Question

An astronomical object has its mass 4 times the mass of earth and radius half of the radius of
earth. If acceleration due to gravity at earth is g, find its value at the surface of the astronomical
object.

Answer 1

Answer on Question #70869 – Physics – Astronomy | Astrophysics

An astronomical object has its mass 4 times the mass of earth and radius half of the radius of earth. If acceleration due to gravity at earth is $g$, find its value at the surface of the astronomical object.

Solution. On Earth we have the following equality:

$$g_{E} = \frac{G M_{E}}{R_{E}^{2}}.$$

For astronomical object

$$g_{A} = \frac{G M_{A}}{R_{A}^{2}} = \frac{G (4 M_{E})}{\left(\frac{1}{2} R_{E}\right)^{2}} = 16 g_{E} \approx 157 m \cdot s^{-2}.$$

Answer. $g_{A} = 157 m \cdot s^{-2}$.

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