That will never happen to the Sun. It isn't massive enough to continue fusion beyond carbon. This site has detailed explanations of how the Sun and other kinds of stars evolve.

Yes, but for new papers ADS is just a catalogue - it doesn't store the full text. Often you can get the paper's preprint on arXiv, but this can differ from the published version (in particular, it reflects the paper as it was before peer review).

ADS has copies of old papers, and links to preprints of new ones on arXiv, but if you want the version of record from the journal site you generally still need a subscription.

Our reference frame is only locally inertial, where "local" means "close enough that the global geometry of spacetime can be ignored". In special relativity spacetime is flat everywhere and there is no such distinction, but in GR the same is not generally true.

Sufficiently distant objects have apparent recession velocities greater than the speed of light, but this doesn't break any physical laws. Special relativity says that velocity measured in an inertial frame will never exceed the speed of light, but cosmologically distant galaxies are not inertial from our perspective.

Locally, the expansion of the universe still obeys the first law of thermodynamics: considering a fixed proper volume of space, expansion acts to dilute the energy density within that volume, doing work in the process.

The energy to do this "comes from" the expansion, which means it slows down over time in the situation where there are attractive forces (i.e. gravity) associated with the energy density. Conversely the present-day universe has its energy density dominated by dark energy, which behaves as a repulsive force which ads energy to the expansion, accelerating it.

For a rigorous derivation of this behaviour your best bet is to get an introductory cosmology textbook and look into the Friedmann equations.

The same amount of dark matter, with the same basic properties, can explain galaxy rotation curves, galaxy cluster dynamics, large scale structure, the CMB anisotropies, and the primordial abundances of chemical elements.

"Something is wrong with the measurements" has none of that predictive power, and even more quantitative ways of stating that (e.g. modified Newtonian dynamics) cannot explain the data as well as dark matter does.

Ship A thinks they are standing still - again, both the Earth and Ship B are moving towards them.

The difference in distances is not because of the speed of the ship, it's because of the speed of light. Ship A receives light from Ship B that started travelling some time ago, when B was further away. As the two ships approach, the time lag decreases until it vanishes when they meet - which means that from A's perspective, time onboard B is running fast.

From either ship's perspective, the Earth is approaching (at the same speed an observer on Earth measures the ships to be travelling at), and the other ship is approaching at a slightly faster speed (which you can calculate with the relativistic velocity addition formula).

But from the ship's perspective, the distance from it to the Earth at any given time is smaller than the distance from the Earth to the other ship. The other ship is approaching faster, but it has more ground to cover. These effects cancel, and the two ships arrive at the same time.

Expanding is "a thing space can do" according to general relativity, but there is no corresponding theoretical explanation for how or why objects would shrink. It's also not clear how objects shrinking would reproduce observations like Hubble's law - why would objects further from us be shrinking faster?

It does. Any finitely-sized region of the universe today shrinks toward zero volume as you approach the Big Bang, but the universe as a whole can still be large, even infinitely so, at the moment of the Big Bang.

Historians and archaeologists work hard to make sure their dating methods are as accurate as possible.

On average, yes, but in reality the recession velocity is neither constant nor linear. Points at the distance of the CMB scattering surface are currently receding from us at more than three times the speed of light.

The Milky Way-Andromeda system is bound together by gravity, and so is unaffected by expansion. Newtonian mechanics is all you need to calculate the time until the two galaxies collide (notwithstanding the uncertainty in the current distance and relative velocity of Andromeda).

Nothing special: black holes are believed to obey something called the "no-hair theorem", which states they can be completely described by their mass, electric charge, and angular momentum. So there is no way to tell, at least from outside the event horizon, whether the black hole formed from matter or antimatter.

As to the second question, the mass in black holes that we know of is only a small fraction of the total mass. So there is no evidence for a large population of (ex-) antimatter black holes.

In principle, no. If you can compress any amount of matter within its Schwarzschild radius, it will become a black hole.

In practice, the only confirmed mechanism for the creation of the black hole is the collapse of a massive star, which sets a lower limit of about eight times the mass of the Sun. A black hole of this mass would have a Schwarzschild radius of about 23km.

An observer always measures their own time to be normal, but will see time running slower for a second observer who is in motion relative to the first. And this is reciprocal: for the second observer, their time is normal and the first observer's clock is running slow.

Space has to be involved because otherwise there are contradictions: consider observers A and B, where A is stationary on Earth and B is travelling at high speed to a distant planet. A will measure B's journey to take a certain amount of time, but because B's clock is running slower, they would conclude that the journey took less time.

If both observers were to agree on the distance B had travelled, then they would have to disagree on their speed. The solution is that they don't agree on the distance: not only does time run slower in moving reference frames, lengths are measured to be shorter. From B's perspective, the planet is approaching them and so the distance to it shrinks. Their clock measured fewer ticks, but the distance they travelled is also less, and so they can still agree with A about their speed.

No, you still need a fluid to carry the heat away. Assuming the point of the reactor is to produce electricity, water would still be a natural choice because it turns to steam which can then be used to drive a turbine.

Io, the most volcanic body in the solar system. It has a close elliptical orbit around Jupiter, and the changing strength of gravity as it orbits stretches and squeezes the planet, with the resulting friction being able to keep the core molten.

If there were only one bogie manufacturer in the world, yes. But in practice the demand for rail vehicles is high enough that countries with different gauge standards can support independent rolling stock industries.

They were always just an efficiency measure. Ring mains let you use less copper, which was in short supply in the UK during the post-war years when a lot of housing was being built to replace what had been lost to bombing.

It's just cheaper. Smaller gauge means smaller earthworks, bridges, tunnels etc.

Mountainous regions of Europe (Switzerland, southern France, the Basque country) also have narrow gauge networks that operate alongside more extensive standard gauge networks.

Hubble and JWST are very different instruments. They are complementary to each other, so we'll keep utilising both for as long as we can - it's been more than a decade since the final Hubble servicing mission, so eventually it is going to experience an unrecoverable failure.

The celestial coordinates are the same for everyone, by definition. But an individual observer must account for when and where on the Earth they are looking from to know where that point will be on the sky.

Because that person wrote a paper where they identified that number and showed some interesting result involving it. You could name a number yourself if you wanted, but unless you give the mathematical community a reason to adopt that name, it won't gain any notoriety.

"Expand" is simply the closest English word to describe a particular behaviour we observe in distant objects.

For a more precise description, you need to turn to mathematics: an expanding space is one where the "metric tensor" - the mathematical object in general relativity that tells you how to calculate the distance between two points in curved spacetime - is time-dependant.