Question

Any object could be compressed until it was dense enough to become a black hole. If tomorrow some mysterious force was to crush the Sun into a black hole with the same amount of mass, how would this affect the orbit of the Earth?

Answer 1

Generally, when a black hole is formed, the explosion that precedes it, reduces the mass (as part of it flies away). But here we are considering the mass to be the same. As expected, Sun would just become a smaller sphere centered at the same point as it is now with the same mass. When we consider Gravitational force or potential due to a sphere, dont we just take the sphere equivalent to a point mass located at the centre? Offcourse yes! So applying the equations of Gravitational force or Potential, we realize that nothing would change for Earth except that there will be no more sunlight available. We generally tend to think that black hole has very strong Gravitational field and that it pulls everything inside. That will be true for distances close to the sun. Hence no change to the orbit of Earth.