass,

and their diameter,

or with an arbitrary horizontal axis, in order of decreasing discriminant,

Suddenly, a natural hard line emerges. If you look only at the mass and the diameter of the objects (shown in the insets above the plots), then there is a pretty continuous spread of values, with bigger gaps between the gas giants and the terrestrial planets than between Mercury and Eris/Pluto. However, if you look at the planetary discriminant, on the vertical axis, you get a very clear grouping into two distinct populations, separated by over four orders of magnitude. There's a finite set of bodies that have "cleared their orbits", and some other bodies which are well, well behind in that respect.

This is the main reason that "clearing its orbital zone" was chosen as a criterion for planethood. It relies on a distinction that is actually there in the solar system, and very little on arbitrary human decisions. It's important to note that this criterion need not have worked: this parameter might also have come out as a continuum, with some bodies having emptier orbits and some others having slightly fuller ones, and no natural place to draw the line, in which case the definition would have been different. As it happens, this is indeed a good discriminant.

For further reading, I recommend the Wikipedia article on 'Clearing the neighbourhood', as well as the original paper where this criterion was proposed,

  What is a planet? S Soter,  The Astronomical Journal 132 no.6 (2006), p. 2513. arXiv:astro-ph/0608359.

which is in general very readable (though there are some technical bits in the middle which are easy to spot and harmless to skip), and from which I took the discriminant data for the plots above.

Edit: I must apologize for having included, in previous versions of this post, an incorrect plot, caused by taking data from Wikipedia without verifying it. In particular, the planetary discriminant for Mars was wrong (1.8×105 instead of 5.1×103), which now puts it below Neptune's instead of just below Saturn's, but the overall conclusions are not affected. The Mathematica code for the graphics is available at Import["http://goo.gl/NaH6rM"]["http://i.stack.imgur.com/CQA4T.png"].

... and, as a final aside: Pluto is awesome. It was visited in July 2015 by the New Horizons probe, which found a world that was much more rich, dynamic, and active than anyone expected, including what appear to be churning lakes of solid nitrogen ringed by mountains of water ice, among other marvels.

(Note the image has been colour-enhanced to bring out the variety of surface materials; the true-colour version of this image is here.) I, personally, don't feel it's at all necessary to 'grandfather' Pluto into the list of planets to really feel the awe at the amazing place it is - it's perfectly OK for it to be a cool place with cool science, that is also not a planet.


Are there more stars than all the words ever spoken by humans? A while ago I saw Neil deGrasse Tyson comparing the number of stars in the universe with the number of words spoken by all of humankind, ever since.

I realize both of these numbers are not strictly defined, but still, we can use our best observations together with our best guesses to find out which number is larger, and by how many magnitudes. It's a good example of making you realize the size of astronomical numbers in the true sense of the word.

What is your answer or guesstimate?

Number of stars in the observable universe
There are about 100 to 200 billion galaxies in the observable universe. Galaxies range in size from a few billion to hundreds of trillions stars. Using 100 billion galaxies and 1 trillion stars in a galaxy yields 1023 stars in the observable universe as a rough order of magnitude estimate. (After getting this result, I found multiple sources that give answers ranging from 1021 to 1024 stars in the universe.)
Number of words ever spoken
We're talkative, but we also sleep and eat and listen. Assuming we talk for the equivalent of 3 hours per day and we speak at about 150 words per minute, or about 10 million words per year. I recall 100 billion as being a rough estimate of the number of modern humans who have ever lived. Many of those people died during or shortly after  childbirth. Assuming an average life expectancy at birth of 25 years (generous), that means humans have spoken 2.5×1019 words since we first gained the gift of gab.
That might be off by a factor of ten, but it's not off by a factor of ten thousand. There are a lot more stars in the observable universe than the number of words ever spoken by humans.


Could the expansion of universe be a side effect of gravity? Could the expansion of universe be a side effect of gravity? I mean maybe gravity "attracts things" at a "small" distances and repells them at "larger" distances?

Do we have any theory/hypothesis/paper on this topic? Is it possible to prove or disprove?

UPD.

There is another, more clear way to ask the same question:

  Could gravity have a repulsive term that dominates at cosmological
  distances and could it be such a term that causes (accelerated)
  expansion?

Thanks to @uhoh and @Richard, for helping to clarify question a bit.

Could the expansion of universe be a side effect of gravity?

Well, everything is possible I suppose. And we do see plenty of material that talks about the expansion of the universe as a kind of repulsive gravity. But I would say no, the expansion isn't due to gravity, and it isn't some side effect of gravity. It's something different.

  I mean maybe gravity "attracts things" at a "small" distances and repels them at "larger" distances?

It doesn't. Gravity attracts things at all distances. It follows the inverse square rule. Some people like Mordehai Milgrom say it doesn't quite follow the inverse square law, see MOND. But he isn't saying it repels at large distance.

  Do we have any theory/hypothesis/paper on this topic? Is it possible to prove or disprove?

We have general relativity. In general relativity gravity sucks. It doesn't blow.

  Could gravity have a repulsive term that dominates at cosmological distances and could it be such a term that causes (accelerated) expansion?

Like I said, everything is possible. But I will say no, the universe is expanding because of dark energy, not because of gravity. I rather like Erwin Schrödinger’s cosmic pressure myself. See the 2014 Cambridge companion to Einstein by Michel Janssen and Christoph Lehner: “Schrödinger [1918] had pointed out another way of treating the cosmological constant: moving it from the left-hand side of Equation [7], where it represents a contribution to space-time curvature, to the right-hand side, where it represents a contribution to the energy-matter distribution. Then it would correspond physically to a kind of cosmic pressure”. Unfortunately Einstein didn’t like it. You can read more in Alex Harvey’s 2012 paper How Einstein Discovered Dark Energy. He gives a translation of Schrödinger’s paper and refers to Einstein’s response. If you were to ask a modern cosmologist, I think the answer would be that Schrödinger was pretty close to the mark. See page 252 of Relativity, Gravitation and Cosmology by Robert J Lambourne:


Binary stars of different ages? In an answer on a different SE someone raised the point that “common” explainations published never discuss stars being captured.  Presumably binaries are formed as pairs, or team up while still in the birth cluster.

It seems quite plausible that an aged star (or stellar reminant) can be paired with a main sequence star in its prime, having paired up well after the old supernova was completed.

Is this mechanism of multi-body reassortment known to occur, presumed, or thought to not occur?

Another mechanism implied but not detailed in popular works is the possible situation with Proxima Centauri: a star going with the flow in the galaxy may find itself loosly attached to another star (or system), and this bond is so tenuous that it can easily be broken by another passing star, so the distant star do-si-dos to different partners over the course of billions of years.  Is this an accurate depiction of the real situation?  This loose attachment out of the general flow can occur with stars of any mass, right?

In any case, a star can be captured with planets, right?  Naturally a close-enough encounter between stars (and reminants) could seriously disrupt a planetary system, but I want to check on the possibility that capture with planets is also a possibility.  I think that’s not a problem for the “loose attachment” case, and Proxima Cen may indeed have a planet.  How about the necessary mechanics of binary reassortment?  Is that necessarily so close and tight thatbplanets would be seriously disrupted, or is it plausible that planets would simply go along for the ride?

Update: PSR B1620-26.  A neutron star captures a star with planet, trading off its original companion.

Stellar encounters are very rare outside dense stellar environments. Such dense stellar environments are only found in a star's birth cluster, where all the stars are coeval to a close approximation.

Thus the switching and capture you refer to is probably common in the first few million years of a star's life, but would occur with stars of a similar age. Thereafter, once a stellar system is "in the field", encounters with other stars hardly occur at all, but are not impossible.

I am not aware of any binary where the components are thought to have a very different age.


How big would a disc have to be to blot out the sun covering 5% of the land mass of earth? Like this, but floating in space.

I imagine that this would also be influenced by the distance of the object from the sun, and that there is some ideal distance for this object to be? (and obviously the distance of the Earth from the Sun as well)

The angular diameter of the sun is approximately 30 arcminutes (roughly .0087 radians), or half of a degree.

The formula for angular diameter of a round object in radians is:
$$
\delta = 2arctang\frac{diameter}{(2)distance}
$$

Given this, we should also think about position. Assuming we want to continually block the same spot on Earth we need to the orbital period to one year. (I'm not sure if there is a technical difference between orbiting the Earth once per year such that you're always between the Sun and Earth, and just plain orbiting the Sun)

According to this calculator, our sun blocker would need at a height of 2,152,050km to orbit Earth once per year. So, given that we can set up our formula with...

$$
.0087 = 2arctang\frac{diameter}{(2)2152050}
$$

...and the needed diameter of an object should come out to be about 18,722km in diameter. Given that, Mr. Burns's terrestrial solution is far more practical, though certainly a nice orbital one is far more devious. Being evil isn't cheap.

Edit:

This answer is a bit rough as it doesn't calculate for the 5% of the Earth's land mass stipulation. The answer which would meet this would depend on whether only an umbral shadow qualifies, or if a penumbral shadow would also suffice. I suspect probably the prior. The shadow would certainly reach the Earth, but probably not cover 5% of it, which is a shame considering its diameter is actually larger than Earth's. Regardless, it's not a very elegant solution.


Influences from outside the observable universe explaining dark energy and expansion? Could some influence from outside the observable universe be causing the expansion?

EDIT - The original question was edited to enable it to be reopened, but my answer below responded to the way the question was initially framed. I've left my answer intact as it may be useful in addressing confusion about the difference between "the universe" and "the observable universe".

  Could some pressure from outside of our universe

According to Wikipedia, the Universe is "all of space and time and their contents". So it makes no sense to talk of something "outside" all of space and time.

You might, of course, be referring just to the observable universe, "a spherical region of the Universe comprising all matter that can be observed from Earth at the present time."

However, if the conditions beyond the observable universe are what is causing expansion, then the Universe is neither homogenous nor isotropic. While we have no way of disproving this idea, all the evidence points to a homogenous and isotropic Universe and the vast majority of physicists subscribe to this model.

  causing the expansion

The metric expansion of the Universe is a generic property of the Universe under the FLRW metric, an exact solution of Einstein's field equations of general relativity. There is no need to propose an external cause for the expansion.


Red Moon a Characteristic of all Total Lunar Eclipses? I understand that the redness of the moon during the total lunar eclipse last night/this morning (April 14-15 2014) is a reflection of the red light caused in earth's atmosphere due to Rayleigh scattering (basically, a reflection of all the sunsets and sunrises happening around the earth).  Because of this, it seems to me that the moon will appear red during every total lunar eclipse that happens.  Is this the case, or are there some lunar eclipses where the moon does not turn red?  If it is the case that all total lunar eclipses produce a red moon, why was the media so hyped up about last night's eclipse producing a red moon?  Was it especially red?

No, not all total lunar eclipses will turn the Moon deep red. Most of them do, but not all.

If you were standing on the Moon during the eclipse, you'd see the Earth passing in front of, and obscuring, the Sun. But the Earth will never become fully dark, even when the Sun is fully covered. A bright ring will always surround the Earth. Why?

That ring is sunlight refracted by the atmosphere. It's there because the Earth has an atmosphere. You could say it's all the sunrises and sunsets of the Earth, all seen at once. It's this light that continues to illumine the Moon during the eclipse.

But why is the Moon red, instead of some other color? This is because the blue end of the spectrum is scattered more easily in all directions (same mechanism that explains why the sky is blue on Earth), whereas the red part of the spectrum is scattered less easily and moves on a straighter path along the refraction lines. The bright ring around the Earth, as seen from the Moon, is probably red, because most of the blue in it has been scattered away.

Now, if the Earth's atmosphere is full of dust particles from huge volcanic eruptions, the bright ring is a lot weaker. That makes the Moon during the eclipse a much darker shade of red. Sometimes the Moon is a very dark, dull grey during the eclipse, no red hue at all - so dark in fact that it's hard to see in the sky while the eclipse is full. This has happened some decades ago after the Pinatubo eruption.

http://en.wikipedia.org/wiki/Lunar_eclipse#Appearance

http://eclipse.gsfc.nasa.gov/LEcat5/appearance.html

EDIT:

A measure of the brightness and color of a lunar eclipse is the Danjon scale. Eclipses are rated between 0 (almost invisible, black or very dark grey) and 4 (bright orange with bluish rim).

http://en.wikipedia.org/wiki/Danjon_scale

http://eclipse.gsfc.nasa.gov/OH/Danjon.html

My estimate is that the last eclipse was a 3.

I can't find a list of recent eclipses rated on a Danjon scale, but here's a list of 20th century eclipses, with a measure of the magnitude of the umbra.

http://eclipse.gsfc.nasa.gov/LEcat5/LE-1999--1900.html

As you can see, the magnitude varies quite a bit.

Bottom line: each eclipse is a bit different. A majority would have some kind of orange, copper or red tint. A minority are too dark to see any color. Unusual colors (outside of the red-yellow interval) are very rarely possible. Brightness and hue varies from one instance to another, since it depends on Earth's atmosphere, which is a system that changes greatly over time.


What does the surface of Mercury look like? What does the surface of Mercury look like?  What color is it (I have seen some images portraying it grey and some a light brownish color), and would the surface be dusty like the Moon, smooth, or even cracked (e.g. see image below) due to thermal expansion and contraction?

The MESSENGER probe was able to take many true-color pictures of Mercury. A full list can be found on JPL's Photojournal. It is clear that Mercury is light grey in color.

(source: nasa.gov)

(source: nasa.gov)

(source: nasa.gov)
In terms of the actual surface, Mercury is very similar to the Moon. It's surface is speckled with craters, with some smaller craters inside them, as can be seen in some of the images above. The smoothness varies - note the inside of the larger crater in the first picture. It's quite smooth, save the smaller crater inside it.
See also this pdf.


Is there a physical limit to how far we can go? Is there a physical limit to how far we can go?  I am thinking there could be based on the following:

1: There are parts of the universe expanding faster than the speed of light that we will never be able to get to (without faster than light travel)

2: There are a finite number of galaxies between here and the distance where 1 takes place.

3: If we travel even at the speed of light, it seems we would at some point pass that finite number of galaxies, and wouled not be able to reach the next one!

Does this mean there is a limit to how far we can go, and furthermore, we will experience the “big rip”?

Your 3 points are spot on.   There is a finite number of galaxies we could theoretically reach for the reasons you say.  The further away the distant galaxy the greater the expansion of space between us and that galaxy and beyond a certain distance, galaxies can't be reached, even by the speed of light.   We can see galaxies that we couldn't possibly travel to.

  Does this mean there is a limit to how far we can go, and furthermore,
  we will experience the “big rip”?

No.  It only means that some galaxies that we can see, we could never travel to.   There's no limit to how FAR we can go but there's still a finite number of galaxies that we could reach with close to the speed of light travel.

This article, using the current size estimate for the observable universe of 46 billion light years in radius, says that 14.5 billion light years distance is the limit that we could theoretically reach, about 3% of the observable universe or about 3 billion galaxies.

As for the big rip.   Nobody knows if that's an accurate prediction.  It's a possible outcome, but we don't know enough about dark energy to say if the big rip will happen or not.   Nobody knows.

And it's a pretty psalm, but I don't see the prediction of dark energy in it.   Only that it says the Universe will age, but life is eternal - which is a nice thought.


What is the gravitational force felt on Earth from the other planets in our solar system? How much gravitational force is felt on earth from the other planets in the solar system? The sun exerts the strongest g-force, holding us in it's orbit, followed by the moon which affects the tides on earth, but how much force do we feel from Jupiter, Saturn, Venus, etc?

Because of the inverse square law for Newtonian gravity we have the acceleration due the gravity $g_b$ at the surface of the Earth due to a body of mass $m_b$ at a distance $d_b \gg r_e$ (where $r_e\approx 6371 \mbox{km}$ denotes the radius of the Earth, note all distances will need be in $\mbox{km}$ in what follows) is:
$$
g_b=g\times \frac{m_b}{m_e}\times \left(\frac{r_e}{d_b}\right)^2
$$
where $g$ is the usual accelleration due to gravity (from the Earth at the Earth's surface $\approx 10 \mbox{m/s}^2$, and $m_e\approx 6.0 \times 10^{24} \mbox{kg}$. We get the maximum acceleration due to a body when that body is at its closest to the Earth, which is what we do from now on (except for the Sun and Moon where the mean distance is used).

Now for the Moon $r_b\approx 0.384 \times 10^6 \mbox{km}$, and $m_b\approx 7.3 \times 10^{22} \mbox{kg}$, so the accelleration at the Earth's surface due to the Moon $g_b\approx 3.3 \times 10^{-5} \mbox{m/s}^2$

Then putting this relation and Solar-System data into a spread sheet we get:


plotting stars in cartessian coordinates using the stars ra and dec produces the wrong location of the stars I am currently running into some problems with plotting some stars locations in a Cartesian coordinate system.
The stars aren't in the right order and I'm not sure where I am going wrong.

I first use the equation (where S is a vector)

S = [cos(ra)*cos(dec), sin(ra)*cos(dec), sin(dec)]

to obtain a vector S of the star.
I now want to obtain the x and y positions of the stars In terms of a 2d coordinate system so I use

c * sx = S * px / S* pz
c * sy = S * py / S* pz

where C is the scale ratio of pixels to tangent of the angle of the camera and P is the vector center of the camera.(Im using this because I'm trying to find the distance between each pair of stars when a photo of the stars is taken by a camera)

px = unit vector X
py = unit vector Y
pz = unit vector Z

and I solve for sx and sy. When I plot the stars location with sx and sy however I do not get the right locations of the stars. Any guidance?

A photograph of stars is essentially a
gnomonic projection
of part of the
celestial sphere.
If $\vec P$ is computed for the photograph center (RA, Dec) in the same way as $\vec S$,
and the north celestial pole is
$\hat{\mathrm k} = (0, 0, 1)^{\mathrm T}$,
then the photograph has basis vectors perpendicular to $\vec P$ and each other,
$$\hat{\mathrm u} = \frac{\vec P \times \hat{\mathrm k}}{\| \vec P \times \hat{\mathrm k} \|},
\hat{\mathrm v} = \frac{\hat{\mathrm u} \times \vec P}{\| \hat{\mathrm u} \times \vec P \|}$$
and you can project $\vec S$ onto the photograph as
$$\left( \frac{\vec S \cdot \hat{\mathrm u}}{\vec S \cdot \vec P},
\frac{\vec S \cdot \hat{\mathrm v}}{\vec S \cdot \vec P} \right)$$
scaling as needed.


Tycho Brahe Danish Astronomer Religious? Does anyone know if Tycho Brahe was religious?

Like nearly everybody at the time, he "believed in God" and was a member of the Danish Lutheran church.  He from time to time used arguments based on bible verses to back up his solar system model (in which the sun orbits the Earth, and the planets orbit the Sun).  According to Tycho, the idea of a rotating and revolving Earth would be "in violation not only of all physical truth but also of the authority of Holy Scripture, which ought to be paramount."

However he was not notably religious. He was suspected of heresy by some in the Lutheran church. He was not personally on good terms with the local bishops in Denmark. His interest in medicine and astrology were not sanctioned by the church and while he was a follower of Philip Melanchthon, he was not viciously sectarian, at a time when many others were.

He believed in God, but was not especially religious.


Is it possible that some of the confirmed exoplanets are in fact primordial black holes? Recently astronomers discovered a black hole lying just 1000 light-years from Earth, in a triple star system (HR 6819) that can be seen with the naked eye. This discovery has increased the possibility that there are many more black holes hiding in nearby star systems.

However, we have not detected any primordial black hole with only planetary mass yet. What if some of the discovered exoplanets are actually the hypothetical primordial black holes?

A exoplanet detected through the transit method are very unlikely to be black holes due to its extremely small size not possible to produce detectable dimming. But how about the exoplanets detected through radial-velocity method? A primordial black hole with 5 Jupiter mass would have the same effect on the motion of the host star as a exoplanet with 5 Jupiter mass.

The first you need to determine if you're looking for a zebra or a unicorn.  That is, if there's a herd of horses before you, you expect to see all horses.  Maybe there's a wayward zebra in there.  Unlikely but possible, but you're not going to find a unicorn because, as far as we know, unicorns don't exist.

We know how planets form and we expect to find mostly planets where planets should be, so if primordial black holes do exist, finding one orbiting a star in a near orbit wouldn't be impossible, but it would be a zebra in a herd of horses.

That said, primordial black holes, at least those with planet-mass, are probably unicorns. People have looked for them without success and some estimates have put a size limit at below the mass of a planet.    Does that prove they don't exist?   Well, no, but they probably don't exist, not at close to planet mass anyway.  They've gotten some attention because a planet-mass black hole is a cool idea, but cool idea or not, they're probably not real.  Quantum black holes may form by additional dimensions and gravity getting stronger at very short distances, but CERN hasn't found any evidence of that, so it remains a neat mathematical explanation without a speck of evidence.

We can only detect exo-planets reasonably close to their star, either by transit or wobble.   A captured primordial black hole would probably have a more distant orbit - like planet 9 is thought to have.   A close orbit that could be detected and pass as a planet would be unusual.   If it formed within the proto-solar-system, it would likely clump matter around it, becoming part of a large planet or the central star, so it would need to be captured later, after the system cleared out and that's harder to do.  Gravitational captures that close to a star are rare.

A primordial black hole, with a planet's mass would be tiny, so, as you noted, detection by the transit method would be unlikely.   An Earth-mass black hole would be about the size of a golf-ball.   A Jupiter-mass black hole would be about 10 feet across.   Even when you factor in that the observed light-halo is about 2.6 times the size of the event horizon and beyond that, the majority of the lensing is just another 5-10 times the size of that, you're still looking at a very small object with just a feet to maybe a few hundred feet of transit.  That's probably much too small to create the kind of shading needed to recognize a planet.  You'd need stellar mass to begin to detect a transit and that would be detectable in other ways.

A theoretical planet mass black hole could create a wobble and could be detected by the wobble method, if it was close enough to the star that a few wobbles could be detected, timed and the planetary mass object confirmed, but for reasons above, we don't expect that kind of black hole to exist and if they did, one getting captured that close to a star would be an unexpected.  The odds are approaching draw a straight flush odds.  Not impossible, but very unlikely, and coming telescopes should provide better insight on this.  Maybe some surprises await us when the next round of telescopes start getting images, but I would guess that planet mass black holes won't be one of them.


Trouble understanding speed-dispersion in (elliptical) galaxies I'm learning about LOSVDs (Line Of Sight Velocity Distributions) and I'm having a bit of trouble understanding the used terms.

As I understand, the LOSVD of a given (elliptical) galaxy is the density distribution of the LOS-velocities. The full LOSVD is difficult to find and it's easier to find 2 parameters of the distribution: $\bar v_{_{LOS}}$ and $\sigma_{_{LOS}}$ by fitting a (Gaussian) model to the spectrum of the galaxy.

I have a limited understanding of statistics, so I'm having trouble intuitively understanding what these 2 parameters mean later on.

I think that $\bar v_{_{LOS}}$ is simply the average value of the LOS-velocity for the whole galaxy while $\sigma_{_{LOS}}$ is the equivalent of a standard deviation.

Now later on in my coursebook, there's an explanation of how to get a LOSVDs for every point (/pixel) in the (projection onto the celestial sphere of the) galaxy by using 3D spectrography.
From this we can get a 3D dynamic model from our 2D kinematic model. In this newly found 3D distribution there's also 3 Sigmas, one for every dimension.

But here comes the part I don't understand:
The book is looking at the movement of stars in a spiral galaxy, the Milky way in particular.

We're trying to find a correlation between the age of MS-stars and their dispersion and so there's a dataset of a few stars in the neighbourhood of the sun with their dispersion in every dimension.

What is the meaning of dispersion in this context? How can a single object have a dispersion if it's a parameter of a density distribution?

The total light of a galaxy is the sum of perhaps billions of stars, each with their own line of sight velocity. You can characterise this distribution with a mean and a standard deviation (dispersion), and this will be reflected in the absorption line profiles of that galaxy.

Equally you might choose to measure this distribution as a function of position in a galaxy, if you are able to spatially resolve different regions. For instance one could put a spectrograph slit across a galaxy and get the velocity dispersion as a function of position along the slit.

When you are talking about nearby stars, you can measure the 3D velocities individually, providing you can measure the radial velocity, proper motion and distance of each star. You can then find the mean and standard deviation for this group of measurements in each velocity coordinate.


a random distribution of RA&Dec How to make random positions in Equatorial coordinate system?

If I divide Dec between -90 and 90 evenly, the space distribution is not random.

Well, your problem is that you have a sphere. To compensate for the polar declination skew, you just calculate $$\sin^{-1}(\mathtt{rand})$$
Where $\mathtt{rand}$ is a number in an evenly divided -1 to 1 range. Alternatively, you can use another trigonometric function based on what you have available, but you get the idea.

RA can obviously be divided evenly.


Scattered Intensity of Light vs Angles of Incidence and Emission So I just derived an expression for the scattered intensity of light from an atmosphere with ideal isotopic scattering: $I/F=\frac{cos(i)}{4(cos(e)+cos(i))}$, where $I$ is intensity, $F$ is flux, $i$ is the angle off incidence, and $e$ is the angle of emission ($i,\ e=0$ are normal to atmosphere).

When I plot the scattered intensity as a function of $i$ with $e$ constant, it decreases while the angle increases. Why is this? My theory is that at a large incidence angle, the light encounters a larger surface area, so reflected light will have a higher variation of emission angle, meaning that scattered light at a given emission angle will be lower. Does this make sense? Or is there another reason for this?

Next, I plotted scattered intensity as a function of $e$ with $i$ constant. This time, the intensity increases with increases emission angle. I don't have a theory as to why this is the case, nor an intuition to back it up. Why would this be the case?

It is easiest to understand if you fix the incident angle and explain why the emergent intensity is largest at highly oblique angles.  Since the light comes from the outside, it only penetrates so far, and this in turn causes the atmosphere to act like a source of scattered light.  But the source of scattered light is brightest near the top of the atmosphere, since that's where more of the external light penetrates.  Whenever the sources are brighter near the top, it produces what is called "limb brightening," where if you look from highly oblique angles, you mostly probe those higher, brighter regions.  Looking down the normal is where you see the deepest into the atmosphere, where the external light does not penetrate as well.

You can also think about what the individual photons are doing, and ask what is their distribution over emergent angle.  If cos(i)=0, all the photons scatter right at the surface, so it is tantamount to introducing an isotropic radiation field right at the surface.  The photons that go outward will of course have an isotropic distribution, and an isotropic incident radiation field must scatter isotropically (that is a consequence of the principle of reciprocity).  So the emergent distribution is isotropic, but intensity is also per solid angle, so accounts for the foreshortening, and that's where the 1/cos(e) in the intensity comes from.  If cos(i)=1, on the other hand, the incident photons tend to penetrate more, and must diffuse their way out, which gives less of an advantage to low cos(e) after the foreshortening is included.

As for fixing the angle at which you are looking and altering i, here your result says that the intensity always peaks as cos(i) rises.  Your expression claims that is true at every e, so to me this suggests a normalization error.  You want to keep the incident F fixed, but that requires you must get the same outgoing F if you integrate over all e.  Your result says the I is higher at all e if cos(i) is higher, but that contradicts the idea that you are keeping the incident F the same.  Maybe your result is actually comparing the incident and emergent intensities, not the emergent intensity to incident flux.  Then at higher cos(i), for the same incident I, the incident F is falling, explaining your rise in I/F.


How long is a "lunar month" in Jupiter? For Earth, the lunar month is well known. But Earth has only one moon.

But on Jupiter, how long does it takes for the same moon configuration to appear in the "sky" of the planet?

For the sake of sanity, you can consider only the four Galileian Mooons.

The three inner Galilean moons are in orbital resonances. For each orbit of Ganymede, Europa makes two orbits and Io makes four orbits.  So after 1 orbit of Ganymede, the two inner moons are in the same configuration. That is 7.154 (Earth) days.

Callisto is not in an orbital resonance, It won't be in the same position, but its orbit (of 16.689 days) is close to a ratio of 7:3 to Ganymede. So after 7 orbits of Ganymede (50.08 days) Callisto will have made just over 3 orbits (50.07 days)

If you want all known moons to be in a similar configuration you will have to wait a while, probably longer than the life of the sun (there are a lot of moons)


Does a star fuse helium to beryllium on the main sequence? When a star has finished fusing all its hydrogen into helium, it will then start fusing helium into beryllium and so on and so forth up until iron.

When the star is fusing to beryllium, will the star still be in the main sequence phase and will it at that point start to grow into the red giant phase, or is there no given rule for when it will start growing?

Does a star fuse helium to beryllium on the main sequence?

Stars don't fuse helium to beryllium except as a very, very short intermediate step toward carbon. Helium-helium fusion to form beryllium is endothermic: It consumes energy. To make matters worse, the beryllium-8 that results has an extremely short half-life, less than $10^{-16}$ seconds. Helium would be the end of fusion in stars (and there would be no us) if not for a fluke: The beryllium-8 formed by helium-helium fusion has almost exactly the same energy as does an excited state of carbon-12.

This greatly increases the probability of a third helium-4 nucleus combining with a short-lived beryllium-8 nucleus to form carbon-12. This is stable. The next stage after hydrogen burning is thus triple helium burning (the triple alpha process), essentially bypassing beryllium except as an intermediary.

  When the star is fusing to beryllium, will the star still be in the main sequence phase and will it at that point start to grow into the red giant phase, or is there no given rule for when it will start growing?

A star leaves the main sequence well before it starts fusing helium. It leaves the main sequence when the star can no longer sustain hydrogen fusion in the core. This happens when the core becomes void of hydrogen. At this point, the helium left behind by hydrogen fusion is essentially ash. Hydrogen fusion proceeds on the edge of the core (shell burning), but the hydrogen-depleted core at this point is far too cold to fuse helium to carbon (not beryllium). So it collapses, and gradually becomes hotter.

The star starts fusing helium to carbon (and also oxygen) if the post main sequence star's mass is large enough. At this point, the red giant collapses and behaves almost like a main sequence star with a second life. That second life doesn't last very long, however.


Can impact craters on the moon act like giant radio telescopes? Could large craters on the moon be used as reflective lenses for radio signals?

Acting like a large radio telescope reflecting radio waves to a satellite positioned over the crater.

Interesting idea. I think the answer is both yes and no -- yes with a manufactured dish but no in the crater's raw state.

The Arecibo telescope sits in a natural crater, but adds a dish which has a couple of important things required by a radio dish:

a radio-reflective surface
a specific curvature, classically parabolic, but also shaped
low surface roughness typically in the order of mm to µm for radio frequencies we're interested in. See http://en.wikipedia.org/wiki/Ruze%27s_Equation
a receiver close to the reflective surface (focal length), a satellite would probably be beyond the focal point
probably some some other things, but that's probably enough.

Edit: Added #4


How did they make a video of the center of the galaxy, and what is it exactly that's flashing there? The ESA video ESOcast 173: First Successful Test of Einstein’s General Relativity Near Supermassive Black Hole includes a clip of images of stars at the center of our galaxy orbiting around SgrA*, a presumed supermassive black hole. This isn't visible light because it's obscured by dust, so it may be radio or long wave infrared, but I don't know.

In the middle, I can see something flashing at whatever wavelength this image has been produced from.

Question:

How are these images obtained, and
what process is it that is believed to be causing that flashing?

GIF made from video at around 02:50:

Six annotated frames from GIF highlighting the flashing that I'm seeing.

Question: How are these images obtained?

Later in the video the narrator says they took the images using ESO's VLT.

  03:40 [Narrator] 14. Making these measurements pushed the power of ESO’s Very Large Telescope to the limits.

(Source: ESO transscript)

Over the whole observation period multiple telescopes and imaging instruments were used. Early observations were accomplished using the NTT. Since around the year 2002 the VLT observed Sagittarius A* with the NACO and GRAVITY instruments too.

This graph puts the rotation period of Sagittarius A* in relation to the time and the observing instruments:

(Source)

Question: What process is it that is believed to be causing that flashing?

ESO provides older footage over a minutes-timescale showing a flare of Sagittarius A* in May 2003: Flashes of light from disappearing matter

  ESO Press Video eso0330 shows the detection of a powerful flare from the centre of the Milky Way galaxy. These and other adaptive optics (AO) images (with resolution 0.040 arcsec in the near-infrared H-band at wavelength 1.65 µm) of the central region of the Milky Way were obtained with the NACO imager on the 8.2-m VLT YEPUN telescope at the ESO Paranal Observatory on May 9, 2003. [...] The position of the 15-year orbiting star S2 (cf. ESO Press Release eso0226) is marked by a cross and the astrometric location of the black hole is indicated by a circle.

The cause of the flickering is probably the same for the video sequence you showed.

A October 2018 ESO publication states:

  ESO’s GRAVITY instrument on the Very Large Telescope (VLT) Interferometer has been used by scientists from a consortium of European institutions, including ESO [1], to observe flares of infrared radiation coming from the accretion disc around Sagittarius A*, [...]. The observed flares provide long-awaited confirmation that the object in the centre of our galaxy is, as has long been assumed, a supermassive black hole. The flares originate from material orbiting very close to the black hole’s event horizon — making these the most detailed observations yet of material orbiting this close to a black hole.

(Source)

ESO also has another video showing the therory with more detail: skip to about 1:00.

Flares associated with Sgr A* are also described in this answer.

Artist's illustration of heated gas orbiting the black hole:

(Screengrab from 1:25 of that video)

See also

Phys.org (2019): Black hole at the center of our galaxy appears to be getting hungrier
Do et al. 2019 Unprecedented Near-infrared Brightness and Variability of Sgr A*
Chen et al. 2019 Consistency of the Infrared Variability of SGR A* over 22 yr

Figure 1 from Do et al. 2019

  Figure 1. Top row: a series of K' images taken on 2019 May 13 centered on Sgr A* showing the large variations in brightness throughout the night. The first image from the left is the brightest measurement ever made of Sgr A* in the near-infrared. Also labeled are nearby stars S0-2 (K' = 14 mag) and S0-17 (K' = 16 mag) for comparison. Bottom panel: K' (black) and H-band light curves of Sgr A* from 2019 May 13. On this night, we alternated between H and K' observations. The H-band magnitudes are offset using H − K' = 2.45 mag. There appear to be no significant color changes during the large change in brightness. Red circles show the location of the four images in the panels above.


How would the sky look if Earth orbited a red giant at a safe distance? Let's say that instead of the sun, we have a red giant, but are orbiting it at a safe distance, within the goldilocks zone. Would the sky actually look more red? Or would it be closer to white/transparent due to a shortage of blue light for Rayleigh scattering?

Rayleigh scattering happens at all wavelengths, but the scattering cross section goes as $\lambda^{-4}$.

On Earth, the atmospheric optical depth to Rayleigh scattering is very small at red wavelengths, so hardly any red light is scattered, even at sunset when the Sun is viewed through a thick atmospheric layer. On the contrary, there is sufficient optical depth to scatter some blue light, even if it arrives from the Sun at zenith. Some numbers are that the optical depth at zenith, from sea level is about 0.36 at 400 mm (blue) and ten times smaller at 700 nm (Bucholtz 1995).

However, the spectrum of light that is being scattered is very different in the case of a red giant. The solar spectrum peaks at about 500 nm and is about a factor of two less intense at both 400 nm and 700 nm. A red giant has a spectrum that peaks at around 900 nm (in the infrared), and the flux is about 100 times lower at 400 nm and two times lower at 700 nm (which is why they are called red giants).

If Rayleigh scattering was all that was going on, and the total flux incident at the top of the atmosphere was the same, then the scattered spectrum from the red giant illumination would be quite different. The overall amount of scattered red light would be about the same as in the solar case, but the amount of scattered blue light would be reduced by about a factor of 50. The net effect would be that the sky was much darker, and rather than being dominated by blue light, would actually have a redder spectrum (what colour this would be perceived as, I'm not sure).

But Rayleigh scattering isn't the only thing going on. The optical depth to scattering can be dominated by particulates in the atmosphere at wavelengths above 600 mm. This scattering is much less wavelength dependent, depends on the size distribution of the particles and is much stronger for small scattering angles. I think that this would enhance the relative redness of the scattered light a bit more, but given that the incoming flux at 700 nm is similar to that of the Sun, it wouldn't increase the sky brightness.

In summary, I think the sky would be much darker (factor of 50) and would have a much redder spectrum.


Recommendation for introductory cosmology text I am looking for recommendations for an introductory text (or texts) on cosmology on the advanced undergrad or beginning grad level. I am coming from primarily a physics undergrad background (doing some undergrad research on galaxy Lyman-alpha emission and attending some of my institution's astrophysics journal club meetings) and will beginning a graduate astrophysics program in the fall. I am looking especially for texts that also provide a good introduction into GR since I have never had a chance to learn GR formally.  I have had a lot of experience with Lyman-alpha radiative transfer and some experience with large-scale structure and baryon oscillation, if there are any books that can play off those strengths.

I don't know any specific text but I can recommend you a course I took last year at Coursera.org. It says "introduction" but I can assure you it is really complete, 12 week that include a lot of mathematics and physics.

https://www.coursera.org/course/introastro


How did the Hulse-Taylor Pulsar Provide Confirming Evidence of General Relativity? What measurements and observations of the Hulse-Taylor Pulsar agreed precisely with the predictions of general relativity, and how did these measurements support the theory?

One of the predictions of general relativity is that certain objects can give off energy in the form of gravitational radiation. This means that over time, the orbits of the two neutron stars should decay, and they should come closer to each other. Using relativistic formulae, it is possible to predict the changes in the orbits and the energy of the emitted gravitational waves; analysis of the system showed that general relativity's predictions were correct.

Studying gravitational waves requires linearizing the Einstein field equations. However, these can be reduced to certain simpler formulae when it comes to detecting waves from a binary system, as was the case with the Hulse-Taylor binary.


What is the danger for Ceres of collision with other asteroids? In the context of possible colonization of Ceres, would not such colony be totally impossible because of high probability of collision of Ceres with other asteroids in the Asteroid Belt?

Sadly, a well referenced answer to this question likely lies behind academic publisher paywalls.
However, Wikipedia claims:

  Collisions between main-belt bodies with a mean radius of 10 km are expected to occur about once every 10 million years.[63]

-Source for citation 63 has disappeared from the internet.

However, the Veritas asteroid cluster, and the Karin cluster reportedly formed by the collisional disruption of 140 km diameter and 25 km diameter diameter objects only 8.3 and 5.8 million years ago. These numbers obviously cast doubt on the Wikipedia claim.

This piece Small asteroid collisional characteristics from 2002 states:

  Orbits of nearly 88,000 astreroids from the main belt are needed to find statistically one encounter within 1000 km distance during 50 years.

Naturally the more abundant smaller asteroids collide more frequently. In fact Hubble seems to have caught the aftermath of such an event back in 2010.

To answer the question. It seems Ceres will remain intact for some millions of years to come. But it does get hit fairly regularly, like the moon. If Ceres regularly took impacts large enough to preclude habitation, we'd expect to see co-orbiting debris clouds like the Veritas cluster, or in the 2010 Hubble images. We do not see such debris clouds near Ceres.


What is the evidence that galaxies rotate? Do all galaxies rotate?  If so, do they rotate in the same direction?

What observations have been made of galaxy rotation?

Rotation:

One of the easiest way to show that galaxies rotates are Doppler observations of atomic or molecular lines. For example, if the observed galaxy is seen edge-on and rotates clockwise, the left side of the galaxy is going away from you, and is then Doppler-shifted in the red. The right side, going toward you, is Doppler-shifted in the blue.

This kind of observations was realized already in the '60, in radio.

The spiral patern observed in spiral galaxies is also a clear signature of their rotation. Note that spiral are linked to density waves in the galactic disk (see for example Lin & Shu 1964).

Direction:

As for their directions, you can convinced yourself that there is no tendency, just looking at this Hubble telescope gallery. You can also think that galaxies probably rotate by angular momentum conservation during their formation history, and that it highly dependent on initial conditions, that are clearly random.


Is the equinox absolutely true east everywhere? I've read that only only in the equinoxes do you get to see the sun rise in the exact east regardless where you might happen to be. However I think this is not absolutely true everywhere, but only in the equator, and in the south the Sun will rise just a tiny bit to the north, but this tiny bit to the north is negligible due to how far the Sun is from Earth. If this reasoning is correct, when would the 'true' equinox be for any country in the south? Can you provide an example and how you did it, please?

The celestial equator's plane intersects the horizon due east and due west, no matter where you are on Earth (except at the poles where the horizon is the celestial equator).

Those that have the sunrise at the exact time of the equinox will see the sun rise in the east (90º). For the rest, it will be too late, the sun will have made the crossing, and it could be something like 90.00001º or 89.99999º, although it will still be perceived as due east.

The last equinox was March 20th, 03:50 (UTC). At that moment the sun was rising very close to Maputo, Mozambique (table), so everybody on that meridian saw the sun rise in the east, exactly at 90º.


How did Batygin estimate when Planet Nine was ejected? Konstantin Batygin has estimated that if Planet Nine was ejected, it would have been ejected 3-10 million years after the formation of the Solar System.

I'm curious as to how he arrived at this figure. Was it through simulations of the early Solar System, a prediction of the alignments of orbits at that time, or something completely different?

Page 12 of Batygin & Brown (2016) says that a speculative formation scenario can be drawn from recent solar system formation simulations by Bromley & Kenyon and by Izidoro et al. These suggest that the core of a nascent ice giant may have been ejected very early in the solar system's history in order to explain the properties of the observed planets; the formation of Uranus and Neptune was probably accompanied by at least one other ice giant.

The source of the claim you mention is actually an article by Eric Hand in Science Magazine.  He points out that possibly, to explain why this planet was ejected yet still remains part of the solar system in a much wider orbit, then you need it to have been slowed down by residual gas in the protosolar disk. So I assume the 10 million year is an (uncertain) upper limit on the dispersal of the disk and I would guess the 3 million year lower limit is just how long it takes to form a 10 Earth mass ice giant core at the distance of Neptune.


Is extraterrestrial mining more difficult or impractical for bodies without plate tectonics? This article talks about the possibility of mining Uranium on the moon. Since the Moon lacks the geological forces that have created veins of concentrated minerals on Earth, would extraterrestrial mining be more difficult or impractical? How does Moon, Martian, or asteroid mining overcome the lack of mineral veins otherwise formed by Earth's geology?

It seems like extraterrestrial mining would be at least as difficult as trying to refine desert sand, which isn't a thing.

A short video on how gold veins form

Wayfaring Stranger added an interesting link on ore genesis.

I vaguely remember my dad talking about this.

Uranium and other heavy elements are dense. When the celestial body was molten (early in it's life) all the heavy elements sank to the core of the body. Now, with tectonics, the heavy elements are brought back up to the surface. This is why we can mine Uranium on Earth near the surface: the Uranium was brought back up due to convention current on Earth.
In conclusion, it's not worth it at all to mine on a non-tectonically active planet/moon

If anyone can extend this, please do.