Very interesting. Orlando, by the time a comet gets anywhere near the Sun it is usually surrounded by a huge cloud of dust and gas boiled from the surface of the nucleus. That cloud can indeed be immense (I think as large as, or even much larger than, Earth's Moon in some cases?).
But the important thing to remember: the size of that cloud is NOT the size of the solid part of the comet! As far as I know, we have never seen a comet whose solid nucleus was any larger than a good-sized asteroid. Astronomers have never, ever seen a comet with a nucleus anywhere near as large as Earth's Moon.
How easy would it be to make the Sun collapse or expand? How well can we predict the large-scale behavior of the Sun? Sir Arthur Eddington said, "It should not be too difficult to understand such a simple thing as a star." (Quoted by George Gamow in A Star Called the Sun p. 93) The reason Eddington said that is, the Sun is so hot that it consists of material called plasma, and the properties of a plasma are very easy to calculate. Well, easy compared to the properties of something like the inside of the Earth where liquids and solids of various kinds are mixing and smooshing together.
It turns out that, for a star made of plasma, the whole thing obeys the simple physics of a gas composed of four things: the nucleii of hydrogen, helium, and everything else; and a bunch of free electrons. The hydrogen contributes a mean molecular weight of .5 to the behavior of the plasma, the helium a mean molecular weight of 1.333..., and everything else comes very very close to a mean molecular weight of 2 (yes, iron, carbon, and sodium all end up behaving, on average, exactly the same with regards to the equations describing pressure and density of the plasma).
So just as Eddington said, the Sun is in some ways a very simple system. It is also an incredibly massive system--more than 99% of the mass of the Solar System is contained in the Sun's ball of plasma. The Sun is about 329,400 times as massive as Earth.
What I think this means is that there is virtually no chance that this massive, simple system could be changed to a red giant or white dwarf right now by a comet falling into it. I bet even a rogue planet the size of the Earth falling into the Sun would not make any appreciable difference in the size or luminosity of the Sun. I would suspect that even a honking big planet like Jupiter could come barrelling out of space, crash directly into our darling Sun, and...the Sun would still not collapse nor would it swell to red-giant size. The Sun is simply too massive, and too stable, for a Jupiter to bother it very much.
("Very much" in the case of a Jupiter is rather relative--I imagine that a Jupiter-impact might cause a temporary increase (or decrease??) in the brightness of the Sun as the plasma convection currents which carry hydrogen to the core would be disrupted at least in one small area of the Sun....but the Sun would not go nova or collapse or any nonsense like that.)
Just as another poster said, a comet hitting the Sun is like a mosquito hitting the windshield of a car. A mosquito hitting the windshield won't cause your gas tank to explode, and it won't cause your car to flip end-for-end off the road. Your car is too big and has too much inertia for it to even notice the mosquito.
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