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My thought experiment:

We repalce our sun with an object of identical mass, rotation, shape, etc. but not the same density, i.e. the object would have a radius of 100km. The "replacement-time" would be instant.

Would our orbit / the gravity that earth experiences change? As far as I know there are some strange effects for very dense objects like black holes or neutron stars.

I guess this question could be boiled down to:

Does the density of an object play a role for it's gravitational effects?

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  • $\begingroup$ Note that the Sun's Schwarzschild radius is only 3km so 100km is well short of any sort of black hole thing happening. Not sure if it would give you the extra space to see any interesting lensing but it's hard to see lensing when you're looking at a really bright thing. $\endgroup$
    – CR Drost
    May 15, 2019 at 14:46

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To the extent that the Sun can be considered totally spherically symmetric and non-spinning the gravitational effects are described by the Schwarzschild solution and the density would not matter.

For the Earth it would not matter but of course you would be able to get closer to the Sun if it were more dense.

If the Sun were to be replaced by a black hole with the same mass instantaneously the gravitational effects on the Earth would be exactly the same, we would be continuing to travel in the same orbit that we do now.

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  • $\begingroup$ Also, I am pretty sure that radial-only expansions and contractions do not have the sort of quadrupole moment that you need for gravitational radiation, but it is not my field of expertise so I am not 100% sure. $\endgroup$
    – CR Drost
    May 15, 2019 at 14:48

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