What would the Earth's peri- and aphelion have to be in order to have the same seasons due to its orbit? Imagine the Earth had no axial tilt but had seasons due to a very elliptical orbit. How elliptical would the Earth's orbit have to be in order to have about the same seasons as it has now (just with the difference that they'd be in both hemispheres the same)? Mercury has a very elliptical orbit. If we scaled Mercury's orbit to a semi-major axis at 1 au, would we have the very same seasons? Mercury's surface temperature in its summer is ~430 °C and in winter ~280 °C (values for daytime). I guess this would translate into a too high difference if the Earth's orbit was as elliptical as Mercury's; it would have to be a bit less elliptical for the same seasons as now.
How far would the Earth have to be from the Sun at its perihelion to have about 30 °C on the midlatitudes and at its aphelion to have about 0 °C?

TL;DR: about 5 times current eccentricity for a deviation by 5 degrees from the mean... but the devil is in the celestial mechanics and climate model details.
It would not quite work, because the length of seasons would be uneven. Currently Earth's north and south hemispheres get nearly exactly as much or little sunlight as the other. But on the eccentric Earth the hot "summer" period would be short while the cool "winter" period would be long since planets spend more time in the outer part of an elliptic orbit.
There is another complication: absorbed sunlight heats up air, water and soil over time causing a lag: the warmest part of summer and the coldest part of winter comes after the time of the highest solar influx.
To add to the modelling woes, the actual temperature of the planet is strongly affected by the greenhouse effect: while CO2 is not going to do anything weird, as the entire planet cools water vapour (a potent greenhouse gas) will decline as rain and snow, and the albedo (how much light is reflected by clouds and ice) will increase.
That said, here is a simplistic model ignoring the atmosphere inertia:
The distance to the star varies as $$r(\theta)=\frac{a(1-e^2)}{1+e\cos \theta}$$ where $a$ is the semimajor axis, $e$ the eccentricity and $\theta$ the "true anomaly" (annual winner for worst name of parameter since 1609). To convert it to and from time you need to solve Kepler's equation numerically.
The temperature in a zero-dimensional atmospheric model is $$T=\left( \frac{ I_0(1-a)}{4 \sigma \epsilon}\right )^{1/4}$$ where $I_0$ is the solar constant at the top of the atmosphere, $a=0.3$ the albedo, $\epsilon=0.78$ the effective emissivity in IR. If we let $I_0(\theta)=I_0/r(\theta)^2$ (measuring orbits in AU) we get a temperature dependency scaling like $T(\theta)=T_0/\sqrt{r(\theta)}$.
So, at perihelion the temperature is $$T(0)=T_0\sqrt{\frac{1+e}{1-e^2}}$$ and the aphelion temperature $$T(\pi)=T_0\sqrt{\frac{1-e}{1-e^2}}.$$ So given a desired $T_{high}$ and $T_{low}$ one can now solve for $e$ to get $$e=\frac{(T_{high}/T_{low})^2-1}{(T_{high}/T_{low})^2}.$$
If we want a 5 degree difference from a mean $T_0=288$ K this means $e\approx 0.067$, about 5 times the current eccentricity. This is probably small enough that the time asymmetry issues will be small enough to ignore (they matter more for more eccentric orbits).


Is it possible to calculate a star's apparent magnitude in another photometric band knowing its visual magnitude? Or, in other words, is it possible to know a star's luminosity in a certain photometric band?
Proxima Centauri's Wikipedia page provides the apparent magntiude in each UBVRIJHK band (getting progressively brighter) as well as the bolometric luminosity and the luminosity in visual wavelengths.
But this amount of information seems limited to Proxima Centauri and a few select other stars.
Is there a way to calculate a star's apparent magnitude/luminosity in another photometric band knowing its visual apparent magnitude/luminosity? Other factors like distance, size, and mass are also known.

No there isn't if you know nothing else about the star. Knowing the distance doesn't help. Knowing the mass and size of the star (how would you know these without other sources of information?) allows you to estimate what sort of a star it is and therefore you have some idea of the spectrum of that kind of star. Given that as a template, then it is possible to estimate what colour the star is an hence how bright it would be in any other photometric band.
e.g. If you have the temperature then you should find a table of temperature vs whatever colour you are interested in - so B-V if you want the B-magnitude. You interpolate on the table, find the B-V and add that to your known V to get B.
This assumes there is no reddening/extinction involved. If there is then your estimate will be wrong (to small for bands bluer than V, to large for bands redder than V).
A suitable interpolation table for main sequence stars can be found at
https://www.pas.rochester.edu/~emamajek/EEM_dwarf_UBVIJHK_colors_Teff.txt


Can the range of the observable universe be extended through an intermediary? I understand that the so called observable universe has a limit we cannot see through.

My question is whether we might get information through an intermediate hypothetical actor located halfway to the limit. This actor would have, I assume, a limit of the observable universe further away than ours.

We, in turn, might interact with this actor in order to get information about a nova we cannot see from the Earth.

Information about such a star might perhaps have reached the Earth earlier at a time before it changed into a nova. The information about the nova would therefore be new.

The simple answer is no, but it might be easier to understand if we look at the difference between the different cosmological horizons.

Since no information can travel faster than light, and nothing can have travelled for longer than the age of the Universe, then the limit of the observable universe is calculated by multiplying the speed of light by the conformal time since the Big Bang (the age of the Universe, adjusted for the scale factor representing the expansion of the Universe). This limit is also known as the particle horizon.

The current limit is a sphere of ~46.5 billion light-years in radius. If we could detect any signals emitted from matter that far away, we'd be seeing the Big Bang itself! However, the most distant light (EMR) signal we will ever be able to detect is the cosmic microwave background radiation (CMBR), which represents the earliest light after photon decoupling, emitted from a shell ~45.7 billion light-years away.

The CMBR was emitted about 380,000 years after the Big Bang, while the earliest stars didn't form for at least another 100 million years, and the earliest galaxy we've observed so far is GN-z11 which dates back to about 400 million years after the Big Bang. Nonetheless, there's been enough time since then for the light from those earliest structures – albeit highly redshifted and extremely weak – to reach us directly, so there's no need for an "intermediary".

While the particle horizon defines the current limit of the observable universe, what about future observations? In a Universe with accelerating expansion, the outer parts of the observable universe are now receding from us faster than the speed of light, and information from those areas may never reach us at all. The point at which light emitted now can never reach us is called the cosmic event horizon. The current cosmic event horizon is around 16 billion light-years away, which is a lot less than the ~46b ly to the edge of the observable universe.

To make this a bit clearer, let's look at the path the information would take via the intermediary. To avoid confusion, let's call your distant object a supernova rather than just a nova, and let's assume the intermediary is at the midpoint of a straight line between us and the supernova.

The information – whether light waves or gravitational waves – leaves the supernova and travels at the speed of light to the intermediary, where (let's say) the information is immediately relayed in a boosted signal – also travelling at the speed of light – towards Earth. Apart from the momentary delay in relaying the signal at the midpoint, the information will be following exactly the same path as if it had left the supernova and travelled directly to Earth. In other words, if we can receive the information about the distant supernova from the intermediary, we must also be able to receive the information straight from the supernova itself.

Now, in the case of a supernova that's just beyond our cosmic event horizon, the intermediary can receive the light from the supernova, but the space between us and the intermediary will have expanded in the billions of years it takes for the supernova's light to get to them. By that time, the Earth is receding from the intermediary so fast that their relayed signal can never overcome the accelerating expansion of space on the second leg of its journey. We never receive their signal, as they too have receded over the cosmic event horizon.


Orbital elements of solar system using Pyephem I'm using the astrometric python module Pyephem, and I would like to get the orbital (keplerian) elements for the  solar system planets.

The only values I found is the heliocentric latitude, longitude, and the distance to the sun. Is there a way to compte the orbital parameters based on thoses values ? Did I missed a function in Pyephem ?

There is a website: http://orbitsimulator.com/formulas/OrbitalElements.html that has a javascript program for converting state vectors to orbital elements and back.

The source of that website is possible to convert to python: Here is a Body class that has a method for calculating orbital elements based on that website. The method takes one argument, a body the is the Principal (ie the Sun)

G = 0.0002946        # in units of seconds, AU and solar masses.
class Body:
    """A body has attributes r and v, which are its position and
velocity in cartesian coordinates and a mass. implied units are
solar masses, AU and seconds."""
    def __init__(self,r,v,mass):
        self.r = np.array(r,dtype="float")
        self.v = np.array(v,dtype="float")
        self.mass = mass
        self.GM = self.mass*G

    def orbital_elements(self,principal):
        '''view-source:http://orbitsimulator.com/formulas/OrbitalElements.html'''
        mu = G*(principal.mass+self.mass)
        # calculate relative position,velocity
        r = self.r - principal.r
        v = self.v - principal.v
        try: #catch division by zero
            R = np.linalg.norm(r)
            V = np.linalg.norm(v)
            a = 1/(2/R - V**2/mu)  # semi major axis

            h = np.cross(r,v)
            H = np.linalg.norm(h)

            P = H**2/mu
            Q = np.dot(r,v)

            E= np.sqrt(1-P/a)  #eccentricity

            e = [1-R/a,Q/np.sqrt(a*mu)]
            i = np.arccos(h[2]/H)
            Omega = 0
            if i!=0:
                Omega = np.arctan2(h[0],-h[1]) #Longitude of acending node

            ta = [H**2/(R*mu) -1,H*Q/(R*mu)]
            TA = np.arctan2(ta[1],ta[0])
            Cw = (r[0]*np.cos(Omega)+r[1]*np.sin(Omega))/R

            if i==0 or i==np.pi:
                Sw = (r[1]*np.cos(Omega) - r[0]*np.sin(Omega))/R
            else:
                Sw = r[2]/(R*np.sin(i))

            omega = np.arctan2(Sw,Cw) - TA  #argument of periapsis
            if omega<0: omega += 2*np.pi

            u = np.arctan2(e[1],e[0])
            M = u - E*np.sin(u) # mean anomaly

            return(a,E,omega,Omega,i,M)
        except ZeroDivisionError:
            #meaningless, but avoids crash
            return(0,0,0,0,0,0)


Gravitation - Pulling or Pushing force? According to Newton, gravity is the pulling - or in fact the attracting - force of any heavenly body towards any object to its center. But, to the contrary, Einstein once said that the four dimensions of space and time push the object downwards.

So can which one of them is correct?

I'm guessing that this misunderstanding is a result of the oft-used rubber sheet analogy. The rubber sheet analogy says that, according to general relativity, mass curves space-time like a heavy bowling ball on a near-taut blanket (or rubber sheet) curves the blanket/sheet. This resulting curve makes other bits of matter/energy move in different ways. I'm guessing that this is your confusion.

The rubber sheet analogy fails massively in one area, any demonstration of it involves gravity on Earth. If I use a bowling ball to deform a sheet, and then role a golf ball along the sheet nearby, the golf ball will move a bit towards the bowling ball because of the force of gravity around me - not "gravity" in the simulation. It thus makes it seem like gravity pulls the golf ball "down" because the bowling ball pulls the rubber sheet "down". This is the result of using a two-dimensional analogy of a three-dimensional universe.

The point is, there is no "pushing" going on in the general relativistic model of gravity. Gravity is attractive (so long as the strong energy conditions holds for the object in question), just like Newton postulated.


Is Higgs Boson mass equal to the missing mass of dark matter? Sorry if this is a very lay question. I am just an armchair physicist.

The Higgs Boson was just recently discovered, and it has a mass which is considerably larger than a proton. If this Higgs Boson was just recently discovered and the Higgs Boson is EVERYWHERE (ie. The Higgs Field), why wouldn't this perfectly explain the missing mass that is "dark matter" ?

To answer this question, we need to understand what dark matter and a Higgs Boson are.

Higgs Boson

A Higgs Boson is an elementary particle in the standard field of quantum physics. It was theorised by a few people, namely Peter Higgs. The Higgs Field is a field which we can now believe exists, as we can detect it through its excitations, which become Higgs Bosons. The quantum excitations of the Higgs Field create Higgs Bosons.

A Higgs Boson is a particle with no spin, infact, it is the only particle with no spin, electric charge or colour charge. It's also extremely unstable and decays into other particles almost instantly.

Dark matter

Dark matter is a heavily researched topic in physics at the moment. Out of all matter in the universe, dark matter makes up about 80% of it!

One example of a theorised candidate for a dark matter particle is a WIMP. These are abbreviations of 'Weakly Interacting Massive Particles'. These particles are not normal matter, therefor we can't detect them. Our efforts to detect them include trying to look at the annihilation of WIMP particles.

The main characteristics of WIMPS are that they only interact through the weak nuclear force or gravity. They also larger than standard particles (a dark matter particle with mass less than a electronvolt is classified as light dark matter)

Wimps move slowly and are therefor cold, making them one of the main candidates for cold dark matter.

Think of dark matter as a 'skeleton' for normal matter.

Conclusion

From looking at both types of particles, we can clearly tell that Higgs Bosons are completely different from dark matter. We are still trying to find out about them both, as both of them can answer fundamental questions in physics.


Population density of stars within $13$ light-years of us This item from Fox News refers to "over 600 stars that came within 13 light-years of the sun". Because of the past-tense "came", they could have meant stars that are not now within 13 light-years of us but were at some time in the past. But that is not made explicit in the article.

It is said that the nearest neighboring star is $4.3$ light-years from us. And $13$ light-years is about $3$ times that. So the volume within that distance of use is about $3^3=27$ times the volume within $4.3$ light-years of us. If there are $600$ stars within that larger volume, then the average number of stars within that smaller volume should be $600/27 \approx 22.$ But we don't have anywhere near $22$ stars within $4.3$ light-years of us.

So are we in a neighborhood that is unusually sparsely populated compared with what is typical in that larger volume?

Or is this about stars formerly near us that aren't now?

Or just confused journalists?

The criteria for sample selection are admittedly not made overly clear in the preprint itself (Wysoczańska et al.). It appears that the authors started with a list based on stars that were previously believed to have come close to the Sun at some point in the past or future. That list was then augmented based on data from Gaia's second data release, to get a total of 820 objects, and the motions of those stars were then integrated backwards and forwards in time from the present, based on a model of the galaxy's gravitational field.

Here's where that "over 600 stars" came from. The authors ended their integration for a given star when either (i) the star went more than 3 kpc from the Sun or (ii) the time reached 50 million years in the past or the future. With those cutoffs in place, the astronomers found that during that timespan (50 million years before or after the present), 647 stars were within 4 parsecs of the Sun at some point in time. That's the figure Fox is referring to.


High quality Space-related blog/website? I don't know if this is the right place for asking this question, my apologies in advance. I would like to be updated on the latests news on space and I am looking for a website devoted to space news, or a blog. I was only able to find minor blogs which were not updated often. Could you suggest me a high quality blog/space related website that you know? Thanks!

Your question for "space" news sites is somewhat vague as space can cover a wide variety of topics.

I have found Innerspace.net  to be a nice blog/news source primarily concerning itself with the space exploration and technology aspects of space. It often reports on recent launches (such as those by Space X), advancements in space technologies, and space ventures by other countries outside the US such as China and Russia.

If you're looking for more sciencey topics of a higher caliber, try something like Science Daily. While this covers a variety of scientific fields, it does also cover space news. In general, this site is a curation of articles by various sources. Usually each article is linked to some specific scientific research or published paper.


How to determine zenith coincidence from date time data sets I have two or more sets of  dates and times for which I am interested in the location of the Zenith at my location and whether they are coinciding. So far I have been comparing pairs of them on two Stellarium windows with the azimuthal grid but its laborious. Can any one tell me of an easier way. I expect I could do it in excel with a bit more knowledge.

Technically, the location of the zenith is constant: 90 degrees altitude, undefined azimuth. :-) I assume that you want it in terms of the coordinates declination and right ascension instead of altitude and azimuth. Declination and Right Ascension are the coordinate system used to locate objects in the sky. They are similar in concept to latitude and longitude. The difference is that one is "locked" to the sky, and the other is "locked" to the Earth.

The declination of the zenith is the same as the observer's latitude. If your location is the same, then the declination is the same. (If the latitude is different, the coordinate of the zenith is different.)
The right ascension of the zenith can be calculated by using the formulas for the local sidereal time (LST or LMST for the mean local sidereal time.) See the post Local Sidereal Time.


Ambiguity in Earth's "Tilt" It’s well-known that the axial tilt of the Earth (with respect to the ecliptic) is about 23.4 degrees. However, two angles is needed to specify the orientation of any rigid body, so it’s unclear to me exactly how Earth is oriented with respect to its orbital plane.

To be more precise, consider the plane that satisfies these two conditions:
1. Perpendicular to the ecliptic plane
2. Contains the line connecting the Sun and the Earth when Earth is at perihelion (Jan. 2).

(Basically, this plane cuts through the orbit of the Earth such that for half the year Earth is one side and for the other half Earth is on the other side.)

Questions:
1. When the Earth is at perihelion, what is the angle between its rotational axis and the plane described above? I would guess this angle is very small from the images of Earth’s orbit. Is there a technical term for this angle?
2. Does the direction of the axis remain approximately the same throughout its entire orbit?

Please ignore precession for this question.

The fact that the perihelion is close to the the winter solstice is purely coincidental. The perihelion might occur in any season. It wanders around in a somewhat chaotic fashion because of the gravitational influence of the other planets. At the moment the perihelion moves a day every 58 years.

Let A = Earths axis, and E = the line perpendicular to the orbital plane. The angle between A and E is called the axial tilt. Let S = the line between the centers of the Earth and the Sun. Let P = the plane containing S and E.

Q1 is (maybe) asking what is the angle between A and P on Jan 2. It will be about 23.4 times sine(2*pi*12/365).  Because there are 12 days from Dec 21 to Jan 2.

Q2. yes.


Does earth's Umbra reach Sun-Earth L2? Moon can be fully eclipsed by the virtue of being fairly close to Earth. Any body distant enough will not be eclipsed fully, Earth's disc not fully covering Sun's disc. How's that for anything at the L2 point? Will it be lit by Sun's corona or will it bask in deep shadow of Earth?

Bonus question: if Umbra does reach there, how large a body could remain fully shaded at L2? What's the Umbra's radius there?

The Lagrangian point $L_2$ is very close to the most distant point from Earth with an umbra.
$L_2$ is like the radius of the Hill sphere at $r=a\sqrt[3]{\frac{m}{3M}}$ for circular orbits, with $m$ the mass of Earth, $M$ the mass of the Sun, and $a$ the distance Earth-Sun. The ratio $\frac{m}{3M}$ of the Earth and the triple mass of the Sun is almost exactly $10^{-6}$, the cubic root hence $0.01$.

The diameter ratio of Earth and Sun is about $1/109$. Therefore the umbra of Earth ends near $92\%$ the distance to $L_2$.

The answer to another bonus question would then be: If Earth would be $9\%$ larger in diameter, but with the same mass, its umbra would end almost exactly at $L_2$.

Earth's orbit isn't perfectly circular, but the aphel/perihel ratio of about $1.04$ is insufficient to question the result qualitatively.
The error of the implicite assumptions $\tan x=x=\sin x$ is negligible at the considered level of accuracy.


Crust thick enough to prevent volcanos Could you have an Earth-like planet with a crust thick enough to prevent volcanos from forming?

It depends on the definition of Earth-like planet.
In terms of size, density and gravity Venus is very Earth-like, but in terms of atmospheric and  surface conditions and its axis of rotation, and period of rotation Venus in not Earth-like.
I will assume you mean a terrestrial or rocky planet similar in size to Earth.
Earth's crust has two subdivision: oceanic and continental. Oceanic crust is between 5 km and 10 km thick whereas continental crust is between 30 km and 50 km thick:

Oceanic: 5 km (3 mi) to 10 km (6 mi) thick and composed primarily of denser, more mafic rocks, such as basalt, diabase, and gabbro.
Continental: 30 km (20 mi) to 50 km (30 mi) thick and mostly composed of less dense, more felsic rocks, such as granite.

Earth's crust is fractured into plates as described by plate tectonics. The boundaries of some plate collide causing uplift in the collision zone. The Himalayas is an example of such a zone. At other boundaries one plate subducts underneath the other plate. It's at these boundaries that most of Earth's volcanoes form.
For plate tectonics to occurs large amounts of water must be present to lubricate the subducting plate. The implication of this is that for plate tectonics to occur large oceans need to be located near subduction zones.
The other type of volcanoes that can occur are intraplate volcanoes which are located far from tectonic plate boundaries in the interior of tectonic plates. Such volcanoes are thought to arise from mantle plumes.
Earth has a diameter of 12 740 km, and Mars has diameter of 6780 km.
The crust thickness of both planets is 5-50 km for Earth and 10-50 km for Mars.
The ration of maximum crust thickness to diameter for both planets is 0.003925 for Earth and 0.007375 for Mars. The ratio for Mars is nearly double that of Earth, yet the Olympus Mons volcano on Mars is larger than any volcano on Earth.
For volcanoes to form, the temperature of the magma must be high enough to melt a hole through the crust and the pressure within the magma chamber must be high enough to overcome the resistance to flow posed by the friction of walls the volcanic vent and the gravity of the planet.
All terrestrial planets will experience volcanism at some period during their formation, it is a matter of when volcanism stops and why. Volcanism on Mercury ceased early due to the planet contracting early in it formation. Even the Moon experienced volcanism.


If my eyes were really big, would I see radio waves? Considering an assertion that the fundamental difference between different ‘types’ of electromagnetic waves is frequency/wavelength, and larger antennas are needed for longer wavelengths, if my eyes were larger proportional to the difference in wavelength between visible light waves and radio waves, would they see radio waves?

No.  But the reasons are biological, not physical.  Your eyes work by the interaction of electromagnetic radiation with certain molecules ( rhodopsin  which consists of the protein opsin linked to 11-cis-retinal, a prosthetic group.)
These molecules are tuned to detect light of particular wavelengths.  But they couldn't be tuned to detect radio-waves, since radio waves are much larger than molecules.  To detect radio waves, you need an antenna, not a light sensitive molecule.


Birthday of the Universe With every improvement of measurement we are able to determine the age of the Universe more exactly. I just wondered how much and what means it would need to narrow the range of age so that it would be possible to determine the exact date of the Big Bang.

I know that this would take a lot of assumptions for the sake of simplicity - I am just curious; this being said: let us assume that all current theories hold and no new side effects or new theories would evolve.

I read this post and some physics articles about the matter, but my question focuses on the accuracy gap between our current best telescopes and the accuracy that would be needed to narrow down the age to "24 earth hours".

The age of the universe as we know t is very hard to determine. Current estimates put down the age f universe to 13.5 billion years +/- 0.8 billion. This is a huge a margin of error when compared to the margin or error you speak of.

Also it will never ever be possible to measure the age of universe because:

The universe started according to the big bang theory and if we take it as true it gives us a near infinite radiation density. We could measure the expansion and try to estimate the age but it is still hazy as we have no way knowing the initial density of the universe.
There is always an uncertainty in any measurement. and measuring something so far away(The edge of the universe) will have a lot of uncertainty.

These measures of today may still have a huge margin of error but they are the best we have till date. And to narrow the error down to about even a few years would take us a lot of time and tremendous development in technologies. So basically we have a very slim chance of determining the precise age of the universe in the foreseeable future


How did water get on Earth I recently read that water more than likely got here by comets (carrying water) hitting the Earth. However it also it says the impact of a comet hitting the Earth is much greater than an atomic bomb. So if comets brought water to Earth how was it not vaporized when the comet hit the atmosphere or in the massive explosion when it hit the Earth itself?

The key finding why we think Earth's water came from Asteroids (big rocks) and not Comets (small rocks) is the Deuterium/Hydrogen ratio that we can measure in several sources.
When a star forms, it has an initial value of D/H that came from the nucleosynthesis in its progenitor nebular / star.

In a protoplanetary disc, as dust grows to rocks grow to planets your nebular gas will be trapped with initial D/H ratios in gas giant atmospheres. But the way to get Water onto Asteroids and Comets (those don't have substantial mass to retain atmospheres themselves!) is sublimation and maybe adsorption.
The latter two processes are strongly sensitive to the gas-mass and therefore different D/H ratios from the protosolar ones are expected.
And in fact we find them to be different:

This was in the news lately, as ESA managed to touch down and measure 67P's D/H ratio which gave another hint on the asteroidic origin of water on earth.

This finding, however does not resolve the question:

There maybe other isotopical tracers like D/H that give a hint on the history of water.
There could have been a decrease in D/H and subsequential increase again, or the other way round.
We know that the protosolar nebula must have had massive amounts of water (Oxygen is the third-most abundand element in normal stellar fusion!), so again the question is, why did Earth retain so much water, while the lighter planets Venus and Mars retained the heavier element $CO_2$
...

I could continue this for quite some time, but the bottom line is: We only have hints, not definitive answers.

To refer to the rest of your question: A hot plume in a colder atmosphere will not necesarily leave the whole gravitational potential well.


How is the size of a distant planet determined? How is an object's size determined from other solar systems than our own? How are new large bodies being found in our solar system currently?

One method of finding planets orbiting stars is to analyze the transit effect. This is when a planet crosses the face of a star between the star and observer.  This will block some of the light reaching the observer. By measuring this decrease in light from the star we can determine how much of the surface area of star is occluded.

The speed of a planet across the face of a star will let us calculate the orbital radius considering a circular orbit. The temperature of the star can be determined from its brightness and location on HR diagram and spectroscopic data. Combining this information lets us determine the size and of the planet.

Using space-based or ground-based telescopes and automated data collection and analysis methods large regions of the sky can be viewed for these transits. This method is highly accurate and will probably surpass the radial velocity method as most common method to discover new planets.

Another method for finding planets is known as the radial velocity method. When a planet orbits a star it is really the planet and star rotating about the center-of-mass of the system. Hence the star wobbles due to the bodies orbiting the star. It wobbles because usually the center-of-mass is inside the star and this results in the star rotating about an axis running thru the star but offset from the center. By doing a doppler analysis it can be determined whether the star is revolving or not and the period of revolution. The radial velocity method is the most effective method. The transit method is very limited by the viewing angle, the planet must pass between observer and star.

A good source to better learn about these methods is here.


Can Axions escape the Black Holes? I read about Tachyons and Gravitational Waves and also about Exotic matter, really nothing can escape a Black Hole, can Axions escape for providing a new hope?

Once you are inside a black hole, every direction leads towards the singularity.  So for every particle, whether it is massless or not, would travel towards the singularity, and not escape.
Axions have not been proved to exist, but they would also not be able to escape.


Any theories about universal expansion due to action at the universal event horizon? I'm curious if there are any theories about the increasing rate of the expansion of the universe that are centered around gravitational pull from matter outside the event horizon of either the observable universe, or the entire universe?

Since observations point to a uniform rate of expansion in all directions, it would make sense (as most theories speculate) that some force is at work. Most theories invoke dark matter/energy, but is it possible that it is simply gravity?

In my thought experiment I considered this in two scenarios:

Finite and Boundless Universe: There is no limit to the size which the universe can expand, but being finite in size and expanding outward, the accumulation of matter at the very edges of the universe is more dense than that in the observable universe. This dense outer boundary is constantly pulling the rest of the universe towards it. As more matter accumulates at the horizon, gravity increases, and the rate of acceleration expands.
Finite and Bounded Universe: The universe is limited in size, as expanding matter and energy reach the event horizon of this limited universe, it is compacted like a black hole that surrounds the entire universe. As the maximum size is limited in this scenario, matter and energy would infinitely accumulate at the horizon; in turn constantly speeding up the expansion of the universe as all matter is pulled outwards towards the ever-growing horizon.

I'm quite the astronomy nerd, and have a good understanding (as much as a non-professional can) of the physical laws governing the universe on a large scale, so I know there are some immediate problems you could pick apart in the above scenarios, this is just an idea I had to jot down before I forgot. I am interested in whether or not any fleshed out theories similar to this idea exist.

There are no such theories because there is an immediate problem with both scenarios as stated.

It is a fact that a spherical shell of material has no net gravitational influence on material anywhere inside it. https://en.wikipedia.org/wiki/Shell_theorem


could dark energy be a force coming from the hyperspace outside the universe? It seems to me that the expansion of the universe is only being looked at one way. a repelling force, basically being the opposite of gravity.  After pondering this for many nights, I began to wonder if its possible that the changing pressure outside the universe could cause the expansion thst we observe.

Nobody really has any idea what "dark energy" is. But there is a principle known as Occam's razor. It can be expressed in various ways, for example "When an observation can be explained in many ways, the one with fewest assumptions should be used."

To explain the properties of dark energy as being due to changing pressure of hyperspace, requires the assumption that "hyperspace" exists, that it has a property that pressurizes the universe, that this "pressure" is changing, and that affects the rate of expansion of the universe.

There are other hypothesis: a cosmological constant, or a as yet undiscovered force field. None have much observational evidence, but have the benefit of requiring fewer assumptions.

As Rob mentioned what you describe is similar to "brane cosmology", in which the universe is embedded in a higher dimensional space. These could influence our space, by controlling the scale of a cosmological constant, making it small, but non-zero. As with much of string theory, the experimenters are well behind the theorists.


Could the barycenter orbit of our sun be greatly underestimated? The radius of the suns orbit around the barycenter of the solar system is often measured to be roughly the radius of the sun. Based on the same type of bias that has made humans miss things about their solar system because they are looking at it from the vantage point of Earth orbiting inside the system, is it possible that the suns orbit around the barycenter is actually much larger?

This is basically equivalent to asking whether there's an undetected massive object in the outer Solar System.

Starting from the basics, the location of the centre-of-mass of a system of point masses is given by

$$\mathbf{X} = \frac{\sum_{i} m_{i} \mathbf{x}_{i}}{\sum_{i}m_{i}}$$

Note that the quantities in bold are vector quantities. Without loss of generality, we can use a reference frame where $\mathbf{X} = \mathbf{0}$, i.e. the origin of the coordinate system is the centre-of-mass. For a two-body system, this gives:

$$m_{1} \mathbf{x}_{1} = -m_{2} \mathbf{x}_{2}$$

So the second particle is located in the opposite direction of the first from the centre-of-mass, with the ratio of the distances $r_{1} = \left\| \mathbf{x}_{1} \right\|$, $r_{2} = \left\| \mathbf{x}_{2} \right\|$ depending on the mass ratio $q = m_{2} / m_{1}$:

$$r_{1} = qr_{2} = \left( \frac{q}{1+q} \right) r$$

Where $r = r_{1} + r_{2}$ is the total separation between the two objects. This means that the trajectories of the two objects around the centre-of-mass are scaled mirror-images of each other. So the semimajor axis of the reflex orbit of the Sun $a_{1}$ for a planet of mass $m_{2}$ with orbital semimajor axis $a$ is given by:

$$a_{1} = qa_{2} = \left( \frac{q}{1+q} \right) a$$

This orbit is larger for more massive planets (higher $q$) and for wider planetary orbits (higher $a$). Working this out for the major planets, the largest reflex orbit is due to Jupiter (1.06 solar radii), followed by Saturn (0.59 solar radii), Neptune (0.33 solar radii) and Uranus (0.18 solar radii).

If Planet Nine exists with the predicted properties given by Batygin et al. (2019), a ~5–10 Earth mass planet in a ~400–800 AU orbit would give a reflex orbit of ~1 to ~5 solar radii, which would likely be the largest contribution to the Sun's orbit around the Solar System barycentre.

The hypothesis that the Sun may have a distant binary companion or a giant planet in the Oort cloud (which would both be more massive than the proposed Planet Nine, and much further out), which has variously been termed "Nemesis" or "Tyche" would result in an even larger orbit around the Solar System barycentre. So far, these hypotheses have not held up to observational evidence.


Calculation of Horizontal Coordinates Given a fixed coordinate location on Earth (i.e. a latitude and longitude), and a fixed equatorial coordinate location of a particular astronomical object in the sky (i.e. right ascension and declination), how can I calculate the horizontal coordinates as a function of date and time on Earth?

You can't, not with that information. However if you also have the date and time, you'll be good to go: there are plenty of sites in the web with this information, such as: RA and DEC to ALT and AZ


Why celestial objects appear brighter in the night sky than in photographs from closer proximity? The moon, for example, appears very bright in the night sky, but quite dark from photographs on/near its surface.

Similarly, Mars and Venus appear as bright dots in the sky but in closer photographs they're quite dark.

The Moon, Mars, Venus are seen against a dark sky using an eye whose aperture is adjusted to the average brightness of the visual field. So bright small sources are over-exposed and so appear bright.

Photographs of planetary surfaces are taken with aperture and exposure set for proper exposure. So appear closer to how they would look if they filled your eye's field of view and so the aperture would be set to properly expose the surface.


Cosmic microwave background radiation: why did it take so long to get here? I understand that the universe after the big bang was a super dense cloud of elementary particles, and because of this high density was "not transparent" to light.
Then, roughly 400.000 years (380.000 to be exact) after density and temperature lower enough for the first hydrogen atoms to form. Thanks to the lower density, now photons were free to travel. Theoretically the Cosmic Microwave Background Radiation (CMBR) should be this light that "became free" 400.000 years after big bang.
Let's reason in 2d for simplicity. If the universe was a circle, the maximum radius could have been a bit less than 400.000 light years (it's probably an exaggeration, but let's simply assume that matter can't travel faster than light). So, if we imagine that the matter that eventually generated the earth was on the border of this circle (and somehow we are still close), the most far photon at that time should have been at 800.000 light years.

If my reasoning is correct, I can not understand how it is possible that we see that photon after 13 billion years. It should have reached us long long time ago.

Here's a very, very simple explanation:

"why did it take so long to get here?"

There's two aircraft carriers, A and B, fifty miles apart on the ocean. You've got a helicopter that flies 50 mph.  Of course, it takes one hour to make it from A to B.

Now, imagine A and B are both moving - they're steaming away from each other at a good speed.

Of course, it now takes longer than an hour for the chopper to make it between A and B.

Regarding the many, many mysteries of the metric expansion of space, this trivial observation is just one thing to bear in mind. Note that of course this is not a full and complete analogy, and the analogy is indeed utterly wrong / totally irrelevant to many aspects of the broader discussion.

"I thought that the photons were "trapped" in an expanding ball" sure, the chopper can only move at 50 mph over the water underneath it meaning that at any given time it can only have moved so far over the water underneath it (a sort of "circle of achievablity", if you will).  But you can see with the carriers moving the hell all over the place, it's just an open question whether the chopper reaches B in much less than an hour, much more than an hour, or can never reach B at all.


Quantum Mechanics after the detection of Gravitational Waves Of course everyone knows by now of the detection of Gravitational waves

But, since General Relativity and Quantum Mechanics don't get along, can we say now that this detection proves that Quantum Mechanics doesn't actually apply and that General Relativity did prevail?

Another question: how can we identify the ripple's origin (let's say whether it's a result of the big bang or another big event)?

EDIT 16-2-2016

I was reading an article today and I thought I'd share it here; It's basically saying that without a third detector we can't triangulate the signal.
Some scientists tried ways to observe the light of the event directly after the observations of the wave but they couldn't detect the merger simply because it's too far away or too faint to be observed with our current technology.

No more than the observation of light waves disproves quantum mechanics.

Light has properties of both a particle and a wave. At low energies, the particle nature of light is hard to detect: radio waves are made of photons, but individual radio wave photons are pretty hard to detect. I'm not sure that we have directly detected individual photons with energies below the infrared band.

Gravitational waves (probably) also have both a wave and a particle nature. The gravitational field is probably quantised. But at the frequencies and sensitivity at which LIGO operates, individual quanta cannot be measured. So this detection does not prove the ascendency of GR over QM.

If anything, understanding extreme events like black hole mergers might lead to a theoretical understanding of the quantum nature of gravity.


What's the furthest object observable by the naked eye from earth? From XKCD:

Caption: 'The light from those millions of stars you see is probably many thousands of years old' is a rare example of laypeople substantially OVERestimating astronomical numbers.

So, what is the furthest object visible to the naked eye in the night sky from the surface of the earth? Assume a person with good eyes, on a clear, dry night at sea level, away from bright lights.

This is partly a question of 'limiting magnitude' - the faintest magnitude that is visible using a particular instrument, or in this case, just the eye.

+6 - maybe +6.5  - magnitude is sometimes used as a baseline expectation of what can be seen in dark skies sites.

The most distant star that can easily be seen is Deneb. It is actually quite bright, at brighter than +2 Magnitude, but is (probably) 1425ly away. So though it is at quite some distance, it's luminosity means that actually, it isn't limiting magnitude that is at play.

There are stars much further away that are at the barely perceivable limit, and seeing them will depend on conditions. The +4 mag mu Cephei is probably fairly achievable, at 5900ly, and V762 in Cassiopeia is about +6 mag and maybe 16000ly, which would probably be the record if you can actually see it, but you'll need special conditions.

When it comes to galaxies, Andromeda is 2500000ly away, and +3.4, very visible and much further away than any individual star. If you have good conditions, the +5.7 mag M33 is slightly further away at 2900000ly, but it would be much harder to see.

While the generally accepted limit is maybe +6.5, some people claim to have seen to +8. If it is possible, M83 is 14700000ly away at +8.2, with naked-eye claims reported.


What are the most popular computer programming languages in observational astronomy? I would like to work in the field of observational astronomy (not so much theoretical astronomy).

I currently know two computer programming languages: C# and MATLAB.

I have read that computer programming is absolutely essential to every astronomer, and that it takes a very significant part of the time of the work of most astronomers.

Therefore I would like to learn a few more programming languages. Hence my question:

What are the most common programming languages in observational astronomy?

Python is gaining popularity and replacing MATLAB in many fields of science as the tool for fast prototyping and writing research code.
For example, have a look at:

https://www.astropy.org/
http://www.astropython.org/
https://python4astronomers.github.io/
https://www.astroml.org/
https://asteca.github.io/

(I'm not working in astronomy as a researcher but in some other field.)


Why were two galaxies named "The Sagittarius Galaxy"? Is this common? Phys.org's  says:

  The formation of the Sun, the Solar System and the subsequent emergence of life on Earth may be a consequence of a collision between our galaxy, the Milky Way, and a smaller galaxy called Sagittarius, discovered in the 1990s to be orbiting our galactic home.

and I checked Wikipedia which says:

  Sagittarius Dwarf Irregular Galaxy Not to be confused with Sagittarius Dwarf Spheroidal Galaxy.

and

  Sagittarius Dwarf Spheroidal Galaxy Not to be confused with Sagittarius Dwarf Irregular Galaxy.

Question: But my question is how did they both get named after a very well known constellation? Is it common to name galaxies after constellations? Do many constellations have namesake galaxies?

  The Sagittarius dwarf galaxy has been orbiting the Milky Way for billions for years. As its orbit around the 10 000 more massive Milky Way gradually tightened, it started colliding with our galaxy's disc. The three known collisions between Sagittarius and the Milky Way have, according to a new study, triggered major star formation episodes, one of which may have given rise to the Solar System.  Credit: European Space Agency

Screen shot from the ESA video Dwarf galaxy collisions make stars form in Milky Way

In addition to the Andromeda Galaxy (M31)
and the Triangulum Galaxy (M33),
the Local Group includes several dwarf galaxies named after the constellations in which they appear.
In most cases, nearby dwarf galaxies in the same constellation are distinguished by a letter or Roman numeral suffix.


Are mass extinction events more likely during meteor showers / passing through comet debris? Meteor showers happen when Earth passes through the debris left by a comet in its orbit. Meteors are generally tiny, like snow flings or pebbles and don't make it to the ground as meteorites. But periodic comets sublimate and disintegrate. Don't they shed kilometer sized fragments too? Maybe it is not only the comet which is the threat, but its entire orbit is a minefield too? Are bolides and observed meteorite falls more frequent during meteor showers?

The American Meteor Society FAQ page notes that about 95% of observed meteors are probably of cometary origin. But they're apparently so fragile that they're only about 1/3 of observed fireballs, and 0% of known meteorites.

Also, since the Earth passes through streams of cometary debris several times a year, and yet there's been only one plausible mass extinction due to cometary or asteroid impact in the last few hundred million years (the one that did in the dinosaurs), it appears to be extremely unlikely for cometary debris to be a meaningful danger.


What would we notice if the Sun stopped fusing atoms? (This question was stimulated by Would we have more than 8 minutes of light, if the sun "went out"?)

According to this answer, the "Sun has enough gravitational potential energy to supply its current luminosity for tens of millions of years."

Does "current luminosity" mean that the same spectrum will be radiated, or will it be just as bright, but radiating at different wavelengths (like not in the violet-blue and reddish orange-red wavelengths which chlorophyll requires, or the IR that keep us warm)?

As stated in my answer to Would we have more than 8 minutes of light, if the sun "went out"? , the Sun would cool at roughly constant luminosity for some tens of millions of years. That means "we" would not notice anything change on human timescales (apart from the lack of neutrinos, which has no measurable effect on anything apart from the odd atom in a vast vats of cleaning fluid or water, underground in South Dakota and Japan).

If $dL/dt$ was roughly $-L_{\odot}/30$ in solar luminosities per million years, then it would be 1000 years before the luminosity of the Sun fell by 0.1%, which is roughly the kind of variations we see over the course of the solar cycle.

However, the most likely evolution of the Sun is for it to contract, maintain a stable luminosity and compensate by increasing its surface (photospheric) temperature.

Given that luminosity is provided by gravitational contraction and the rate of change of gravitational potential energy, then
$$ L_{\odot} \simeq  -\left(\frac{GM_{\odot}^2}{R^2}\right)\frac{dR}{dt}, \tag*{(1)}$$
where $R$ is the radius.

If the luminosity is constant and given by
$$L_{\odot} = 4\pi R^2 \sigma T^4,$$
where $\sigma$ is the Stefan-Boltzmann constant and $T$ is the effective (photospheric) temperature, then
$$ \frac{dL_{\odot}}{dt} = 4\pi \sigma \left(2R T^4 \frac{dR}{dt} + 4R^2 T^3 \frac{dT}{dt}\right) = 0 \tag*{(2)}$$

Combining equations (1) and (2) we find
$$\frac{dT}{dt} = \frac{T R L_{\odot}}{2 GM_{\odot}^2} = 90\ {\rm K/Myr}$$
i.e. The Sun surface would heat up by 90K every million years.

This gradual warming would change the spectral type of the Sun, moving it towards an F-type star. The spectrum of light it emitted would shift to shorter wavelengths (according to Wien's displacement law, the peak wavelength in the spectrum is inversely proportional to temperature) and a greater fraction of the Sun's light would appear in the ultra-violet part of the spectrum.


Can't find Cassiopias Schedar or Caph in Tycho-2 catalog supplement 1 I'm trying to locate three stars inside Cassiopeia, gam cas, Schedar, and Caph. I have found gamma Cas inside the Tycho-2 catalog supp1.dat file, however when I look for Schedar or Caph I have no luck. I converted their RA and dec to decimal degree, Schedar = (10.12, 56.53) and Caph = (2.29, 59) and used the Vim command

:/|002\.

to find their location in the star catalog, but I haven't found any stars that match the RA, dec, or even visual brightness, which are 2.24 for Schedar and 2.28 for Caph. I'm kind of stuck at this point and not sure where to head from here.

Alpha Cas (Schedar) is  TYC 3663-2668-1 or HIP 3179 in the Hipparcos catalogue.

http://simbad.u-strasbg.fr/simbad/sim-id?Ident=Schedar&NbIdent=1&Radius=2&Radius.unit=arcmin&submit=submit+id

Beta Cas (Caph) is not in the Tycho-2 catalogue but is in the Hipparcos catalog as HIP 746

http://simbad.u-strasbg.fr/simbad/sim-id?Ident=Caph&NbIdent=1&Radius=2&Radius.unit=arcmin&submit=submit+id

Gamma Cas is also does not have a Tyc number but is listed as HIP 4427 in the Hipparcos catalogue.

http://simbad.u-strasbg.fr/simbad/sim-id?Ident=Gamma+Cas&NbIdent=1&Radius=2&Radius.unit=arcmin&submit=submit+id

All three of these stars are right at the bright limit of the Tycho-2 catalogue.


What made cooler temperatures suitable for atom formation? I have read in relation to Big Bang theory that after 300,000 years of big Bang temperature was reduced to 4500 Kelvin and this gave rise to Atomic matter.So,my question is why reduction in temperature makes it suitable for atom formation?

The temperature of a gas is a measure of the kinetic energy of the particles. For molecules you can have rotational and vibrational energy, while for single atoms you just have translational energy, or "thermal motion". At a given temperature, the particles don't have exactly the same energy, but a distribution of energies, and hence velocities.

Most (>90%) of the gas in the Universe is hydrogen. The energy needed to knock the electron off (i.e. ionize) a hydrogen atom is 13.6 eV. For a gas of $T \gtrsim 3000\,\mathrm{K}$, the fraction of particles with sufficient energy to ionize hydrogen is so high, that the majority of the atoms are ionized$\dagger$, i.e. split up in protons and electrons. This was the case in the beginning of the history of the Universe. Everytime a proton and electron met and recombined to form a neutral atom, the electron would almost immediately be knocked off again by a high-energy particle (usually an electron, but it could also be a proton or photons, since all particles were in "thermodynamic equilibrium", i.e. shared the same distribution of energies).

As the Universe expanded, the gas cooled. At some point, 380,000 years after Big Bang, the temperature had decreased enough that it was no longer possible to keep the atoms ionized, so over a rather short period of time ($\sim10^4$ years), they all recombined. This epoch is hence called the epoch of recombination.

Until this point, all photons kept scattering on the free electrons. With the electrons "trapped" in atoms, they could now stream freely, and "decouple". They have been traveling freely ever since, but since they travel through an expanding Universe, they become redshifted along the way. Since then, the Universe has expanded by a factor of ~1100, and so have the wavelength of the photons, so that today they have temperature of $3000\,\mathrm{K}/1100\simeq2.7\,\mathrm{K}$. This is what we see as the cosmic microwave background.

$\dagger$In which case they're in principle not "atoms", but a plasma. However, in astronomy it's quite normal to call it atoms anyway.


Are the Jupiter-Saturn conjunctions and winter solstice related? There is conjunction of Jupiter and Saturn on Dec 21. And there is another celestial event on that day the winter solstice.
So I'm just wondering that are these two events are related or not?

Not in any way, no.
The December solstice is the moment when the Sun reaches its southernmost point in its daily path in the sky (the June solstice, when the Sun reaches its northernmost point). It only depends on the tilt of the Earth on its orbit and the Sun.
On the other hand, Jupiter and Saturn being in conjunction is a phenomenon that doesn’t depend at all on the Earth’s axial tilt. It does involve the Earth, though, as it’s our vantage point. From Earth, Jupiter and Saturn appear close in the sky then. Seen from Mars, for example, they may or may not appear close together in the sky at the same moment.
The last time a Jupiter–Saturn conjunction happened near a solstice was in June 2000. You can find a list of Jupiter–Saturn conjunctions happening within ±24 hr of a solstice at https://astronomie.quebec/conjsols.html.
Solstices, on the other hand, happen twice a year (one in June, one in December).


Composition of planets' core It is often possible to find a list of the materials that compose the cores and the mantle of plantes (often they are iron and/or nickel).

How can these materials be determined in our Solar system? In other words, for example, how can we know that Jupiter's core certanly contains iron?

With the volume and mass of a planet concludes are possible of its material composition. But there is more, for example auroras been observed at Jupiter. This is only possible if Jupiter has a magnetic field just like our earth. A magnetic field is a strong evidence for an iron core.

The next point is, heavy materials accumulate in the center, so one could ask why there isn’t gold or even heavier stuff in the core of a planet. The most common material in the universe is hydrogen. Hydrogenis burned through atomic fusion into helium. All heavier materials are produced if a star dies in an explosion. So really heavy materials like gold are less likely and iron or nickel are more common so cores more likely made of these materials.


Beta profile fit of Virgo cluster gas? I'm looking for the parameters $r_c$, $\rho_0$ and $\beta$ in a $\beta$-profile fit of the Virgo cluster's ICM density. I just can't find a reference for it. Unlike for Coma (Abell 1656) where it's in Mohr et. al. 1999.

Beta profile:

$$\rho(r) = \rho_0 \left[ 1+ \left(\frac{r}{r_c}\right)^2 \right]^{-\frac{3\beta}{2}}$$

Schindler et al. 1999: Morphology of the Virgo Cluster: Gas versus Galaxies has details for $\beta$ model fits for Virgo and its subclusters.


How to evaluate the fit of an isochrone to a stellar population? Consider that I know the extinction, distance modulus, reddening, and metallicity for a particular star cluster.

I need to determine it's age from isochrone fitting.

After generating the required isochrones, what should be a parameter for the goodness of fit for the isochrone?

Is there something like a 'best fit line' that also exists for general curves?

Finding the best-fitting isochrone, a.k.a. isochrone fitting, is a standard approach to determine the age of globular clusters. This problem can be solved with a least-square method, where the data to be fitted are the points on the color-magnitude diagram and the fitting curve is the isochrone. Since there are many ways to apply this method, I will first outline the general approach and then I will provide you with a real case application.

Outline of the method

Let's first break down what is isochrone fitting via least-square method. You have your CMD with all your photometric data scattered around. You assume your sources belong to a coeval stellar population (almost true for many globular clusters), and so you want to exploit a theoretical isochrone to find the age.  So you built a set of isochrone with different ages, fixing carefully all the other parameters (e.g. [Fe/H] and [$\alpha$/Fe]). Then you define an error function and you find the isochrone that minimizes it. The simplest choice for the error function is
\begin{equation*}
\chi^2=\sum_i(C_{i,\textrm{obs}}-C_{i,\textrm{exp}})^2
\end{equation*}
where the sum is over all the sources in the CMD, $C_{i,\textrm{obs}}$ is the color of the $i$-th source, and $C_{i,\textrm{obs}}$  is the color of the isochrone at the magnitude of the $i$-th source. Heuristically, $(C_{i,\textrm{obs}}-C_{i,\textrm{exp}})$ is the horizontal distance of the $i$-th point from the isochrone and we assume the best-fit isochrone is the one that minimizes the sum of the distances.

This $\chi^2$ could be the parameter you're looking for. Similar parameters can be obtained using the vertical distance or the minimum distance instead of the horizontal distance.

Application to 47 Tuc

Let's see a real application of the $\chi^2$ minimization technique. I will use some plots that I've made for didactical purposes, obtained from the photometric data of 47 Tucanae in the HUGS catalogue (Piotto et al. 2015, Nardiello et al. 2018). I've used the HST ACS/WFC bands $F606W$ and $F814W$, which are similar to the $V$ of Johnson and $I$ of Cousins.

First point: usually we do not use all the sources at once, and there are several reasons for that. The main one is the dispersion on the CMD, which can lead to a bigger uncertainty on the final age measure. For example, your sources can have a huge dispersion on the CMD due to photometric errors, or they can have an intrinsic dispersion (e.g. due to differential reddening, binaries above the main sequence, multiple populations, and so on). You want to get rid of those outliers, you want to narrow the distribution of sources in the CMD to have a more robust determination. Second point: instead of using all the sources at once, we can bin them and average their position on the CMD. In this way, we have to deal just with a few fiducial points that represent the whole distribution.

So we bin the sources in magnitude, and for each bin we calculate the clipped mean of the colors.  in finding the standard deviation of colors $\sigma$, discard all the sources outside e.g. $3\sigma$, eventually iterate this selection some times, and at the end calculating the mean color. In this way we get rid of the outliers and obtain the fiducial points. The results is shown in the image below: in black, the CMD of 47 Tuc; in grey, the final clipped selection, in red, the clipped mean color in bins of width $\Delta m_{F606w}=0.1$, i.e. the fiducial points. The error bars on the fiducial points are the standard deviations in both dimensions.

$\hskip2in$

With these fiducial points, we can easily apply a least-square method. I've downloaded a set of isochrones from the Dartmouth Database, with fixed chemical abundances and different ages ($\Delta\textrm{age}=0.2$ Gyr). I've then calculated for each isochrone
\begin{equation*}
\chi^2=\sum_i(C_{i,\textrm{obs}}-C_{i,\textrm{exp}})^2
\end{equation*}
where the sum is over all the fiducial points, $C_{i,\textrm{obs}}$  is the color of the $i$-th fiducial point, and $C_{i,\textrm{exp}}$ is the color of the isochrone at the magnitude of the $i$-th fiducial point. The results are in the image below. In the panel above, you can see the $\chi^2$ for each age. In the panel below, the red crosses are the fiducial points, while the colored points are the points extrapolated from each isochrone at the magnitude of every fiducial point (colors in the two panels are matched). Now you see that, for a given isochrone, in the $\chi^2$ we are summing the horizontal distances between the colored points and the red crosses.

$\hskip2in$

Conclusions

  After generating the required isochrones, what should be a parameter for the goodness of fit for the isochrone?

It depends on the method you are using. Assuming you're using a least-square method, the parameter you're looking for is the sum of the squared residuals (e.g. my $\chi^2$).

  Is there something like a 'best fit line' that also exists for general curves?

From the context of the question, I suppose you're asking if there's something beyond linear regression, i.e. something beyond finding the best-fitting line. If so: yes, as you can see from this wikipedia page. In fact, least-square methods are not limited to lines, neither linear functions, and the method I've outlined is an example.

Remark

It is well known that the determination of the absolute age of globular clusters carries considerable uncertainties (e.g. Bolte & Hogan (1995)). Therefore, to do meaningful science is necessary to analyze the error budget (e.g. how the uncertainties in distance, metallicity, and reddening propagate to the final uncertainty, or what is the entity of the photometric errors) and to take actions to mitigate these uncertainties (e.g. rejecting sources with high errors, using clipped averages, transposing theoretical isochrones into observational CMD and not observational data into theoretical CMD to control error propagation).


What is the relevance of the Tropics and the Polar Circles? Do they Exist on other planets? The middle line is the equator, the second and fourth line are the tropics, the first and fifth are the polar circles.

What is the relevance of these bands on Earth? Do these exist on other planets? What purpose do they serve?

The Tropics (Capricorn in the South and Cancer in the North) are the furthest point from the equator where the sun reaches a point directly overhead at any time during the year. The Arctic and Antarctic circles are the points at which the sun remains above the horizon for a full rotation of the Earth (i.e. 24 hours), commonly called "Midnight Sun". Any planet that has axial tilt while have similar lines.


Why is dark energy density given in grams per cm$^3?$ According to Wikipedia article,

  The density of dark energy ($~ 7 × 10^{−30} g/cm^3$) is very low, much less than the density of ordinary matter or dark matter within galaxies. However, it comes to dominate the mass–energy of the universe because it is uniform across space.

Other sources I found also give the density either as percentage of mass of the universe, or just as mass density like above, $kg/m^3$ or similar.

In about all other applications and contexts of usage of energy density, I'd find MJ/L, or other units of energy per volume. Why is energy of density given as mass per volume, and how do I convert it to more familiar units? Using $E=mc^2$ ?

This is a case of using a sort of natural units (similar to geometerized units), which are often convenient in relativity (special and general). Take, for instance, the Minkowski metric of special relativity. In dimensional units, it is
$$\mathrm{d}s^2=-c^2\mathrm{d}t^2+\mathrm{d}x^2+\mathrm{d}y^2+\mathrm{d}z^2$$
Setting $c=1$ makes it a bit more convenient, and gives time and space the same units - which is more intuitive, if you think of time as another dimension.

You also brought up $E=mc^2$. This is a special case of the energy-momentum relation:
$$E^2=p^2c^2+m_0^2c^4$$
Setting $c=1$, we have the much more convenient form
$$E=p^2+m_0^2$$
This comes up again and again. Add to this the mass-energy equivalence that is also important in relativity (especially the right-hand side of the Einstein field equations), and it simply makes sense to treat energy and mass as the same thing. In fact, it becomes perhaps even more useful than in special relativity, because we also often set $G=1$ - and that comes up a lot in general relativity.

Now, the units of density under this system are $\text{Length}^{-2}$, and the density above is clearly not in those units. I'm guessing that this just isn't a case of setting $G=1$ - and that makes sense, because in cosmology and astronomy, many types of densities are measured in g/cm3: dark matter, interstellar gas and dust, and sometimes dark energy. Keeping it in $\text{Mass}\cdot\text{Length}^{-3}$ makes it easy to compare these, working in a system that is more commonly used.

In a nutshell, then: Cosmologists sometimes like $c=1$ (and sometimes $G=1$) because it makes a lot of equations a lot easier to write out. Here, it becomes really easy to compare mass densities and energy densities.


nonagesimal in Kepler's parallax computation I'm starting to learn Kepler's Astronomia Nova using William Donahue's translation . In the translator's introduction, it is demonstrated how Kepler did his parallax computation. I failed to understand the following paragraph:

specifically:

1) nonagesimal's definition: there are 2 points of intersection between the ecliptic and the horizon: one in the East, the other in West. another ambiguity is the direction of the $90^\circ$

2) I can't see why the altitude of the nonagesimal is "the same as the angle between the ecliptic and the horizon". It does make sense to me, but I'm missing a kind of "proof" for that.

3) Actually I also failed to understand what follows in that paragraph - but maybe your explanation for the points above, will clarify that for me.

your help is very much appreciated

It looks like the assumption regarding the 90° point is that the amount of the ecliptic visible is 180°. So the 90° direction is the halfway point.

The nonagesimal is on the ecliptic, so the altitude approximates the arc. The wording in the initial part has that correct, but then it goes on to say "the same as the angle" - this seems to be a mistake. The arc is directly related to the angle, yes, but it is not the angle.


How Are Radioactive Decay Rates Influenced by Neutrinos - On Earth and Other Dense Planets I read a science report recently that mentioned an accidental discovery where radioactive decay rates shifted slightly slower in advance ( about a day and a half) of solar storms or in sync with sun's 33-day pattern/rotation of the sun's core. Seems that neutrinos emitted from within the sun or at surface of the sun arrive in advance of other wave/particle radiations AND effect earthly atomic natures.

Aside from predicting solar flares/storms, does this imply decaying atoms/elements absorb or block neutrino emissions to any substantial degree that might of use in other areas of science?

Resurrection alert.

I was Googling the subject and found this paper refuting an earlier paper claiming to have observed a neutrino-based effect on beta decay in radon.

Edit: another study here finding there to be no correlation.


How did ancient astronomers know to order the planets from the closest to the farthest from the Sun? If we assume a geocentric model of the universe (like ancient astronomers did) how could we ever find out (again, like ancient astronomers did) the right distances of the planets? For example, how did they know that Jupiter is
further than Mars, if Jupiter is brighter?

According to the Cambridge Concise History of Astronomy (p 33 of my edition), essentially the Greeks took the (not unreasonable) view that the planets that moved more slowly were further away and were orbiting on larger spheres.

That's obviously not the same as suggesting they knew "the right distances" to the planets, merely the order. They did develop a mathematically sound means of estimating the distance to the Moon, though their observational data let them down on a correct estimate.

They also thought the Sun was in the fourth sphere around the Earth (to explain the observed behaviour of Mercury and Venus).

Not all Greeks thought the Sun revolved round the Earth and those who argued for a heliocentric universe said the reasons the stars did not move as the Earth did was because they were very, very far away.


A "strange" unit radio astronomy I'm reading up on radio astronomy, and I came across this paper from 1964. At the bottom of page 193, the author uses a unit that I've not seen before in discussing radio power emission from stars:

  Now the outbursts on the Sun give an intensity on Earth of $10^{19}$ to $10^{20}$ $wm^{-2}(c/s)^{-1}$

I'm guessing it's "Watts per square meter per [something] per second", but I'm not sure what the [something] is.

A similar unit appears in this paper on the first line on page 364:

  The comparison band in the radiometer, being separated approximately 3.25 Mc from the signal band, never encounters the hydrogen range of frequencies.

Again, this looks to me like mega[something]. Can anyone shed some light on this?

On page 362 of the second paper, the unit appears as $(Watts/M^2
)/(C/S)$ as a unit of flux. There, the $C$ looks like coulombs, but that makes the $3.25 Mc$ in the second quote seem weird.

I would expect the authors to be talking about the signal in terms of janskys, the now-commonly-used units of flux density. The typical definition is
$$1\text{ Jansky}=10^{-26}\text{ Watts meters}^{-2}\text{ Hertz}^{-1}$$
One hertz is one cycle per second, which makes me suspect that the "c" stands for cycle. It might seem curious that the authors choose to use cycles/second instead of hertz, but as the papers were published in 1964 and 1955, and the hertz was only adopted on a large scale in 1964, the older term "cycles per second" is more fitting, given the time period.


What causes random irregularities in the earth's rotation accounted for by dynamical time I read in a book that the earth's rotation sometimes shows unpredictable irregularities(not caused by precession, nutation, tidal forces) which are accounted for using dynamical time. What would be the cause of these?

On short scales, atmospheric phenomena can cause variations in mass distribution.

  On relatively short sub-annual to annual timescales, variations in the length-of-day have been clearly shown to arise primarily as a consequence of the exchange of angular momentum between the solid Earth and its overlying atmosphere (e.g. Hide et al., 1980) and oceans. On the inter-annual timescale an important recent discovery concerning l.o.d. variability has been the documentation of a significant excitation associated with El Nino-Southern Oscillation events (Cox and Chao, 2002; Dickey et al., 2002). Concerning the sources of wobble excitation, it is clear that on the timescale of the seasonal cycle of climate change the excitation of the annual component of wobble variability is due to the inter-hemispheric exchange of atmospheric mass. The Chandler wobble, however, a free oscillation of Earth’s spin axis in a body fixed frame of reference with a period close to 14 months, is apparently significantly forced by the dynamical state of the oceans (e.g. Gross, 2000) as well as by the atmosphere. These most recent analyses of the problem of Chandler wobble excitation, to be reviewed in what follows, appear to have finally resolved what had remained an unresolved problem for decades.

-- "History of Earth Rotation", W. R. Peltier, Department of Physics,University of Toronto, Toronto, Ontario, Canada

On longer time scales, glacier distribution, mantle convection, and effects from the larger planets on the orbit of Earth (which by altering the geometry of earth's orbit, would also alter solar tidal forces).


Can a black hole rip spacetime Can a black hole which has an enormous mass and spins so fast cause spacetime to to be stretched to is absolute limits that it  start so rip?

There is a useful model of spacetime as a rubber sheet that is bent by masses laying on it. But it should be remembered that this is an analogy (Obligatory xkcd) and most analogies fail if pushed too far. Spacetime isn't made of something that can rip.

A rotating black hole, a "Kerr black hole" is stranger than a static one, as it pulls spacetime around it and can accelerate objects passing close to it. Even so there are no rips, no singularities outside the event horizon.

However in another way, at the centre of every black hole there is a singularity, and a singularity is a single point "rip" in spacetime. General relativity can be used to predict what happens to spacetime around the black hole, and even inside the event horizon. But at the singularity the gravity becomes infinite, and at that one point, spacetime doesn't exist.

It is suggested that a "naked" singularity, not surrounded by an event horizon, cannot exist.


Can electromagnetic waves be affected by gravity? Can electromagnetic waves change their properties in the presence of gravity?

Yes (and somewhat No apparently too)
If you follow Einstein's theory of general relativity then gravity has no direct effect on electromagnetic waves itself.
Gravity however affects space time itself warping it towards the gravity source. Thus any electromagnetic wave passing close enough to the gravity source will bend towards that source when observed from the outside.
From the point of the wave however, it follows a straight path and is not affected by gravity at all.
If you mix in quantum theory, it's getting even more weird, because suddenly parts that work well for general relativity no longer work within the quantum model. This is part of current research in physics to bring general relativity and quantum theory into alignment.


Amateur radioastronomy: dish suggestions What kind of amateur radioastronomy can any interested citized do with:

a) A 2 m dish antenna.
b) A 2,5 m antenna.
c) A 3 m antenna.
d) A 5 m antenna.
e) A >5 m <10 m antenna (likely I can not afford this or the previous but I just want to know...).

Of course, space is sometimes a logistic issue for big stuff, but I wondered what kind of objects or sources can someone do with suitable instruments and with aid enough if not an expert. Projects and links would be welcome!

The size of your dish determines two things:

Along with the temperature of your electronics, determines the signal-to-noise ratio of your telescope.
The size of your dish determines the angular resolution you can expect. This has an approximate relationship of $$ R = \lambda / D$$ where $R$ is your angular resolution, $\lambda$ is your wavelength of light and $D$ the width of your aperture (dish).

Instead of talking about dish size lets talk about interesting things to look at and see what the requirements are:
The Sun
The sun is a good source of radio waves in the 10cm wavelength. Since the sun is around half a degree, we would need a dish at least 11.5 meters before you could expect to see the sun as anything more than a point source.
Jupiter
Jupiter has some magnetic field effects that produce radio waves in the 10-100cm wavelength range. Of course Jupiter is 50 arcseconds across, and would need a dish 412 meters in diameter to do any amount of resolution.
Cosmic Microwave Background
The CMB was one of the earliest measurements of radio waves from space. The strongest peak of the CMB is in the 1mm wavelength. However it is very weak. The original investigators cooled their radio detector with liquid helium, and I imagine something similar would be required.
Terrestrial and Man-made sources
There are plenty of man-made radio sources. Airports have a radio wave emitter in the 10cm range for radar. There are plenty of geosynchronous satellites along the equatorial plane that use the X-band in the ~2-5cm range. These by definition have a strong enough signal to be seen from Earth with even a small dish.
Summary
Resolving power is likely out of the reach of an amateur radio astronomer since the dishes have to be either very large, or you must use a much more sophisticated radio interferometry method to achieve any angular resolution. You can however still see things as point sources in the sky if you are so inclined. An excellent example of what is likely accomplished by most people would be this project here.


orbital angular momentum and the longitude of ascending node Consider the motion of a planet around an oblate star. Because of the oblateness the star has a non-zero quadrupole moment which causes the orbital angular momentum of the planet to precess around the symmetry axis of the oblate star. My naive question is: is this precession rate exactly the same as the precession rate of the longitude of the ascending node or are there subtle differences between the two?

My naive question is: is this precession rate exactly the same as the precession rate of the longitude of the ascending node or are there subtle differences between the two?

They're the same, assuming the star's equator is the principal plane of the coordinate system. One way to calculate the longitude of ascending node as $\Omega = \arctan(h_x, -h_y)$, where $\arctan(a,b)$ is the two-argument inverse tangent function and $h_x$ and $h_y$ are the x and y components of angular momentum vector.


gravitational energy and internal energy So assume we have a planet of temperature T, and mass M, We can calculate it's internal energy/heat content by the formula $U=cMT$ where $c$ is the specific heat.

And if we also know the gravitational energy of the planet via $\frac{GM^2}{R}$

how do I approach the following question?

Can the release of gravitational energy during planet formation in principle (is there enough) explain this much heat

Any help would be appreciated.

Can the release of gravitational energy during planet formation in principle (is there enough) explain this much heat

Planets in general can have internal heat sources (like radioactive breakdown or a complex hot core).  During planetary formation there are thought to be multiple collisions with large proto-planets before things settle down to a more-or-less stable set of orbits and planets.  These collisions add energy to the planets as they develop and increase temperature (a lot), as does ongoing bombardment from boring-old asteroids.

Now all of this energy does basically come from gravitational sources, but as you can see it's a complex (messy) business and there are many significant events that can alter temperature.

It might be instructive for you to read about existing theories on the formation of Solar system as well as material related to the structure of the Earth.


How do I create a galaxy stellar mass function? Suppose that I have an array of stellar masses of tens of thousands of galaxies, and that I also already know what the total "survey volume" is (in Mpc^3) within which all of those galaxies are contained. For context, my data is from a simulation of galaxy formation at redshift ~ 0, rather than from an observational simple -- so in principle I don't think I need to worry about incompleteness corrections at the faint (low-mass) end.

Given my array of stellar masses and the total survey volume in Mpc^3, how do I create and plot the "galaxy stellar mass function" that I always see people talking about? Isn't it just basically a histogram of the stellar mass array, and then divide the # of galaxies in every bin by the survey volume (it's almost just like a normalization constant)?

(Of course this question could equally apply to galaxy luminosity functions.)

Your approach is completely correct, just note three things:

Logarithmic distribution

First, since the distribution of masses is logarithmic in nature (as is most other things), be sure to bin them logarithmically. Otherwise you will oversample (undersample) the bins at the low-(high-)mass end.

Comoving densities

Second, to be able to compare mass functions at different redshifts, ones uses the comoving volume rather than the physical volume, such that the expansion of the Universe is factored out. The two are related as $V_\mathrm{com} = V_\mathrm{phys}(1+z)^3$.

Damn you, little $h$!

Finally, observers and modellers tend to use a slightly different definition of the unit volume. Whereas observers usually use $\mathrm{Mpc}$ for distances, and hence $\mathrm{Mpc}^{-3}$ for number densities, if your galaxies come from a cosmological simulation where the cosmological parameters can when tuned at will, it is custom to factor out the Hubble constant $H_0$. In simulations, masses and distances are then measured in $h^{-1}M_\odot$ and $h^{-1}\mathrm{Mpc}$, respectively, so number densities are measured in $h^3  \mathrm{Mpc}^{-3}$. Here $h\equiv H_0\,/\,(100\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1})$.

This is probably a reminiscence of the time when the Hubble constant was rather uncertain. Nowadays, in my opinion there is no need to do this, but since everybody does, it's difficult to go against the stream. For a discussion of this issue, see Croton (2013).

Python code

Since you've tagged the question with python, I wrote this little snippet that should do the work (I randomly chose $10^5\,\mathrm{Mpc}$ as your survey volume; note also that in this example I don't factor out $h$):

import numpy as np
import matplotlib.pyplot as plt

M     = np.loadtxt('Mstar.dat')         #Read stellar masses in Msun
logM  = np.log10(M)                     #Take logarithm
nbins = 10                              #Number of bins to divide data into
V     = 1e5                             #Survey volume in Mpc3
Phi,edg = np.histogram(logM,bins=nbins) #Unnormalized histogram and bin edges
dM    = edg[1] - edg[0]                 #Bin size
Max   = edg[0:-1] + dM/2.               #Mass axis
Phi   = Phi / V / dM                    #Normalize to volume and bin size

plt.clf()
plt.yscale('log')
plt.xlabel(r'$\log(M_\star\,/\,M_\odot)$')
plt.ylabel(r'$\Phi\,/\,\mathrm{dex}^{-1}\,\mathrm{Mpc}^{-3}$')
plt.plot(Max,Phi,ls='steps-post')


Accuracy of predicting an asteroid strike in 1987 Good People,

I am writing a short story, and I wanted to include a section wherein a family is told that an asteroid is going to strike their home. The thing is, I would like to set the story in 1987, but I'm not sure if there was the capability of that kind of prediction back then. To be honest, I'm not even sure that kind of accuracy is possible now! But I will allow myself some creative freedom in that area, but I don't want to stretch it so much that someone would keep thinking to themselves, "Really, in 1987 they could predict that?" Would such a thing have been possible then? If not then, what about sometime in the 90s?

While I have your eyes, is there a specific size that an asteroid would have to be in order to just destroy one home (or a couple on the side of the home).

Thank you for any insight and info! I appreciate the resources here. I did some digging around before asking this question: nothing seemed to be particular to my frame of reference. If it exists, please let me know.

There are problems with this:

What happens when an asteroid hits the atmosphere

The asteroid will be travelling fast, more than 10 km per second. In front of it the atmosphere will be compressed and heat up, this causes the "meteor" (a streak of light in the sky). It also causes puts a lot of stress on the asteroid.

If the asteroid is very small (sand grain to pebble sized), it gets destroyed completely.  If it is larger it can explosively break up. But several chunks can continue at terminal velocity (ie no faster than a stone dropped from a high building) and don't form craters. These chunks can later be picked up as meteorites.

If the body is very large it can survive the atmosphere, hit the Earth at hypervelocity (several km/s) and form a larger crater.

If you want the body to survive, but only form a small crater you need either a very strong body (a solid iron asteroid) or an odd set of events, such as at the Carancas impact. In these cases a small crater or crater field can form. The size of the impactor is about 50cm.

Detecting and forecasting impact

A 50cm asteroid is not currently detectable until very close to the Earth.  We have seen asteroids that are a couple of metres across, but they need to be close to the Earth (and we need to be lucky).

In 2008 we did get lucky and saw a small object before it hit Earth. In that case we had a few hours of observations and by about an hour before impact we were able to narrow the impact zone down to "Northern Sudan".  Now (North) Sudan is huge, an area about 3 times the size of Texas. And in 2008 we already had an active Near Earth Object search program, something that we did not have in 1987.  Even if the asteroid was noticed by lucky amateur, before the internet it would have been very hard to coordinate the observations needed even to predict "Northern Sudan". This meteorite exploded at altitude and did not form a crater.

To conclude, most meteorites will not take out a single house and leave neighbours standing.  Such meteorites that could are not currently detectable before impact.  Even with current technology and lots of luck we could not predict the impact location better than "somewhere between New Mexico and Florida" but not a single address.

There are other things that can destroy a house, perhaps a sinkhole? Perhaps these are more predictable (with luck) than an asteroid impact.


Does the Sun and Moon basically appear to "move on the sky" identically regardless of location and date? For a long time, I've been trying to use Stellarium (simulation) and many visualizations and animations in order to get a good idea of how the Sun and Moon move across the sky, as seen by a human from the surface of Earth.
It's surprisingly difficult to grasp this, at least for me.
It seems to me that the Sun always "rises" in the "East", goes slowly up to "above our heads", and then sets to the "West" in the same manner, making a kind of half-circular path. After that, after some unknown time, the Moon kind of "follows" the Sun in this (more or less) exact path, also coming up from the East and "setting" in the West.
The fact that the Moon is orbiting around Earth, and Earth orbits around the Sun, and yet they move like this, makes no sense to my brain. It seems like the described path would only be true for the Sun, or the Moon, but not both.
And is it always (roughly) the same? Or does this vary depending on where you stand on Earth, and what date/year it is? It was very difficult for me to make my own experiments in Stellarium. It seemed like it would vary a bit, but not too much.
The reason I'm trying to figure this out is both because of general curiosity, and wanting to accurately describe the Sun and Moon in my story. In The Lord of the Rings, Tolkien frequently talks about the movement and look of these objects, which appear to follow the same rules as in our world. It's clear that he had very deep knowledge of how these things appear to move on the sky over the day, and I like such "details" to be accurate.
Basically all the animations and illustrations I find of the movement of the Moon and Earth around the Sun are focused on a "space overview" rather than how it looks from Earth.

The Moon's one month orbit makes the Moon rise about 50 minutes later each day for people who aren't at extreme latitudes. (I'll examine extreme latitudes later). The Moon's orbit is inclined by 5° with respect to the ecliptic. This means that the new Moon more or less follows the path of the Sun that very day, while the full Moon more or less follows the path the Sun took six months earlier. This is why the winter full Moon rises so high in the sky in temperate latitudes.
What about more extreme latitudes? The Amundsen-Scott South Pole Station is the epitome of extreme latitudes. At the South Pole, the Sun sets six months after it rises while the Moon sets two weeks after it rises. In winter, the moon rises about a week before full Moon and sets about a week after full Moon. In summer, the moon rises about a week before new Moon and sets about a week after new Moon.


Finding angle between a given sky position and ecliptic pole Given a right ascension in degrees and declination in degrees (say, 88 degrees RA, -63 degrees DEC) I want to find the angle between that location and the ecliptic pole (90 degrees RA, -66 degrees DEC... are these the right values? What are the decimals following the 66? Most of my values that I'm working with are similar to the one I give, so which ecliptic pole, if any, does this correspond to?) How would I find this angle, I need a convenient formula (such as a dot product to find this angle). Thank you!

The angle between an ecliptic pole and another sky position is complementary to the ecliptic latitude of that position.
To find ecliptic (λ, β) coordinates, one method is to convert the equatorial (α, δ) to Cartesian form:
$$ \begin{align}
x_\mathrm{equ} &= \cos \alpha \cos \delta \\
y_\mathrm{equ} &= \sin \alpha \cos \delta \\
z_\mathrm{equ} &= \sin \delta
\end{align}$$
then rotate by ε = 23.44° on the x axis:
$$ \begin{align}
x_\mathrm{ecl} &= x_\mathrm{equ} \\
y_\mathrm{ecl} &= y_\mathrm{equ} \cos \varepsilon + z_\mathrm{equ} \sin \varepsilon \\
z_\mathrm{ecl} &= z_\mathrm{equ} \cos \varepsilon - y_\mathrm{equ} \sin \varepsilon
\end{align} $$
and convert to spherical form:
$$ \begin{align}
\lambda &= \mathtt{atan2}(y_\mathrm{ecl}, x_\mathrm{ecl}) \\
\beta &= \arcsin z_\mathrm{ecl}
\end{align} $$

If you are not interested in the ecliptic longitude λ, you can express the ecliptic latitude as
$$ \beta = \arcsin (\sin \delta \cos \varepsilon - \sin \alpha \cos \delta \sin \varepsilon) $$
Then the angle off the north ecliptic pole (α=18h0m, δ=+66.56°) is 90° - β.

Working your example (α=5h52m, δ=-63°),
I get (λ=75.63°, β=-86.34°),
and the angle off the south ecliptic pole (α=6h0m, δ=-66.56°) is β + 90° = 3.66°.


Cubic spline interpolation in light curve of pulsating stars Why is cubic spline interpolation used to analyze light curve of pulsating stars? Is there any scientific justification of such usages?
One example of using the cubic spline interpolation is here, section 4.

The main thing a cubic spine lets you do is have a continuous second derivative.  If all you need is a continuous curve, connecting the dots with straight lines suffices, with no overshoot, but a very discontinuous derivative.  So if you want to think about the derivative of the light curve, you'd have to go at least to a quadratic spline, which allows a continuous first derivative but introduces the potential for overshooting (a curve that goes outside the range of the points themselves).  If you actually want to think about the second derivative also, then you'll need that to be continuous, so that will require a cubic spline.  But the potential for overshoot keeps getting worse when you add more continuous derivatives.  Personally, I find cubic splines to be very unreliable, the overshoot can be terrible unless you have a very nicely resolved curve with not much noise, but that may be just what they do have.


Do Enceladus' geysers fall back to its surface or do they achieve escape velocity? Enceladus, a moon of Saturn, has a very low surface gravity at 0.114 m/s² or 0.012 g. It has a subsurface ocean of liquid water and is ejecting plumes of it. Does the ejected water eventually fall/rain down to the surface or does it (or some of it) achieve escape velocity due to Enceladus' very low mass and gravity? If so, is Enceladus losing mass and will eventually run out of water?

We start by calculating the moon Enceladus surface escape velocity $v_e$ as
$$v_e=\sqrt{\frac{2GM}{r}}$$
where $G = 6.674×10^{-11}m^3kg^{-1}s^{-2}$ is the universal gravitational constant, $M=1.08×10^{20}kg$ is the moon mass, and $r=2.52×10^5m$ is the radius of the moon. Evaluation of the above equation gives us an escape velocity of about $239m/s$.
Perry et al. provide high fidelity observations of Enceladus vapor plumes from the Cassini spacecraft.

The above graph is just for the high velocity plumes as described in the paper:

The H2O neutrals measured during E8 had a Mach-4 distribution centered
on 1.2 km/s with a width of  ±300  m/s,  which  corresponds  to  a
temperature  of 65K

Since the average high speed plume velocity of 1.2km/s is about five times greater than our calculated escape velocity of 239m/s, we can conclude that some of Enceladus's plumes certainly achieve escape velocity.
Teolis et al. agree:

The expression assumes radial expansion of the gas from the surface
sources at constant speed, neglecting gravity since the mean molecular
speed in the jets significantly exceeds (by at least a factor two) the
240 m/s Enceladus escape speed.

Enceladus is losing mass through it's (mostly water) jets. I couldn't find a conclusive analysis of mass loss rate. Eventually I would expect that enough water will be lost that the current mechanism for creating the jets under the 10 km ice crust will no longer be in effect, but this is just my intuition.  I don't have a credible source or calculation to back this up.


Do all total solar eclipses have the ring of fire when observed from ground? I was recording the phenomenon and then I soon realised that the ring of fire don't dissappear, is it because of the apparent size of the moon and sun as well as the relative distance so that every eclipses I see would alway have the ring of fire on it? Also I ruled out lensing because the moon is not massive enough right?

No, some solar eclipses are annular and some are total.
The difference is in the Moon's distance at that moment in its eccentric orbit around the Earth.
Hermit Eclipse has some illustrations which may be helpful.

In an annular eclipse, the Moon is farther than average and appears slightly smaller than the Sun.
Some of the solar photosphere remains exposed, briefly appearing as a ring for observers on the central path.
The phrase "ring of fire" applies to annular eclipses.
The eclipses of 2019-12-26 and 2020-06-21 are annular.

In a total eclipse, the Moon is nearer than average and appears slightly larger than the Sun.
Along the central path, the photosphere is completely obscured, briefly allowing observation of the solar corona.
There may be a "diamond ring" effect before and after totality as a bit of photosphere shines past low regions on the lunar limb.
The eclipses of 2019-07-02 and 2020-12-14 are total.

In the present few centuries, annular eclipses are slightly more frequent than total eclipses.


Can a star be massive enough to go 'supernova' yet not be massive enough to leave behind a neutron star? Or, perhaps vice versa? From what I understand, stars that explode as a supernova at the end of their lives become either a black hole or a neutron star, and less massive stars that do not explode become white dwarves, but...
Do those two mass limits overlap exactly?

This diagram from the Wikipedia article on supernovas mostly answers your question I think.

There is in fact an interval that is expected to not produce a remnant, but it is not at the lower end of the mass range, interestingly. Instead it's a result of the particular mechanism that triggers the supernova for these heavy stars, which blows the core apart entirely.