Question

1. An alien race passing through our solar system turns the Sun (1.98x10³⁰ kg) into a black hole

   using advanced gravity technology.

   1. Determine the radius of the Sun if it were made into a black hole.

   2. In 2-3 sentences, describe the effects on Earth and the rest of the solar system after the

      Sun is converted to a black hole.

Answer 1

Part 1 :
The radius of a black hole of mass M is given by

So, given the values,

we get the radius of the black hole
  
  


Part 2 :
If hypothetically, sun is converted to a black hole with the same mass as it has today, this will not effect the orbits of the planets around it ( e.g., earth and other planets in the solar system ), because as the radius of the black hole is around 3 km (this is where the event horizon is ), the planets of the solar system outside the event horizon will feel this as a point like object with the same mass as the real sun. And so its gravitational influence on the solar system will be the same. So, the earth and rest of the solar system will continue to revolve around without getting pulled into it.
However, as black hole emits no light, so, an eternal darkness would surround earth and the rest of solar system and making life impossible on earth and an extreme coldness would prevail everywhere.