Question

According to the law of universal gravitation, what would happen to Earth if the Sun were somehow replaced by a black hole of the same mass?
a. Earth's orbit would not change.
b. Earth would be quickly sucked into the black hole.
c. Earth would slowly spiral into the black hole.
d. Earth would slowly fall into the black hole.

Answer 1

a. Earth's orbit would not change.

Explanation:

The force that keeps the Earth in circular motion around the Sun is the gravitational force between the Earth and the Sun, whose magnitude is given by:

$F=G\frac{m M}{r^2}$

where

$G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}$ is the gravitational constant

m is the mass of the Earth

M is the mass of the Sun

r is the distance between them

From the equation, we observe that this force depends only on three factors:

• the mass of the Earth
• the mass of the Sun
• their separation

If the Sun is replaced by a black hole of the same mass, none of these factors would change (the central mass M would remain the same), therefore the gravitational force F would not change, and therefore the orbit of the Earth would not change.

Learn more about gravitational force:

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