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Well it's not wet, but if you stopped the reactions, the sheer force of gravity of the upper layers on the inner layers would start them again. Not that that has any effect on its mass. (I mean it does, because the nuclear reactions convert mass to energy, but that's a very long process.)
Asking weight doesn't really make sense, because weight is a product of gravity. The sun has a mass of 1.9891x10^30 kg, and at 1g that's 4.384x1030 lb, at least according to the Google result summary I copy-pasted from.
How much would the earth weigh if it was sitting on the frozen surface of the switched off Sun?
The Earth's weight is 1.317×10^25 lbs. Gravity on the "surface" of the sun is about 28 times Earth's, so if the Earth was a point mass (it isn't) on the surface of the sun (there isn't one, it's a soup of plasma 250 mi deep) the Earth would weigh 3.687×10^26 lbs.
Of course that couldn't happen anyway because part of the reason the sun is the volume it is, is because of the nuclear reactions blowing it apart. If you stopped the sun, it would collapse (and that crushing energy would restart the reactions).
Also the earth isn't a point mass, so the point where the Earth and Sun are touching would experience more gravity than the point on the opposite side of the earth.
I'm sure it would be the same as it currently does.
Weight depends on location. For example, you would weigh less on the moon.
So if I was on a less gravity planet it would be easy to pick up?
Weight is determined by gravity, which is determined by the mass of the objects.
Regardless of gravity, objects still retain their mass, so you wouldn't be able to move anything that massive.
Moving an object requires force, the amount of force required is related to the object's mass and current velocity (momentum). Even sitting still you'd have to accelerate the mass from zero.
I forget the acceleration formulas, physics was a few decades ago. F=M*A?
Yes, that's right. So the force required to accelerate an extremely massive object is very high.
But, if you only want to accelerate it a little tiny bit, you only need a little tiny bit of force. So all other things being equal, you could push on the sun and maybe after some days, weeks, months, or years, you'd start to notice that it moved a little bit.
It would have to be near zero gravity, and you would have to have something even bigger to brace yourself against, and you would only be moving it an infinitesimally small amount at a time, but yes it would be possible.
That's ignoring a very long list of things that would kill you before you even got to try, anyway.