Question

If the Sun suddenly became a black hole without gaining or losing mass, what would happen to the Earth?

a. The Earth would slowly spiral into the black hole because of the increased gravi- tational force on the Earth.
b. The Earth would fall directly into the black hole.
c. The Earth would be crushed by the tidal forces.
d. The Earth would fly off into space because the gravitational force at the Earth would decrease.
e. The Earth would continue in its orbit without a change

Answer 1

If the Sun became a black hole without changing its mass, Earth's orbit would remain unchanged because the gravitational pull on Earth would not increase, and the dangerous tidal forces are only significant very close to a black hole's event horizon.

Step-by-step explanation:

If the Sun suddenly became a black hole without gaining or losing mass, the gravitational pull on Earth would remain unchanged. Therefore, the Earth would not spiral into the black hole due to increased gravitational force (option a is incorrect), nor would it be directly pulled in (option b is incorrect), and it also would not be crushed by tidal forces unless it ventured very close to the black hole (option c is incorrect). The Earth certainly wouldn't fly off into space, as the gravitational force at its orbit would not decrease (option d is incorrect). So, the correct answer is that the Earth would continue in its orbit without a change (option e is correct).

A black hole has the same mass as the previous stellar object before collapse. Thus, Newton's laws of motion would predict the same orbital motion for a planet if the central mass remains constant. Also, tidal forces are a function of differential gravity, so if Earth remains at its current distance, tidal forces would not be significantly different because the intense gravitational gradient of a black hole only occurs very close to the event horizon.