Question

For any planet, if the planet were to shrink, but have constant mass, what would happen to the value of gravity acceleration (g) on the planet's surface?
will it increase or decrease? Why?

Answer 1

The value of the gravity acceleration on the planet's surface increases

Explanation:

The gravitational acceleration on the surface of a planet is given by:

$g=\frac{GM}{R^2}$

where

G is the gravitational constant

M is the mass of the planet

R is the radius of the planet

In this problem, we are told that the planet shrinks, therefore the new radius is smaller than the original radius:

$R'$

while the mass remains the same:

$M'=M$

Therefore, the new acceleration of gravity is

$g'=\frac{GM}{R'^2}$

We see that the value of g is inversely proportional to the square of the radius of the planet: therefore, since $R'$, it means that $g'>g$, so when the planet shrinks, the value of the gravity acceleration on the planet's surface increases.

Learn more about gravity:

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