What's a good model for the vernal equinox year? Can it increase forever?

The main factors that affect the length of the March equinox year (*1) over time can be divided into three components:

Changes in the length of the solar day
Changes in the length of the mean tropical year
Difference between the mean tropical year and March equinox year

Of these, the change in the length of the solar day is most significant in the long term.

The length of the solar day

The length of the solar day is continuously increasing at a rate of roughly 1.75 milliseconds per century on average. This means that if we measure any type of year in terms of solar days, its length will decrease simply because our measuring unit is becoming longer; this comes to about 0.64 seconds per century, or 7.4 millionths of a day per century. In particular, calendars count solar days, which means that any calendar with a fixed average year length will inevitably become inaccurate.

Change in the mean tropical year over time

The change in the mean tropical year over time (as measured in atomic time) is mainly an oscillation of period around 41,000 years and amplitude around 15 seconds, which is linked to the obliquity cycle. The long-term average (over millions of years) is relatively stable in the vicinity of 31,556,924 seconds (365 days 5 hours 48 minutes 44 seconds).

Combined with the above, the mean tropical year when measured in solar days decreases over time at a slightly varying rate.

Difference between the March equinox year and mean tropical year

The difference between the March equinox year and mean tropical year depends on where the vernal equinox is in Earth's orbit, and is thus affected by the precession of Earth's orbit. In short, when the March equinox is near perihelion the March equinox year will be longer than the mean tropical year, and when it is near aphelion the March equinox year will be shorter (as a reminder, perihelion is when the Earth is closest to the Sun, and aphelion is when the Earth is furthest away). (*2)

Kepler's laws tell us that the Earth moves faster in its orbit when it is nearer to the Sun; this leads to variations of a few days in the lengths of the seasons. Due to apsidal precession, the aphelion and perihelion move slowly over time; this movement causes the variation to show up when computing the March equinox year. Specifically, as the apsides move forward in Earth's orbit over time, a tropical year is slightly less than one orbit relative to the apsides (one such full orbit is known as an anomalistic year). As a result, a small chunk of the orbit is left out, and the duration of that chunk depends on where it is relative to the apsides i.e. shorter near perihelion and longer near aphelion. (*3)

Since perihelion is currently in January and advancing towards the March equinox, the March equinox year is increasing relative to the mean tropical year; the same holds for the June solstice. The rate of this increase will slow down as perihelion approaches the equinox. Once perihelion passes the March equinox in around 6000 CE the difference between the March equinox year and the mean tropical year will decrease; at the same time the June solstice year will be increasing at its fastest rate, and the September equinox year will begin increasing relative to the mean tropical year as the perihelion advances towards that equinox.

Note that the size of this effect will be influenced by the obliquity of Earth's orbit; as the obliquity decreases over the next few tens of thousands of years, the magnitude of these differences will also decrease.

Results

When we combine these effects, we find that each equinox and solstice has a period of relative stability alternating with a period of fast decrease. In stable periods, the increase due to apsidal precession cancels out the decrease due to lengthening of the day, while in fast decrease periods both effects add together.

It just so happens that the March equinox has been in such a stable period for thousands of years. The March equinox year will stop increasing around 3000 CE, then begin to decrease. By that time, the June solstice year will be increasing, while the September equinox year will continue decreasing for a long time, and the December solstice year will be in the middle of its fast decrease period.

All of this is most easily seen in the graphs on Irv Bromberg's excellent page.

(*1) Of course, the same factors apply for any other year based around a fixed solar longitude, such as the June solstice year or the Besselian year.

(*2) This is largely a reminder for myself -- I mixed them up while writing this post.

(*3) If Earth's orbit was in the opposite direction for some reason, this would be reversed, with a tropical year being longer than an anomalistic year and an extra chunk of orbit being added.


Are there neutron stars whose magnetic axis and rotating axis are the same, and if so what will happen?

It is believed that old pulsars may have their rotational axes closely aligned with their magnetic field. This would happen over a timescale of $\tau\sim10^7$ years (Lyne & Manchester (1988)). There are three sets of phenomena driving the dynamics of the alignment (Casini & Montemayor (1998)):

Short-term ($\sim50$ days) variations caused by glitches
Intermediate increases of the alignment angle $\theta$, moving the magnetic dipole moment towards the equator
A set of long-term ($\sim10^7$ years) dynamics leading to a decrease in $\theta$

Only in older pulsars does this last set of dynamics dominate. What this means is that the pulses from the neutron star would appear wider than pulses from neutron stars with significant misalignment. We also would not see interpulses, signals from the opposite magnetic pole, which we see in a number of young (or simply short-period) pulsars; we would just observe one pulse per rotation period.

I will add that Lyne & Manchester identified some young pulsars (including PSR 1800-21 and PSR 1823-13) that exhibited near alignment, a possible indication that the initial offset between the two axes may have a uniform distribution. Therefore, there should be examples of young pulsars with magnetic and rotation axes almost aligned. I would assume the intermediate-timescale mechanisms would then lead to misalignment before the long-term dynamics began to dominate.


How moon is visible during sun is still shining, simple explanation please!

Let's look at what the difference is between day and night.

In the day time, the air that's between you and the Moon is in the sunlight, but at night, that air is in the dark.

Day or night though, the air is still transparent (you can see the Moon through it), and the light from the moon is mostly unaffected.

When it's in sunlight, the air scatters some of the sunlight in your direction. For the parts of the Moon that are bright, they are so bright that they look white.

But the dark parts of the moon don't look black to you on Earth because there's still the fainter blue-sky light scattered by the air.

Moon during the day with bright blue sky light

Source

Moon at sunset with faint blue sky light mixed with Earthshine

Source


how far away could we detect that Earth has life?

I had put off answering this question because it seems too broad without specifying what sort of detection methods are proposed. But if you answer it directly from the perspective of - if we were to take the solar system and put it at some distance from us, would we able to detect signs of life on planet Earth - then the answer is probably not.

Using current technology (and by that I mean experiments and telescopes that are available now) we would probably be unable to detect life on Earth even if observed from a distance of a few light years. Therefore there are no stars within this sphere (other than the Sun).

No planets quite like the Earth have yet been detected around another star. That is to say, none that have a similar mass, radius and orbit at 1 au (or close to it) from a solar-type star [EDIT: There is of course now a close contender in Kepler-452b, though it is 60% bigger than Earth; Jenkins et al. 2015.]. With current technology, it is just about in reach. Therefore any directed search for life on Earth has a limited number of places in which to start. If you can't detect the planet at all then there is absolutely no chance of looking at its atmospheric composition to look for biomarkers (e.g. oxygen along with a reducing gas like methane, or chlorofluorocarbons from an industrial civilisation - Lin et al. 2014). The only exoplanets for which atmospheric compositions have been (crudely and tentatively) measured are "hot Jupiters". - giant exoplanets orbiting very close to their parent stars.
A "blind" search could look for radio signatures and of course this is what SETI has been doing. If we are talking about detecting "Earth", then we must assume that we are not talking about deliberate beamed attempts at communication, and so must rely on detecting random radio "chatter" and accidental signals generated by our civilisation.
The SETI Phoenix project was the most advanced search for radio signals from other intelligent life. Quoting from Cullers et al. (2000): "Typical signals, as opposed to our strongest signals, fall below the detection threshold of most surveys, even if the signal were to originate from the nearest star". Quoting from Tarter (2001): "At current levels of sensitivity, targeted microwave searches could detect the equivalent power of strong TV transmitters at a distance of 1 light year (within which there are no other stars)...". The equivocation in these statements is due to the fact that we do emit stronger beamed signals in certain well-defined directions, for example to conduct metrology in the solar system using radar. Such signals have been calculated to be observable over a thousand light years or more. But these signals are brief, beamed into an extremely narrow angle and unlikely to be repeated. You would have to be very lucky to be observing in the right direction at the right time if you were performing targeted searches.

Hence my assertion that with current methods and telescopes there is not much chance of success. But of course technology advances and in the next 10-20 years there may be better opportunities.

The first step in a directed search would be to find planets like Earth. The first major opportunity will be with the TESS spacecraft, launching in 2017, capable of detecting earth-sized planets around the brightest 500,000 stars. However, it's 2-year mission would limit the ability to detect an Earth-analogue. The best bet for finding other Earths will come later (2024 perhaps) with the launch of Plato, a six-year mission that again, studies the brightest stars. However, there is then a big leap forward required to perform studies of the atmospheres of these planets. Direct imaging and spectroscopy would probably require space-borne nulling interferometers; indirect observations of phase-effects and transmission spectroscopy through an exoplanet atmosphere does not require great angular resolution, just massive precision and collecting area. Spectroscopy of something the size of Earth around a normal star will probably require a bigger successor to the James Webb Space Telescope (JWST - launch  2018), or even more collecting area than will be provided by the E-ELT in the next decade. For example Snellen (2013) argues it would take 80-400 transits-worth of exposure time (i.e. 80-400 years!) to detect the biomarker signal of an Earth-analogue with the E-ELT!

It has been suggested that new radio telescope projects and technology like the Square Kilometre Array may be capable of serendipitously detecting radio "chatter" out to distances of 50 pc ($\sim 150$ light years) - see Loeb & Zaldarriaga (2007). This array, due to begin full operation some time after 2025 could also monitor a multitude of directions at once for beamed signals. A good overview of what might be possible in the near future is given by Tarter et al. (2009).


How does gas in accretion disks of supermassive black holes create orbital torques on smaller black holes within the disks causing them to migrate?

Not really my area, but this question is probably related to the planetary migration in circumstellar disks. In this case, the migration is caused by gravitational interactions between the planet and the gas in the disk. There are two explanations for this effect

Impulse approximation: consider a parcel of gas in the corrotating frame. If the gas is close enough to the orbit of the planet in an internal orbit, it will eventually reach the planet and its gravitational pull will move it to an external orbit. From the change of velocity in the gas, you can calculate the torque exerted to the planet. This approach is relatively simple in terms of math, but uses a lot of assumptions which are not true. However, it can be used to get an order of magnitude estimation.

Resonant torques: Decompose the torque exerted to the planet in the sum of individual torques at resonant locations in the disk. Much more complicated, but better results.

You can find the complete deduction in Astrophysics of Planet Formation by Armitage, or the compact version in this paper.
There are surely differences between planets and black holes (GR corrections, larger accretion rate, etc.), but I'd assume the physical principles are basically the same


What does less than one count from an x-ray detector mean? (Swift BAT detector)

I think there is a missing piece of information. The BAT is a coded mask telescope. The imaging is done by photons passing through a mask and falling onto an array of 32768 detectors. http://swift.gsfc.nasa.gov/about_swift/bat_desc.html

The "mask-weighted" light curve is produced after a complex ray tracing exercise using an estimate of the position of the source. Looking at some of the software specifications (eg https://heasarc.gsfc.nasa.gov/ftools/caldb/help/batmasktaglc.html ) it seems that the count rate is divided by the number of active detectors.

So in this case it looks like the detection rate was more like 200,000 counts/s in the peak 2ms of the event. There would be 400 detected counts, assuming there are no other corrections for sensitivity or vignetting. However,  I think there probably are - the mask must take out about 50% of these counts and there are gaps between the detectors. A background rate has also been subtracted. So overall I guess that the first point in the burst is due to around 100 detected photons, and so on.


Size and Mass of a typical "small" asteroid that impacts the Earth?

For the asteroid not to break up it needs to either be big, or tough.
You can experiment with the impact effects calculator but you should notice that a rocky asteroid with a diameter of less than about 1km will partially break up on impact with the atmosphere, and there may be multiple craters formed.

If the asteroid is less than about 100m in diameter than the breakup will be complete enough that the resulting meteorites will fall at terminal velocity, and won't form craters in rock.

Iron meteorites are tougher, but even these are likely to break up if they are less than 500m in diameter.

Needless to say, these are not small events, and we have never actually witnessed any object hitting the Earth that is large enough to make it through our atmosphere in one piece.

The direct answer to the question is that there are no typical small impacts of bodies that don't break up. The Barringer "meteor crator" impactor was an iron asteroid, with a diameter of about 40 or 50m, that broke up on impact with the atmosphere, and fell in a circle of about 150m in diameter, forming the 1km diameter crater we see now. The mass of the impactor was about 1 to 2 million tonnes. It hit the atmosphere at about 15 to 17 km/s but by the time it reached Earth, it had slowed to less than 12 km/s. It exploded with the energy of about 10 Megatonnes of TNT. The dispersal of the fragments was not enough to from several craters. See a barringer type impact Or read about the impact


Why would all places appear to be at the center of the universe's expansion?

This is a famous analogy, which was prbably given to you in the video. Imagne that you are on a ball of dough full of raisins. You obviously perceive yourself as the center. Then, the dough starts to grow. The raisins are still the same size, but there is constantly more and more dough between them. From your position it would seem like there is always more and more space between you and everything else. You don't see yourself moving, but you see everything else moving away from you. This effect would happen anywhere in the universe, not only at the center. In fact, you would think - correctly, relatively speaking - that the center (if you can see it) is being pushed away from you. So basically, it all comes down to your point of view.

This expansion is thoroughly studied presently. The most common theory is that the universe contains a giant amount of energy (called dark energy) that is so far undetectable and that is causing the the space to expand. Think of it as yeast. There are other theories that are much more complicated, which a non-professional such as I wouldn't be able to explain. (For instance, there is one that suggests that our universe adheres to other universes, like soap bubbles, which adds space). But dark energy is the most likely candidate, so far.


Is the moon "perfectly" tidally locked and, if not, how long would it take us to observe it's rotation?

The question is interesting, but I suspect the answer is that the Moon will never show its "far side" to the Earth, because there are differences between the side that faces us and the far side that suggest there is something quite permanent about its orientation.  So while the rotation was locking, it either settled into a state of minimum potential that it has maintained ever since, or it built up the differences between the side we see and the side we don't after it tidally locked, but either way, this means it has showed us the same side for billions of years, so will likely continue to do that.  I don't think anything would likely knock it out, but we can't rule out chaotic orbital effects so I don't really know.  The Moon's orbit varies a lot with time, so maybe it's possible that the orbit itself could change, showing us the other side of the Moon.  Or, an asteroid hit or some such thing might occur.  A billion years is a long time, but I'll bet humanity will always see the same side from Earth.


Is the Sun prograde or retrograde with respect to the rotation of the Milky Way?

Prograde. This is usually the case for stars in spiral galaxies outside the most central regions.

A galaxy can be either rotation-dominated or dispersion-dominated, depending on whether its kinematics is dominated by ordered or random motion. Spiral galaxies such as the Milky Way belong to the first class, while ellipticals belong to the second. Irregular galaxies can be somewhere in between, with random motions but with an overall rotation.

In spirals, stars and gas generally rotate in the same direction (although they can have more random motion in their bulges, i.e. in the central parts). The Sun follows the overall rotation of the Milky Way, except for roughly 20 km/s in the direction wrt. the overall rotation; this direction is known as the Solar apex.

However, following a major merger event, the product can be two kinematically decoupled components. This is described well in Corsini (2014). Such a merger is required to perturb the system sufficiently.

On smaller scales, however, the turbulence of the gas clouds giving birth to stars are more random. Hence the rotation of a star may very well be in another direction than the overall disk rotation. As you say, the plane of the Solar System is tilted by 63º wrt. the plane of the Milky Way, in the direction that the Sun is traveling. This can be seen e.g. in this infrared IRAS image, where the angle between the bright Milky Way disk and the blue stripes — which is emission from dust in the plane of the Solar System — crosses at roughly 60º:

credit: Caltech.

The rotation of the Sun is also prograde wrt. the Milky Way (or else we would say that the tilt was 180º – 63º = 117º).


What good is the Einstein de-Sitter model?

The scale factor of the universe depends on the matter and energy density in a way that depends on which component is dominant.  This is discussed in the question How does the Hubble parameter change with the age of the universe? on the Physics Stack Exchange, and from that I have taken this graph showing how the scale factor changes with time for our universe:

For a (cold) matter dominated universe we get a dependence:

$$ a(t) \propto t^{2/3} $$

and for a dark energy dominated universe we get an exponential dependence of $a(t)$ on $t$. Just by looking at the graph you can see that the $t^{2/3}$ dependence was good up to about half the current age of the universe and after that the exponential growth becomes increasingly dominant.

So you are quite correct that the Einstein de Sitter model is not a good description of our universe right now, but it is a good description of the first half of the lifetime of the universe. Furthermore, because when we view distance regions of the universe we are viewing them as they were in the past it turns out that all the parts of the universe we can see beyond a redshift of about $Z = 2$ are still well described by an Einstein de Sitter model.

I would take issue with your statement that the Einstein de Sitter model is still taught and used to calculate the age of the universe. The most precise calculations of the age of the universe come from the Planck observations of the cosmic microwave background, and these most certainly do not use the Einstein de Sitter model. As for being taught, if you do a general relativity course you will be taught the FLRW metric and Friedmann equations. The Einstein de Sitter model is just a special case of the more general result.


If Venus had moon before and it fell back to Venus, why don't I see a unique, very big crater?

Venus has volcanism and weather, and those can cover or erode craters.  There are relatively few impact craters on Venus today, indicating that the surface of Venus is at most 600 million years old -- meaning that any older surface features have been erased.  The Earth's surface is even younger.

During the Late Heavy Bombardment, in the very early history of the Solar System, there was a period of time when many asteroids hit the Moon, creating many large impact craters.  It seems likely that the Earth and Venus got hit by many asteroids then, too.  Yet, no evidence of these craters is visible on Earth or Venus today. So, if Venus had a moon and that moon crashed into Venus thousands of millions of years ago, then the impact crater would likely have been erased by now.

And if Venus got hit by a sufficiently large object, then the energy of the impact might melt the entire surface of Venus, so that no lasting crater can form.

So, absence of very big craters from Venus is not evidence that Venus never had big moons.


Could an ejected "extra ice-giant" still be lurking in distant solar orbit?

Since I'm a hobbyist, I usually wait to see if someone a bit smarter wants to answer first, but I can give a couple thoughts on this.

  Hot Jupiters are thought to have migrated inwards, implying that
  another giant planet has been ejected in order to conserve the orbital
  momentum of those planetary systems.

In the article you posted (I'll pull the quote)

  The conservation of orbital momentum dictates, as planetesimals move
  from the outer disk inward, that Saturn, Uranus and Neptune must move
  outward. This process is known as the planetesimal driven migration

The conservation of orbital momentum he's talking about happens when objects cross each others orbits and interact, one gains orbital energy, the other loses energy.   That's not the only way planetary orbits can change.   Over time, there's tidal effects, orbital resonance and a sun can lose mass leading to gradual drifting or perhaps a sun can gain mass if the solar system passes through a dense dust/gas cloud.

But mostly what we're talking about here is a form of gravity assist as 2 planets get close enough that they kind of swing past each other, one moves in the other out.

More on that here:   http://science.howstuffworks.com/nomad-planet2.htm

Now, were gas giants ejected from our solar system, according to this question, somebody said no:

Is there any evidence that the Gas Giant planets in our solar system are experiencing orbital migration?

But, this article, and the article you posted that suggests otherwise, that it probobly did happen based on models, but when the solar system was young, like about 4 billion years ago, this model suggests the Solar system could have lost 1 or 2 ice giants.

http://www.space.com/13584-extra-giant-planet-solar-system.html

and we could still lose Mercury (though we probobly won't).   http://www.universetoday.com/14032/could-jupiter-wreck-the-solar-system/

  Where would such a hypothetical ejected ice giant be today? Should it
  be closer or further away than hot Jupiter-ejected planets because it
  is much smaller?

Tough call.  Using basic gravity assist mathematics, the closer to the sun the faster an object could be ejected from the solar system so a hot Jupiter probobly eject inner planets at a faster velocity on average than more distant Jupiter, but the bigger factor is the size of the star system, not the size of the planet.   The more massive the star, the faster the orbital velocities, the faster the Ejection is likely to be, even after accounting for escape velocity.

it's also important that the object being ejected is smaller than the object doing the ejecting, for example, Jupiter could pull Mercury away from the sun but Mercury couldn't pull Jupiter into the sun.   More massive wins the tug of war, but how much smaller the ejected object needs to be isn't that relevant.  Jupiter could throw a Neptune sized planet out of a solar system at almost the same speed as it could throw a Mercury sized planet out of a solar system.

Now, as to where it would be, planets aren't likely to escape a solar system at too fast a speed.   Jupiter orbits the sun at 47,000 KM/Hour and an optimal gravity assist could eject something way from Jupiter at 94,000 KM/Hour, (plus any velocity of the object's own, which would depend largely on eccentricity, but since it would cross Jupiter's path, probably wouldn't be hugely different than Jupiter's), and if you subtract escape velocity from the sun at that distance (47,000 * square root of 2), or 66.4 KM/Hour, your left with a maximum exit the solar system velocity of, roughly 28,000 KM/Hour, plus a bit - and that's maximum.  Average escape velocity would likely be less, but lets say 20,000 KM/Hour, which works out to be 1 light year every 50,000 years.  considering it left the solar system an estimated 4 billion years ago, that's 80,000 light years, which from where we are, is pretty much the far end of the Milky way and who can say how it's orbital velocity might have changed over that time as it passed by other stars, but basically, it could be anywhere in the Milky way, and, if you consider, our sun might have come from the Sagittarius dwarf galaxy, not the Milky way, it could be practically anywhere, even ejected from the Milky way.  4 billion years is a long time, even for a slow ejection.

or, it could be orbiting another sun - article on that here:  http://www.universetoday.com/94656/rogue-planets-can-find-homes-around-other-stars/

  Could it stay in an Oort cloud type orbit during several billion years
  (maybe ~15 orbits around the Milky Way) without being pulled off by passing stars?

Entirely possible though billions of years is a long time.   Passing stars usually don't pass very close, but I'm sure it's happened at least a few times in the past 4 billion years.

close enough to disrupt the inner planets - that's different and more rare.   Close enough to disrupt the Oort cloud, probobly happens every so often - but I wouldn't want to guess how often.

  At what distance could we today observe a Uranus sized planet? Should
  it stay in the ecliptical plane or could its orbit have become greatly
  inclined when it was ejected?

it depends if we know where to look.    If we saw it pass in-front of a star and we could plot it's path, then a number of light-years.   Looking into the blackness of space, much less distance, and it would depend on the planet's reflectivity too.   I wouldn't even know what to guess, but Eris, for example is 1/20th the diameter of Uranus and it's one of the larger Kuiper belt objects.   With relative ease, they could likely spot a Uranus sized object at well over 20 times the distance of Eris.   Now, if the question is, what's the furthest a Uranus sized object could be and not have been seen yet - that's hard for me to say but an object that size and at that distance would likely have it's own Trojans and I find it hard to believe it would have gone unnoticed.

as to "would it stay in an elliptical plane" - not necessarily.   A gravitational assist around a planet can alter the elliptical plane depending on the angle of approach.

hope that's not too wordy.  I can try to tidy up later.


Active Galactic Nuclei - categorisation on the basis of observer?

Yes, but most probably not in your mentioned example.
You need larger distances to make a difference, I guess.
However, it is by now largely accepted a unification model for AGNs, where the difference are mostly due to the angle of line of sight.

First introduced by Urry & Padovani, then developed for further observations.

Anyway, this is only half of the truth, since the AGNs evolve, and in this evolution feedback on the host galaxy is exerted. Also, the amount of feeding/obscuring gas is varying with time (redshift) and this has to be taken into account for a correct classification.
For the jets too, it is also possible that they forms only in certain stages of the AGN life...
As usual in astronomy, things are much more complicated than simple catalogs/models !


What is the time/size/rigidity ratio for a space object to become mostly round?

Based on observable data, I assume that there is a relationship
  between the size, rigidity and the passage of time; that will result
  in all objects subject to only their own gravitational influences
  (Given: no body is ever truly uninfluenced by others) becoming
  spherically shaped (round).

That's called hydrostatic equilibrium. That's one of the main factors that distinguish a dwarf planet from a smaller random piece of rock out there.

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

"A dwarf planet is an object the size of a planet (a planetary-mass object) but that is neither a planet nor a moon or other natural satellite. More explicitly, the International Astronomical Union (IAU) defines a dwarf planet as a celestial body in direct orbit of the Sun that is massive enough for its shape to be controlled by gravity, but that unlike a planet has not cleared its orbit of other objects."

There is no fixed size limit, because it depends on the composition.

https://en.wikipedia.org/wiki/Hydrostatic_equilibrium#Planetary_geology

"It had been thought that icy objects with a diameter larger than roughly 400 km are usually in hydrostatic equilibrium, whereas those smaller than that are not. Icy objects can achieve hydrostatic equilibrium at a smaller size than rocky objects. The smallest object that appears to have an equilibrium shape is the icy moon Mimas at 397 km, whereas the largest object known to have an obviously non-equilibrium shape is the rocky asteroid Pallas at 532 km (582×556×500±18 km). However, Mimas is not actually in hydrostatic equilibrium for its current rotation. The smallest body confirmed to be in hydrostatic equilibrium is the icy moon Rhea, at 1,528 km, whereas the largest body known to not be in hydrostatic equilibrium is the icy moon Iapetus, at 1,470 km."

So the range of transition between hydrostatic equilibrium and non-equilibrium is between approx 400 and 1500 km diameter and depends on a number of factors such as composition. There is no simple formula.

Dwarf planets are a good related topic, and I used them in the discussion, because many of them are above the limit of HE but close to it. But any cosmic body is subject to the same laws. Planets proper, moons, stars, etc - these all may be placed above or below the HE limit, depending mostly on size.

E.g. the Earth is clearly above the HE limit. But probably all comets are below it. A rock sitting in the dirt below your feet is clearly below it.


How accurate and complete is the Hubble sequence diagram?

The only way the Hubble sequence is truly incomplete is that it assumes such a classification applied to all stages of the universe. We now have telescopes that can see much further in space—and thus in time—and so we can see many more galaxies at different periods of time in the universe. Observations show that the Hubble sequence is still valid with one modification.

As this Hubble Space Telescope article explains, peculiar galaxies—so named because they exhibit odd features, including sizes and shapes—appear to constitute over 50% of distant galaxies observed by Hubble, while they make up only about 10% of local galaxies. Elliptical and lenticular galaxies made up roughly the same fractions (3-4% and 13-15%) in both periods, while spiral galaxies make up 72% of local galaxies and only 31% of distant galaxies.

The Hubble sequence classification still seems to organize galaxies well in this earlier period, with the glaring exception of peculiar galaxies. The conclusion the team has drawn is that many of the peculiar galaxies, one way or another, became spiral galaxies through collisions or other processes.


Is radar interferometry used, or feasible, for ground based astronomy?

For obvious reasons you cannot use active radar to observe anything much further away than the Moon. There are plenty of phased-array microwave/radar passive sensing systems that map the energy in those wavelength bands that are emitted from stars, quasars and various other "hot" astronomical bodies.

To answer one of your examples, measurement of volatiles is usually done by measuring absorption spectra; which is tough to do with Mercury since we can't look at the solar-illuminated side (with special exceptions for certain short-lived orbital positions). Basically, that's why we send off probes to get close to various planets and asteroids, so that we can collect high-resolution visible and microwave images and, in some cases, do some active illumination (radar).  I am not aware of any interferometric active radar on such probes, but someone more knowledgeable may well correct me.


Is there anything like a supermassive white hole? How are they formed? And where are they present?

White holes are a theoretical construction of General Relativity.

Despite extensive searches, nothing has been found: not a supermassive white hole, not a stellar-sized white hole, nothing. Thus, the answer to your question is: on our current knowledge, they don't exist anywhere.

It is unclear how could they be formed. The geometry of the Kerr-solution (i.e. rotating black holes) suggests a white hole could exist on the "other side" of a black hole, but currently it is pure speculation.


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.


Which kind of strategy should we take to discover Planet 9 and other KBOs?

This question already discusses the challenges of discovering planet 9

The main problem of the hypothetical planet 9 as compared to Sedna and 2012 VP113 is:

Sedna and 2012 VP113 have orbits that reach far out but currently they are near their perihelion so it was possible to observe them in the visible light spectrum. Planet 9's orbit is far out or at least it is currently near its aphelion. Otherwise it probably would have already been discovered.

Also the planet's orbit is probably tilted towards the ecliptic and it moves very slowly compared to the stars in the background.

At this position the maximum of its radiation would be emitted in the far infrared and it moves before the background of the Milky Way.

So to summarize:

We would need a long term observation with an far-infrared capable, spaceborne, telescope (because our atmosphere absorbs far infrared radiation) which has to include the background of the Milky Way. The telescope has to be able to detect faint infrared sources. We could be lucky and planet 9 just happens to pass in front of a star as we are observing it. Then we could get our first hint with an optical telescope. But that's pure luck and we can't plan towards that.

WISE already tried to find planet 9 but did not find it. The James Webb Telescope may be our sole instrument capable of discovering planet 9 directly. But it's not built to permanently survey an area of the sky although it could confirm a finding.

Gaia could probably detect planet 9 if it happens to pass in front a star.


The star at the center of TRAPPIST-1 is called 2MASS J23062928-0502285.  It was discovered by the Two Micron All-Sky Survey (2MASS), which imaged the whole sky in the infrared between 1997 and 2001.  This resulted in a catalog of over 300 million objects.  TRAPPIST-1 itself was cataloged in 1999.  The name is actually its coordinates in right ascension and declination.

The planets of the TRAPPIST-1 were discovered by the method of transit photometry.  The way this works is a telescope watches a star for a period of time and records the amount of light coming from the star.  They chart how much light is coming from the star as a function of time, creating a light curve.  If they see periodic dips in the intensity from the star, there is a high likelihood that that star has a planet in orbit around it.  The planet blocks the light from the star every time it passes between us and the star.  This causes the dips in the light curve.  One advantage to this method is that you can scan multiple stars in the same field of view, analyzing them all for planets.

By measuring how long it takes planets to pass in front of the star, how much light it blocks, and how often they orbit, scientists can calculate the masses of these planets and how far away from the star they are by using Kepler's laws of motion.

TRAPPIST-1 was initially determined to have planets orbiting it by the Transiting Planets and Planetesimals Small Telescope - South team.  From their data they determined that it had at least 3 planets.  One of these planets was in the habitable zone of the star.  They published their results in the journal Nature in May 2016.

Once TRAPPIST had determined that the system had planets around it, NASA trained the Spitzer Space Telescope on it.  Ground-based observations of Trappist-1 are difficult because it is so dim.  Spitzer, an infrared telescope, made more precise measurements of the light curves and determined that there were at least 7 planets in orbit around it, 3 of which were in the habitable zone.  Additional observations were made by numerous other telescopes including the Very Large Telescope, UKIRT, the Liverpool Telescope, and the William Herschel Telescope.  The results were also published in Nature.

Here's an image showing the light curve of the TRAPPIST-1 system as measured by Spitzer.


How to properly observe Solar Total Eclipse in 2019?

You can get some equipment especially designed for the eclipse.
But don't forget about a simple pinhole camera
Important to note that you shouldn't look through the pinhole. Instead, you are using the pinhole to project an image of the sun on the ground behind you.
The gaps between leaves in a tree act as natural pinholes so if there are any trees around you, you should be able to see lots of eclipse images

One of the easiest ways to safely watch a solar eclipse is to use 2 sheets of cardboard and make your own simple pinhole projector.
A partial solar eclipse projected on cardboard. Solar eclipses can look spectacular, but the Sun’s UV radiation can cause permanent eye damage or even blindness. Make your own pinhole projector to view a solar eclipse.
Projecting the Sun through a box projector, or projecting using binoculars or telescope (edit: shown below), or simply 2 pieces of card is a safe and easy way to view a solar eclipse.

Source

Light filtering through the leaves of trees during a solar eclipse creates images of the crescent sun, like the image created by a pinhole camera. (Bigstock)

Source


What are the arguments against the Feng and Gallo thin disk explanation of galactic rotation curves?

Feng & Gallo have published a series of extremely similar papers, all of which essentially claim that they have "discovered" a major flaw in the way (some) astrophysicists think about rotation curves. Instead of assuming spherical symmetry, they try to solve for the mass distribution, using a rotation curve, without assuming spherical symmetry, instead adopting a planar geometry with cylindrical symmetry.

Of course they do have a point; statements that the flat rotation curve can be compared with a Keplerian prediction (that assume spherical symmetry, or that all the mass is concentrated at the centre) are overly simplistic. So far so good, but they then go on to claim that their analysis is compatible with the total stellar mass of galaxies and that dark matter is not required.

So, in their planar model (and obviously this is open to criticism too) they invert rotation curves to obtain a radially dependent surface density distribution that drops pseudo-exponentially.

Problem 1: They concede (e.g. in Feng & Gallo 2011) that "the surface mass density decreases toward the galactic periphery at a slower rate than that of the luminosity density. In other words, the mass-to-light ratio in a disk galaxy is not a constant". This is an understatement! They find exponential scale lengths for the mass that are around twice (or more for some galaxies) the luminosity scalelengths, so this implies a huge, unexplained increase in the average mass to light ratio of the stellar population with radius. For the Milky way they give a luminosity scalelength of 2.5 kpc and a mass scale length of 4.5 kpc, so the $M/L$ ratio goes as $\exp[0.18r]$, with radius in kpc (e.g. increases by a factor 4 between 2 kpc and 10 kpc). They argue this may be due to the neglect in their model of the galactic bulge, but completely fail to explain how this could affect the mass-to-light ratio in such an extreme way.

Problem 2: In their model they derive a surface mass density of the disk in the solar vicinity as between 150-200 $M_{\odot}/pc^2$. Most ($\sim 90$%) of the stars in the solar neighbourhood are "thin disk" stars, with an exponential scale height of between $z_0= 100-200$pc. If we assume the density distribution is exponential with height above the plane and that the Sun is near the plane (it is actually about 20pc above the plane, but this makes little difference), a total surface mass density of $\sigma = 200M_{\odot}/pc^2$ implies a local volume mass density of $\rho \simeq \sigma/2z_0$, which is of order $0.5-1 M_{\odot}/pc^3$ for the considered range of possible scale heights.  The total mass density in the Galactic disk near the Sun, derived from the dynamics of stars observed by Hipparcos, is actually only $0.076 \pm 0.015 M_{\odot}/pc^3$  (Creze et al. 1998), which falls short of Feng & Gallo's requirements by an order of magnitude. (This does not bother the cold, non-baryonic dark matter model because the additional (dark) mass is not concentrated in the plane of the Galaxy).

Problem 3: For the most truncated discs that they consider, with an edge at $r=15$ kpc, the total Galaxy mass is $1.1\times10^{11}\ M_{\odot}$ (again from Feng & Gallo 2011 ). The claim is then that this "is in very good agreement with the Milky Way star counts of 100 billion (Sparke & Gallagher 2007)". I would not agree. Assuming "stars" covers the full stellar mass range, then I wouldn't dissent from the 100 billion number; but the average stellar mass is about $0.2\ M_{\odot}$ (e.g. Chabrier 2003), so this implies $\sim 5$ times as much mass as there is in stars (i.e. essentially the same objection as problem 2, but now integrated over the Galaxy). Gas might close this gap a little, white dwarfs/brown dwarfs make minor/negligible contributions, but we still end up requiring some "dark" component that dominates the mass, even if not as extreme as the pseudo-spherical dark matter halo models. Even if a factor of 5 additional baryonic dark matter (gas, molecular material, lost golf balls) were found this still leaves the problem of points 1 and 2 - why does this dark matter not follow the luminous matter and why does it not betray its existence in the kinematics of objects perpendicular to the disc.

Problem 4: Feng & Gallo do not include any discussion or consideration of the more extended populations of the Milky Way. In particular they do not consider the motions of distant globular clusters, halo stars or satellite galaxies of the Milky Way, which can be at 100-200 kpc from the Galactic centre (e.g. Bhattachargee et al. 2014). At these distances, any mass associated with the luminous matter in the disk at $r \leq 15$ kpc can be well approximated using the Keplerian assumption. Proper consideration of these seems to suggest a much larger minimum mass for the Milky way independently of any assumptions about its distribution, though perhaps not in the inner (luminous) regions where dark matter appears not to be dominant and which is where F&G's analysis takes place. i.e the factor of 5-10 "missing" mass referred to above may be quite consistent with what others say about the total disk mass and the required dark matter within 15kpc of the Galactic centre (e.g. Kafle et al. 2014). To put it another way, the dynamics of these very distant objects require a large amount of mass in a spherical Milky Way halo, way more than the luminous matter and way more even than derived by Feng & Gallo. For instance, Kafle et al. model the mass (properly, using the Jeans equation) as a spheroidal bulge, a disk and a spherical (dark) halo using the velocity dispersions of halo stars out to 150 kpc. They find the total Galaxy mass is $\sim 10^{12} M_{\odot}$ and about 80-90% is in the spherical dark halo. Yet this dark halo makes almost no contribution to the mass density in the disk near the Sun.

Problem 5: (And to be fair I do think this is beyond the scope of what Feng & Gallo are doing) Feng & Gallo treat this problem in isolation without considering how their rival ideas might impact on all the other observations that non-baryonic dark matter was brought in to solve. Namely, the dynamics of galaxies in clusters, lensing by clusters, the CMB ripples, structure formation and primordial nucleosynthesis abundances to state the obvious ones. A new paradigm needs to do at least as well as the old one in order to be considered competitive.


As a star begins to age and exhaust its hydrogen supply, pressure will build in its interior until temperatures rise enough to begin fusing helium into carbon. If the star is massive enough, this process will continue, using heavier elements each time.

Referring to this link on stellar fusion, depending on their mass, stars use a variety of elements from hydrogen to silicon as 'fuel'. Stellar cores of stars towards the end of their giant stages will have cores of iron, but iron doesn't fuse into anything heavier in a stellar core.


Is there any known asteroid or comet whose path goes through the Earth?

JPL and ESA provide tools to search for small bodies meeting user-defined criteria.
I tried:

H <= 24
MOID <= 1e-4 au

with each and got these results in common:

(89959) 2002 NT7, an H=16.5 (~1.4 km) asteroid with a 2.29 year period.
MOID≈4000 km but closest approach between 1900 and 2200 is 0.37 au; orbit rather highly inclined (i=42.3°).

(292220) 2006 SU49, an H=19.4 (390-780 m) asteroid with a 1.68 year period. MOID≈10,000 km; 3.2 lunar distance (LD) approach expected in 2029.

2014 DA, an H=22.7 (85-170 m) asteroid with a 1.85 year period and MOID≈4000 km. Discovered after a 9.3 LD approach; other approaches uncertain (JPL condition code 7) due to limited observational data.

2008 BO16, H=22.9 (80-160 m), 3.78 year period, MOID≈15,000 km, condition code 7.

2010 VB1, H=23.2 (70-140 m), 1.21 year period, MOID≈8000 km, 1.5 LD approach expected in 2068.

Each tool also listed a few bodies which the other didn't.
MOID computation methods vary, and I wouldn't assume that it's known very precisely even for numbered asteroids.
The ESA database appears to store MOID at a resolution of 1e-5 AU (1500 km).
JPL Sentry uses different criteria and shows different results including Apophis and Bennu.


Why Is The Expansion of The Universe Allowed To Move Faster Than Light?

You are not allowed to move faster than c in sense of classical motion that is velocity can't be greater than  c but ,universe is expanding not because objects are moving away but new space time is being created between them which increases distance between them and that can happen such that expansion is faster than c , there is no violation of theory of relativity.
I hope that's clear


Is a wavy path possible for a shooting star?

I saw a zig zag meteorite in Bukuru, Northern Nigeria, when I was about 13 in 1959. That started from small to increasing swings, then went out near the horizon. For many years I puzzled about this, but rarely mentioned it, because no one would believe it. Years later I attended an astronomy lecture at college in London. I cornered the astronomer with this sighting and he said we know what this is. A flat dish shaped meteorite enters the atmosphere shallowly & flies in a circular motion that gets wider as it approaches the earth then extinguishes. Seeing this from the horizon, it appears to zigzag down. He told me that I was very very lucky to witness this meteor show, and I am glad that others have seen it too. Adios, UFO folks.


What are the current accepted theories of the formation of the Uranian moon Miranda?

As Miranda is a rather small object (only 235km diameter) it may simply have not enough mass to make it matter settle into hydrostatic equilibrium under the influence of its gravity, thus it basically retains the irregular shape most asteroids have. This nice arxiv paper discusses the mass limits necessary for a stellar body to settle into a nice round shape:

http://arxiv.org/ftp/arxiv/papers/1004/1004.1091.pdf


Why would atmospheric absorption increase rather than decrease the antenna temperature in Penzias and Wilson's famous CMB observation?

Short answer.

Great question! Ask yourself what absorbs better, something that is white, or black.Then ask yourself what radiates better. The answer is the same thing. It turns out that absorptivity and emissivity are linked pretty closely.

Kirchov's Law of Thermal Radiation can be stated as:

  For an arbitrary body emitting and absorbing thermal radiation in thermodynamic equilibrium, the emissivity is equal to the absorptivity.

If you know that the atmospheric absorption at a given wavelength is 0.01, then you could estimate the emissivity to be 0.01 as well. It doesn't mean it's exactly right, but it's a great start.

If you then say the average temperature of the atmosphere in the region where absorption (and thermal radiation) at 4080 MHz is 230K, then the Noise Equivalent Power (NEP) will be 0.01 time 230 K or 2.3 K.

How can we express power in terms of a temperature?

Wait a minute, thermal radiated power varies as something like temperature to the fourth power! How can we add two temperatures together, or multiply them by 0.01?

It's because the energy of the photons we're talking about is way down on the left edge of Planck's blackbody distribution. See for example this answer to the question Why doesn't thermal radio emission from a DSN “hot dish” completely swamp the benefits of a cold LNA? Down at photon energies well below $k_B T$ we can use the Rayleigh-Jeans law where the power at a given frequency depends linearly on temperature.

Plotted on a log-log graph, you can see that the peak heights increase three times faster than the straight-line low-frequency segments do, showing the $T^3$ dependence of the spectral density peak height versus the linear behavior in the Rayleigh-Jeans regime. If you integrated the total area under the curve, you'd get the $T^4$ dependence of the total power radiated by a blackbody.

below: From New Jersey Institute of Technology's Dr. Dale Gary's nicely-written Physics 728 Radio Astronomy; Lecture #1 notes:


River-like artifact in perseverance rover's photo of Mars

The image in question appears to come down from the rover "down-look" camera.  Here is a raw image of that, while this is a raw image taken next to it (you can line up the crater part in the left of the first with the main crater in the second).
While both list Sol 4 as the acquisition date, they list Feb. 23 and Feb. 24 as the Earth dates, while local time is separated by just 14–15 minutes.  Despite those dates, which seem pretty incompatible to me, I have a feeling that that's when the images were downlinked to Earth from the rover.  The "down-look" camera is "mounted beneath the rover, looking downward at the surface during landing."  And, those do not look like images of the surface to me that I would expect if you were just a few inches away, instead they look like meter-scale pixels, not millimeter-scale pixels.  So, I think these were images taken while it was landing, a few minutes apart.
Given that premise, I looked at a close-up of the HiRISE image of the landing site, which is nominally 25 cm/pix, and that crater in the second image matches the crater in the HiRISE image on the left, just rotated about 90° clockwise.  So, this was a descent image, not an image from the surface.
With that knowledge, those are sand ripples, which are basically small dunes.  These are all over Mars, so it's nothing unusual and does not have anything to do with it being near or in a lakebed, but just have to do with the wind and particle size of the martian regolith.


This frustrated me as well when I first used the Tycho-2 catalog. Not finding a well known bright star can be disconcerting. Quoting from http://heasarc.nasa.gov/W3Browse/all/tycho2.html

  Supplement-1 (not part of this HEASARC database but available at
  ftp://cdsarc.u-strasbg.fr/cats/I/259/suppl_1.dat.gz) lists stars from
  the Hipparcos and Tycho-1 Catalogues which are not in Tycho-2.

I only skimmed that file, but I think this might be the line you're looking for:

5331 01752 1|H|078.63446353|-08.20163919|    1.9|   -0.6|  0.6|  0.5|  0.7|  0.5| | 0.312|0.012| 0.283|0.010|999|T| 24436

(the "-0.6" is the U-B color index, not the magntiude)


What is the line of light in galaxy cluster MACS J1206?

I have highlighted the feature I believe you are talking about. It looks like a galaxy that has been repeated (smaller green oval). There are several foreground objects that appear to be causing additional gravitational lensing (red arrows). Due to the shapes of the objects causing the lensing effect, the apparent image can be affected in many different ways, such a image duplication (multiple identical images of a galaxy, etc.), magnification, distortion, etc. The universe is massive and three-dimensional and we still don't understand that much of it yet.


The formula you have written resembles the Stefan-Boltzmann law, and its correct form is $$T^4 = \frac{L}{4\pi R^2 \sigma_{SB}}$$.  It relates the luminosity of a blackbody of a given radius to its effective temperature. Earth as a whole can be assumed to be a black body at an effective temperature. So you can calculate the effective temperature of the "earth". This is very well explained in the example section of this wiki page: https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law

For calculating the effective temperature of the polar region, first assumption is that polar region is a black body. Then the question to ask is: what is the effective teperature of the polar region given that the it reaches equilibrium when the Sun light falls on it. To calculate this further, you would need to calculate the angle at which the sun light fall on the polar region you are interested in and also the distance travelled by the sun light in the atmosphere. These parameters will vary with respect to the time of the year, time of the day and the region you are interested in (North pole, South pole). Some calculated temperatures are given on the same wiki page. I hope that helps.


What is it exactly about these flares of infrared light from Sgr A* that "confirms" it is a supermassive black hole?

We have reasonably good measurements of the mass of Sagittarius A*, thanks to measurements of the movements of stars like S0-2 over several decades. It's been well-established that the mass of the central object is $M\approx4\times10^6M_{\odot}$; this alone is fairly good evidence for a supermassive black hole, and we can constrain the size of the object with the measurements (Ghez et al. 2008). Models of the orbits of other stars have further improved these results.

The recently-published paper (Abuter et al. 2018) uses a similar technique. The motion of the flares is well-described by the rotation of a "hot spot" of gas in the inner reaches of the accretion disk, with the flares arising from magnetic recombination or some similar event. In particular, it lies near the innermost stable prograde circular orbit (ISCO) - just outside it, actually (the orbital radius can be found because we know the mass of the object and the period of the orbit, with the best-fit model of the latter being $40\pm 8$ minutes). This both constrains the object's size and even qualitatively provides support for the black hole model, as we might expect to see such events around a supermassive black hole.

Looking at those articles, I think the use of the word "confirm" is inaccurate. As far as I can tell, the term is only used by the project leader, Reinhard Genzel, in that ESO statement - and it's not a claim repeated in the paper. The team describes their results as "strong support" for the supermassive black hole model, and say that their findings are "consistent with" that theory. As scientists should be, they're cautious. The results don't definitely confirm that Sagittarius A* corresponds to a supermassive black hole; they're simply additional (excellent) evidence for it.


How to make motion of the Sun more apparent at seconds scale?

The obvious answer is to use a telephoto lens -- or any other magnification scheme.  As an extreme example, if you had a post 1 km tall, the shadow of its top (think sundial) would move pretty clearly.  If you re-image a short post, or just re-image the sun itself, which enough magnification, you'll see the motion.

This is kind of the same as trying to observe a celestical object with a high-power telescope. If you don't have an equatorial mount, everything in your field of view will move quite noticeablly.


What would change if Venus rotated at a speed and direction similar to Earth?

I'm interested about changes in the core and mantle behavior, a
  potential magnetosphere, changes in the atmosphere and tectonic
  plates.

A lot of this is very theoretical.   Venus' atmosphere is nearly 100 times as massive Earth's atmosphere.  It's also nearly all CO2, a greenhouse gas, which means it's good at trapping heat.   That wouldn't change if Venus' rotation rate was faster.

"Core and mantle behavior" is a bit of an unusual statement, cores rotate with the planet and they slowly cool, there's some convection vs conduction going on, but it's difficult to study the cores of other planets.  It's hard enough studying the core of Earth.   But what we know of the core of Earth, or think we know is that Earth's core and Earth's crust rotate at slightly different rates.  This may be due to Earth's crust slowing down over time and the core, not slowing down as fast.   There's a slight variation in rotation rate.   Also, Earth's inner core is solid, Earth's outer core is somewhat liquid (though extremely viscus), and as it cools, the inner core slowly grows, the outer core shrinks and in the process heat is released.   This process creates a flow, which may be partially influenced by the Moons orbit, and together the circulations are thought to create Earth's magnetic field.   This isn't certain, but the flow of the outer core is thought to be the cause and Earth's rotation may play a role in that.

So if Venus rotated much faster, in combination with it's proximity to the Sun and the solar tidal forces, it's possible a faster rotating Venus would have a permanent magnetic field.   It's far from certain, but that's a possible outcome.

Plate tectonics is more tricky.  Various studies suggest that planetary size has a lot to do with plate tectonics, and abundant water plays a role too, oceans making plate tectonics easier.   Venus is on the small size and it has almost no water, so it's not a good candidate for plate tectonics.   Venus also has very little granite.    This is geology more than astronomy, but abundant granite (IMHO) plays a role in plate tectonics.   The rocky bodies in our solar-system.   Mercury, Venus, Mars, the Moon, are all, basically basalt like on their surfaces.   Earth formed large granite land masses that float above the more dense basalt like layers under the oceans.   Without granite land masses and without oceans, I don't think Venus is a good candidate for plate tectonics.

Did Venus ever have plate tectonics, like billions of years ago?   Maybe.   I have no idea, but maybe.   Would it have plate tectonics if it rotated faster?   I doubt it.  A magnetic field - maybe.  Plate tectonics, I don't think so.

This question is probably too general for stack exchange and it may be closed, but I don't believe that just spinning Venus faster would change all that much apart from maybe giving it a magnetic field, and that wouldn't change all that much on Venus. It has an induced magnetic field anyway.

If you could give Venus an ocean, maybe make it more massive and move it further away from the sun, then some interesting things might happen like plate tectonics, which could have lead the planet down a different path, perhaps more similar to Earth.

Earth was able to absorb CO2 into it's vast oceans and take in CO2 by photosynthesis and rocks were able to absorb CO2 by plate tectonics, and Earth was far enough from the sun to not have it's surface water evaporated and lost like what probably happened to Venus.

I think planetary formation, based on size, type of star, temperature, initial materials, etc, will be a very interesting field of study when/(if) big enough telescopes are set up to actually get a look at distant planets.   It's very difficult to even observe, much less, study a planet that's light-years away.   The so far twice or three ties delayed James Webb Space Telescope might get the ball rolling on this subject with better observations of exo-planet atmospheres, but it's a long ways away from being well understood.  The James Webb ST is an enormously difficult undertaking, so we should be patient.  With luck, it'll be up and taking in images within a few years.

Finally, would Venus' rotation, if it was faster, affect other planets?    Basically not at all.   Jupiter's rotation doesn't affect Earth.   Rotation rate doesn't affect other objects at great distances.


What percentage of a lunar meteor strike is blown back into space?

There are some invariances that actually lend themselves well to estimating an answer to this question.  From the Deep Impact mission white paper:

A 1 mm projectile striking a target at 10 km/s will yield the same
result as a 1 m projectile striking at the same speed, provided all
distances are scaled by the same ratio of 1,000 = 1 m/1mm and all
times are multiplied by the same factor. Thus, if the 1mm projectile
makes a crater 6 cm in diameter in 300 ms, the 1 m projectile will
create a 60m diameter crater in 300 s.

The same paper gives us a set of three equations to estimate crater diameter. These equations are the result of experimental research combined with modeling the Navier Stokes differential equations governing the conservation of energy and momentum in materials. The first equation is:
$$\pi_2=\frac{1.61gL}{v_i^2}$$
Where $\pi_2$ is the inverse of the Froude number, $g$ is the local surface gravity, $L$ is the projectile diameter, and $v_i$ is the impact velocity. We will use an impact velocity of 12.6 kms taken from this paper. The second equation is:
$$\pi_D=C_p\pi_2^{-\beta}$$
Where $\pi_D$ is a dimensionless measure of crater diameter, and $C_p$ and $\beta$ are material constants. The third equation is:
$$\pi_D=D(\frac{\rho_t}{m})^{-1/3}$$
Where $m$ is the mass of the asteroid and $\rho_t$ is the density of the lunar surface.  The top 10 or so meters of the lunar surface are regolith at about 1.5g/cm³, but the next several km are mixture of bigger, more dense ejecta from billions of years of impacts, combined with finer grained regolith, according to this paper.  Given the overall moon density of 3.34 g/cm³, we'll estimate the density of this top layer as 2.5 g/cm³. Solving for $D$ and then plugging in all the values of our variables gives us a crater radius $R$ of approximately 2.5 km.
In an asteroid impact, the fastest moving ejecta comes from near the center of the crater.  The ejecta closer to the edge of the crater has much lower velocity:

The equation governing the velocity of the ejecta $V_{ej}$ is therefore partly a function of $r$, the distance from the center of the crater.
$$V_{ej} = \frac{2\sqrt{Rg}}{1+\epsilon }(\frac{r}{R})^{-\epsilon}$$
Where $\epsilon$ is a material coefficient of 1.8.
We can solve the above equation for $r$ and solve using $V_{ej}$ as 2.38 km/s, the lunar escape velocity.  This yields a value of 275m for $r$.  That means that from the crater with a radius of 2500m, the only ejecta to reach escape velocity comes from the interior most part of the crater with a radius of 275m.
The depth of the crater can be estimated as $d=L\sqrt{\rho_p/\rho_t}$ where $\rho_p$ is the density of the projectile (asteroid).  Since the density of the projectile (2.6g/cc) and the estimated density of the lunar surface (2.5g/cc) are similar, then the depth would be approximately $L$, or 370m.
If we estimate the volume of the crater as a cylinder, then the total volume of lunar ejecta will be $\pi*R^2d$ is about 7.21e9 cubic meters, and the lunar ejecta to reach escape velocity will be $\pi*r^2d$ or about 8.79e7 cubic meters or a little more than 1% of the total ejecta.  This may not seem like much, but the total volume of Apophis is only 2.65e7 cubic meters.  That means that the ejecta reaching escape velocity will be more than 3 times the original volume of Apophis!
Notes:

The ejecta plume is in an inverted cone, so even given ideal geometry, most won't make it to earth.
The ejecta that are just under escape velocity will obtain an orbit that leads them to crashing back into the lunar surface.
The field of asteroid impact modeling is still in quite a bit of flux. Also, the models tend to perform less well for very large asteroid impacts since we have no ability to perform experiments on that scale.  It wouldn't surprise me if the total escape velocity ejecta calculated above differed by an order of magnitude in either direction to a similarly sized lunar asteroid impact.
My codes is available on request.


Are there any estimates for the combined mass of all near earth objects (NEOs)?

Short answer: The total mass of the known NEOS is about $8 \times 10^{17}\rm\,kg$, if we assume average density of $2\rm\,g/cm^3$.
Long Answer: I used the NASA JPL data query website. Instead of mass, they have diameter for equivalent spherical shape in kilometers for NEOs.
Here are the top 10 results from the query:
1036 Ganymed (A924 UB)      37.675
109P/Swift-Tuttle           26
3552 Don Quixote (1983 SA)  19.0
433 Eros (A898 PA)          16.84
C/2001 OG108 (LONEOS)       13.6
C/1991 L3 (Levy)            11.6
1P/Halley                   11.0
4954 Eric (1990 SQ)         10.8
1627 Ivar (1929 SH)         9.12
1866 Sisyphus (1972 XA)     8.48

Out of 24877 entries for NEOs, there are only 1268 NEOs with an entry for the diameter.  If we convert these to volumes using $V= \frac{4}{3}\pi r^3$ and sum, we get $4.21 \times 10^{5}\rm\, km^3$ of total NEO volume.
If we assume an average asteroid density of $2\rm\, g/cm^3$ = $2000\rm\, kg/m^3$ = $2 \times 10^{12}\rm\,kg/km^3$ , then the total mass is $8.42 \times 10^{17}\rm\, kg$.
As a comparison, the total mass of the asteroid belt is estimated at a whopping $2.39 \times 10^{21}\rm\, kg$. So, even with comets, the NEOs are much less massive than the asteroid belt.
This estimate of total mass may be somewhat conservative, because it leaves out the mass of most of the known NEOs. However, I don't think it is too conservative since about 90% of the mass estimate is accounted for in the largest 10 asteroids/comets listed above.  The smaller stuff doesn't contribute much to the overall estimate.


Influences from outside the observable universe explaining dark energy and expansion?

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

  Could some pressure from outside of our universe

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

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

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

  causing the expansion

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


From the point of view of an observer hovering above the Earth's surface, the rotation of the Earth is eastward. That is, points on the surface appear to move in an easterly direction as the Earth spins.

Extending this to the orbital motion, there are at least two possible interpretations. One is that the spin angular momentum and orbital angular momentum are in the same direction. This is roughly true (and certainly closer to true than the opposite). Another interpretation would be that the Earth moves around in its orbit such that it heads in an easterly direction when referred to a longitude on the Sun. This is also approximately true.

If you are asking what is a general definition of the north pole, then I suppose it could be the direction of the angular momentum vector. Then yes indeed, the right hand grip rule tells you the spin is eastward as it relates to north.


Does the density in the core of a "higher mass" star stay generally constant while it evolves on the MS?

The most important thing that happens is hydrogen is turned into helium, which essentially means that electrons and protons are getting merged into neutrons (the neutrons inside the helium). That reduces the number of particles.  For example, if you turn a pure hydrogen gas into a pure helium gas, you now have half the electrons you had before.  Also, you have 3 particles (a He nucleus and 2 electrons) where before you would have had 8 (in the case of pure H initially, just as an example).  Losing particles means you lose pressure at a given temperature and volume (it would be proportional to number of particles), so the core must contract.  The temperature does go up a little, but not much because nuclear burning is very temperature sensitive.  But the particle density drops a great deal, so for the density to stay the same, the core pressure must drop quite a bit, perhaps by almost a factor of 1/2.

The reason this might not require the core density to change is that the core pressure scales roughly like the radius to the -4 power (because of the requirements of force balance, which balances the pressure times the surface area, which scales like P*R^2, with the gravity, which scales like 1/R^2).   So that's quite a steep drop in P as R rises a little, and apparently the small rise in R is enough to compensate for the large drop in core P, to keep the density the same (based on your professor's statement that it does stay nearly the same).  It must be essentially a coincidence of how these things work out, it's not obvious to show why the density should be exactly constant but at least we can see that a large drop in P is compensated well by a small rise in R.  The physics of convection is pretty tricky, and there is only an approximate treatment called "mixing length theory" but it's never really been clear how to do this in a formally correct way.


From our world's perspective, does the full moon look larger in one city than it does in another?

Your son is more or less correct. The moon's size doesn't change appreciably. At best you only see the size vary by about 13% (in angular diameter).

The variation in the apparent size of the moon comes from the fact that the moon's orbit around us is not perfectly spherical and sometimes it is closer and sometimes farther. The moon will appear largest when a full moon coincides with the moon being at its closest point in its orbit. This is colloquially referred to as a "Super Moon". The opposite, being at its farthest point in its orbit during a full moon, is known as a "Micro Moon" or "Mini Moon". These are really the two extremes, but most often the moon is a more average size that doesn't appear to change much. Shown below is an image of both a Super Moon and a Micro Moon. You can see the size difference, which is noticeable, but not hugely so. If you want to see a large moon, find the time when the next Super Moon occurs (a good upcoming Super Moon is on November 14, 2016).

You also do mention the Moon Illusion, where a Moon on the horizon appears larger than it really is. The cause for this is debatable, but it is a known optical illusion. I believe the reason for this effect is that near the horizon, you have points of reference that allow you to judge the size of the moon different than when it is high in the sky, far from other comparison to other objects. You can attempt to view the Super Moon as it is rising so as to take full effect of this illusion, but try to do so in an area that isn't flat and devoid of structures (e.g., don't watch the Moonrise over a body of water).

As for your father, possibly he saw a Super Moon near the horizon which maximized both the optical illusion and the moon's natural size variability. Possibly he his memory also became exaggerated over the years so he remembered a Moon which was larger than it really was.


How long would it take for a rogue planet to evaporate in the late stages of the Universe?

Before the evaporation of black holes that you mention, our universe will enter what is known as the Black Hole Era. About $10^{40}$ years from now, all the protons and neutrons in the universe will have decayed into positrons and neutrinos. This is how the last of the planets will pass away.

The Black Hole Era is so named because at this point only black holes and elementary particles will remain.

It should be noted that there is currently no evidence for proton decay, and so this phase of the Universe is strictly theoretical.

Source:

The Decay of Heaven - DeepAstronomy.com


What are the Kinematics / Dynamics behind the motion?

Imagine you are watching a car drive down the street from right to left (in front of a building.  It goes from right to left.
Now imagine watching that car with your head on your left shoulder.  The car goes from the bottom of your point of view to the top.
If you move your head as the car is driving past, you will see it come from the right but leave to the top of your point of view.  This doesn't mean that the car changes direction, only your head is turning.
This is relevant because the rotation of the Earth means that over the time of the eclipse, your head turns. If you make a representation that keeps the horizon level and the sun in the centre, the motion of the moon relative to the sun will appear to curve.  This is nothing to do with the actual motion of the moon it is just an effect of the turning of the observer by the spinning of the Earth.


First, Azimov was writing (Edge 1982, and Earth 1986) before the first extra solar planets were tentatively detected (1989), or definitely detected 1991 or 1992. So what he wrote could not be based on any real data on extra solar planets, and must have been an educated guess.
However both books were written after the discovery of Charon, so he may have been ill advised to claim that large moons were unlikely around non-gas giants.
Personally I think both the large moon and broad planetary ring guesses are unlikely to pan out. Uncommon maybe but not uncommon enough for Azimov's purpose.
If you believe it, we have already discovered an exoplanet with a more impressive ring system than Saturn's


How can neutron stars have gaseous atmospheres?

Gravity is only important insofar that it is capable of compressing the material to high densities. Whether that material is capable of solidifying depends on the competition between Coulombic potential energy and the thermal energy of the particles. The former increases with density, the latter increases with temperature. A dense plasma can still be a gas if it is hot enough.

A rough formula for the exponential scale height of the atmosphere is
$$ h = \frac{kT}{\mu m_u g},$$
where $T$ is the temperature of the gas, $m_u$ is an atomic mass unit, $\mu$ is the number of atomic mass units per particle and $g$ is the surface gravity, with $g = GM/R^2$.

For a typical neutron star with $R=10$ km, $M= 1.4M_{\odot}$, we have $g=1.86\times 10^{12}$ m/s$^2$. The atmosphere could be a mixture of ionised helium ($\mu=4/3$) or perhaps iron ($\mu = 56/27$), so let's say $\mu=2$ for simplicity. The temperature at the surface of the neutron star will change with time; typically for a young pulsar, the surface temperature might be $10^{6}$ K.

This gives $h = 2$ mm.

Why is this not a "solid"? Because the thermal energy of the particles is larger than the coulombic binding energy in any solid lattice that the ions could make. That is not the case in the solid surface below the atmosphere because the density grows very rapidly (from $10^{6}$ kg/m$^{3}$ to more than $10^{10}$ kg/m$^{3}$ (where solidification takes place) only a few cm in, because the scale height is so small. Of course the temperature increases too, but not by more than a factor of about 100. After that, the density is high enough for electron degeneracy, and the material becomes approximately isothermal and at a small depth the "freezing temperature" falls below the isothermal temperature.


Is it possible for planetary rings to be perpendicular (or near perpendicular) to the planet's orbit around the host star?

Yes, the plane of the rings of Uranus are at about 98 degrees to the plane of its orbit around the Sun.
This means that the ring system looks as in your picture twice per orbit. As the planet orbits the Sun, the rings, although still inclined at 98 degrees to the orbital plane gradually become "face-on" when viewed from the Sun. This will happen about quarter of an orbital period after the configuration illustrated in the picture. Then another quarter of an orbital period later, Uranus will be on the other side of the Sun, but with its rings tilted as shown.


Well it kind of makes sense, but what is important here is the Earth's velocity relative to the Moon, not the Sun!

Roughly: the Moon-Earth separation is 400,000 km and a complete orbit takes 27 days. Thus the relative orbital speed is more like 1 km/s and so a 20km diameter beam easily covers the expected relative motion of about 2.5 km during the 2.5s round trip.


Most general purpose observatories release the data taken on their facilities after the expiration of the proprietary period (this is the time, typically 12-18 months, where the data is only available to the proposers for the telescope time so they can work on it without being "scooped"). "Focused telescopes" in the sense of those that are performing surveys or looking for specific types of objects, tend not to release the raw data, instead releasing processed data or catalogs.

Some examples of data archives that provide raw or processed data include:

the NOAO Science Archive: provides access to 40 telescope+instrument combination from the US National Optical Astronomy Observatory
the ESO Science Archive Facility: access to raw and processed data from the four 8-m VLT telescopes plus the VLTI and the smaller (1-3.6m) telescopes on La Silla, Chile
the MAST archive at StSci: contains data from Hubble, Kepler and K2, TESS, SwiftUVOT, XMM and many others
the ING archive: for the Isaac Newton Group of telescopes of La Palma (1.0m JKT, 2.5m INT, 4.2m WHT telescopes)

Querying multiple archives for data is the role of the Virtual Observatory; there is a page of links to tools at SAAO and the Data Discovery Tool


Help in determining the features of an unusual, fictional star system

First it will be important to consider the term 'relativistic speed'. If by that you mean something like 0.1c, it will only change the colour of the stars as you mentioned in the bounty description. However, if it means something with higher Lorentz Gammas (like 0.9c or 0.99c), all other relativistic effects come into play. There's relativistic beaming and aberration combined, which means that all the light that you receive from systems with respect to which you're moving at relativistic speeds will only be received in small beams towards the direction you're moving in and those will be strongly blueshifted and intensified. Watch this animated video for an illustrated view of what I mean - https://www.youtube.com/watch?v=JQnHTKZBTI4. (It's not a high quality video, but it is very effective in demonstrating what I just wrote.)

So, in effect, you will possibly see only three major sources of light in the sky:

The parent planet
The parent star
The bright patch of the sky in the direction of motion, highly blueshifted, with brightness dependent on your speed

Their relative brightnesses will depend on:

distance to parent star
distance to parent planet
albedo of the parent planet
speed of motion through the ism

For a day and night cycle:

The parent planet will obviously be at the zenith the whole time (or fixed location in the sky if you're at a different location).
The parent star will appear to move around the sky with the same period as the revolution period of the moon - say a few days at the most (will be fairly small as compared to the 12 year revolution period of the planet, so you can ignore 'synodic' effects to the first order for a single day/night cycle).
The sky will also move with roughly the same period as the sun, ignoring synodic effects.

Winds will be very complexly affected by the three sources (since heating due to radiation affects winds). There will also be tidal effects due to the parent planet which also play a role in the winds (similar to how tides work on the earth). So, you will have to take into account heating from the star, heating from the planet (which is constant due to tidal locking), tidal effects of the planet (again constant) and heating from the sky. Now the radiation from the sky can also act in a weird way, since blueshifting can give rise to strong emissions in UV, X-ray and Gamma ray photons, plus relativistic cosmic rays (everything you encounter will be in the form of cosmic rays due to the relativistic speed of your motion). These can ionize the atmosphere, heat it, cause there to be particle showers and aurorae, which can all affect wind patterns in complex ways, which I cannot exactly say much about, given my limited knowledge in atmospheric sciences.

As I mentioned above, yes, all interactions will be relativistic and will be similar to cosmic ray bombardment onto the moon you live on. Things will get nasty and you'll be having geomagnetic storms all the time. Satellite communications will probably never work. Expect these particles to arrive in the previously mentioned bright region of the sky due to aberration still applying to this case. You will see similar aurora like regions on the parent planet (http://www.spacetelescope.org/static/archives/postcards/screen/hst_postcard_0008.jpg), and the star will probably not be affected that much.

Oh and by the way, due to the antimatter nature of your system and the matter nature of the ism, the atmosphere would thin over time, and later these antimatter cosmic rays will start bombarding the moon. So if you stay in the ism for long enough, living on the moon will be difficult. Also, I am assuming that life evolved on your moon in an antimatter ISM and you have entered the matter ism only recently, as otherwise, the moon won't be stable for long enough for life (intelligent life) to evolve.

I will try to see if I can think of some other effects, but for now, I guess this will do?!


On gravitational wave radiation and arrangement of galaxies post- big bang

When you go back in time, take collisions into account. A very highly elliptical orbit primarily leads to chunks colliding at the very first periapsis.

Even if they are not chunks but very dense and small objects (point-like), if you extrapolate back in time so far as to the straight line "orbit", what does it mean? Extreme case of objects with zero relative initial velocity going against each other on a collision course - ups, this "orbit" does not have a chance to "decay due to gravitational wave radiation". Two smaller chunks collide and form a larger chunk, which has now a non-zero velocity (probably, if the chunks weren't exactly equal momentum). The chunk won't enter a straight line "orbit" around (towards) anything, but either an elliptical or hyperbolic.

Your extrapolation does suggest that initial "chunks" hadn't ideally equal momenta (masses*velocities); that's all.


Do astronomers and astrophysicists more often use diameters or radii when discussing about planets, dwarf planets, exoplanets and stars?

Definitely radii, with one notable exception...

When observers talk about how large an object is on the sky, they usually discuss angular size, which is related to the diameter of an object, not the radius.  So when discussing the angular size of, say, Alpha Centauri A (a few milliarcseconds), this is related to the diameter of the star, not the radius.


Why is the TESS spacecraft finding fewer exoplanets than expected?

I am not using TESS to find planets, but I'm reasonably sure that the answer is that nobody has looked very carefully at all the data yet.

The TESS data comes in two flavours. There were a subset of about 200,000 stars that were observed with a 2 minute cadence. These targets were chosen to be a combination of bright and small, heavily weighted towards nearby K and M dwarfs - to optimise the chances of finding a few thousand small planets. The vast majority of the reported planet discoveries so far will have come from this list.

https://tess.mit.edu/science/data/

In addition, the most of the sky was mapped repeatedly such that there is "full frame images" of patches taken every 30 minutes over at least 27 days.

In principle, every star in the sky is present in the full frame data. In practice, only stars brighter than about 15th magnitude have reasonable data that might allow the detection of larger planets; the so-called hot Jupiters.

There are expected to be about 20 million stars that are bright enough to facilitate hunting for hot Jupiters. The majority of these will be solar-type stars or more luminous. The occurrence rate of such objects is known to be about 1%, suggesting 200,000 stars will have them. But then only a fraction of about 10% of those happen to transit in front of the star, which is where the estimate of 20,000 comes from.

Extracting and analysing 20 million light curves from the full frame images is not a straightforward task and it simply hasn't been completed yet.

EDIT:

Chapter and verse on this can be found in Barclay et al. (2018). They study the likely numbers of planets to be found by TESS. They split the study into three samples. The 2-minute cadence sample of 200,000 stars, a 3.2 million candidate target list (CTL), which are generally fainter (but still with $V<13$) main sequence stars of solar-type and cooler, where there is a good chance of finding small planets, then a final list of about 20 million main sequence stars with $V<14.7$ around which giant exoplanets might be found; 16 million of these have $T_{\rm eff} >5500$ K and only 4 million have $T_{\rm eff}<5500$ K.

The estimated yields from these three samples are 1250 in the 2 minute cadence sample; about 4400 in the CTL sample and of order 10,000 in the faint full field image sample. Basically in agreement with what I wrote above.

A further important point is that the large full field image sample of giant exolanets will be heavily contaminated by false positives (i.e. not planets). It is understandable therefore that most of the effort so far has been on investigating and verifying the smaller sample of planets found around brighter stars.


How do astronomers detect gases that are in the atmosphere of exoplanets?

It is only possible to detect gases in transiting Exoplanets. The spectrum of the star is taken when the Exoplanet is not in transit and again when in transit. The differences between the spectrums is due to a small amount of light from the parent star passing through the upper atmosphere of the Exoplanet and being absorbed by gases in the atmosphere.
The effect is VERY small and difficult to detect.


Does the sun have a vertical movment?

Sure it does!

People who follow solar system bodies with the highest accuracy, including NASA's JPL, use the solar system barycenter (center of mass) for the origin of the plane of the ecliptic.

Since the big planets (Jupiter et al.) have some inclination, they pull the Sun up and down out of the plane of the Ecliptic by tens of thousands of kilometers. It's a small fraction of it's 600,000 kilometer radius, but it certainly happens.

You can see the data from the JPL Horizons website, or if you like Python, you can get virtually the same numbers by running the Skyfield package.

From Horizions I downloaded the position of the Sun and the four major planets of the solar system in 10 day steps from the years 1900 to 2100. Below I plot the three components X, Y and Z in the J2000.0 Solar system barycentric coordinates using the ecliptic as the reference frame. The black line is the motion of the Sun, and the color lines are for the four planets, but I have multiplied each by the the mass of the planet divided by the Mass of the Sun.

In the second plot, I added the four together, and you can see that together they mirror the motion of the Sun.

The last two show the movement of the Sun in 3D (two views). Note that the vertical scale is much smaller than the horizontal scale.

Horizons setup:

below: Black thick line: motion of the Sun in barycentric coordinates in the J2000.0 X, Y and Z directions, relative to the ecliptic. Four thinner color lines: motions of the four largest planets, each weighted by its mass relative to the Sun's mass. Short period lines are Jupiter and Saturn with Jupiter the largest amplitude, long periods are Uranus and Neptune, with Neptune the largest amplitude.

below: Black thick line: motion of the Sun in barycentric coordinates in the J2000.0 X, Y and Z directions, relative to the ecliptic. Thin red line: sum of the motions of the four largest planets, each weighted by its mass relative to the Sun's mass.

below: Two views  of the 3D motion of the Sun in barycentric coordinates between the years 1900 and 2100. Units are kilometers, and note that the scales are different for each axis.

class Body(object):
    def __init__(self, name):
        self.name = name

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

names = ('Sun', 'Jupiter', 'Saturn', 'Uranus', 'Neptune')

bodies = []
for name in names:
    fname = 'sun motion ' + name + ' horizons_results.txt'
    body  = Body(name)
    bodies.append(body)

    with open(fname, "r") as infile:
        lines = infile.read().splitlines()

    iSOE = [i for i, line in enumerate(lines) if "$$SOE" in line][0]
    iEOE = [i for i, line in enumerate(lines) if "$$EOE" in line][0]

    print (name, iSOE, iEOE, lines[iSOE], lines[iEOE])

    lines = [line.split(',') for line in lines[iSOE+1:iEOE]]
    JD  = np.array([float(line[0]) for line in lines])
    pos = np.array([[float(item) for item in line[2:5]] for line in lines])
    body.lines = lines
    body.JD    = JD
    body.pos   = pos.T.copy()

years = 2000 + (JD - JD[3652])/365.2564
Sun, Jupiter, Saturn, Uranus, Neptune = bodies

for body in bodies:
    body.rsun = np.sqrt(((body.pos - Sun.pos)**2).sum(axis=0))

planets = [b for b in bodies if 'sun' not in b.name.lower()]

massdict = {'Jupiter':1.898E+27, 'Saturn':5.683E+26, 'Uranus':8.681E+25,
            'Neptune':1.024E+26, 'Sun':1.989E+30}

for b in bodies:
    b.mass = massdict[b.name]

if True:
    plt.figure()
    for i, thing in enumerate(Sun.pos):
        plt.subplot(3, 1, i+1)
        plt.plot(years, thing, '-k', linewidth=1.5)
    for p in planets:
        for i, thing in enumerate(p.pos):
            plt.subplot(3, 1, i+1)
            thing = thing * (p.mass/Sun.mass)
            plt.plot(years, thing)
    plt.show()

all_four = Body('all_four')
all_four.pos = np.array([p.pos*(p.mass/Sun.mass) for p in planets]).sum(axis=0)

if True:
    plt.figure()
    for i, thing in enumerate(Sun.pos):
        plt.subplot(3, 1, i+1)
        plt.plot(years, thing, '-k', linewidth=1.5)
    for i, thing in enumerate(all_four.pos):
        plt.subplot(3, 1, i+1)
        plt.plot(years, thing, '-r')
    plt.show()

if True:
    fig = plt.figure(figsize=[12, 10])  # [12, 10]
    ax  = fig.add_subplot(1, 1, 1, projection='3d')

    x, y, z = Sun.pos
    ax.plot(x, y, z)

    plt.show()


How can a very old star be formed among Population III stars?

Many astronomers and cosmologists conjecture that Population III stars were very massive, perhaps even extremely massive. While this opinion is not universal, it does appear to be dominant. If this is the case, at least some of the very first stars died shortly after they formed, within a million years or less. This in turn would have meant the seeds for the first Population II stars would have been present in some places shortly after the very first stars formed and then died.
The Population III stars did not all form (and die) at the very same time, and those seeds needed to create the first Population II stars would not have been dispersed uniformly. So at least for some period of time in the early history of star formation, there would have been a mix of Population III stars in some places, Population II stars in others.


If the moon still had a magnetic field how long would have been possible to keep an atmosphere?

I'll give a slightly different answer: The escape velocity at the surface of our Moon is about 2.38 km/s. Derived from this paper, as a rule of thumb, an atmosphere can survive 4.5 billion years, if it's average molecule velocity is below 1/6 of the escape velocity of the planet/moon. Applied to our Moon, it's 2380 m/s / 6 = 396.67 m/s.

Carbon dioxide has a molecule mass of 44u.
The according temperature for an average molecule velocity for carbon dioxide is hence
$$\mbox{temperature}=(v_{\mbox{gas}}/157)^2 \cdot \mbox{molecule mass}\mbox=(396.67/157)^2\cdot 44\mbox{ K}=280.87\mbox{ K}.$$
Moon's mean surface temperature at the equator is about 220 K. That's well below the allowed 280.87 K. A carbon dioxide atmosphere could have survived 4.5 billion years according to these oversimplified assumptions.

When looking closer to the atmosphere, it turns out, that the higher layers of the thermosphere and the exosphere can reach more than 1000 K.
Even carbon dioxide can escape from Moon at this temperature over time:
The average molecule velocity for carbon dioxide at 1000 K is
$$157\cdot \sqrt{\frac{1000}{44}}\mbox{ m/s}= 748.5\mbox{ m/s}.$$

This results in a Jeans escape parameter of
$$\lambda_0=\left(\frac{v_{\mbox{esc}}}{v_{\mbox{gas}}}\right)^2 =\left(\frac{2380}{748.5}\right)^2= 10.1,$$
resulting in an escape rate of about $10^{-4}$ relative to a free molecular flow.

From this it isn't yet straightforward to calculate the period of time, Moon would loose a carbon dioxide atmosphere, since it's a function of the height-dependent temperature curve of the atmosphere. But it's at least clear, that Moon wouldn't loose a carbon dioxide atmosphere suddenly, since this is likely just for $\lambda_0 < 3$.


Copernicus did not figure out that the Sun was at the centre of the solar system. He merely proposed that a heliocentric model simplified the calculation of planetary orbits. Epicycles (circles within circles) were still needed in the Copernican model, for instance for the orbit of Mars, but there were fewer of them than in the Ptolemaic model.

The Copernican model received a boost when Kepler, discovering that planetary orbits were elliptical, removed the need for epicycles completely, thus increasing Copernicus' advantage over Ptolemy.

The first evidence that the Copernican model was a true representation of actual reality came with the observation of stellar parallax in 1806. Until then, it was preferred only because it was a simpler description - a much simpler one, after Kepler.