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

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 on Question#37374 – Physics - Astronomy

We have according to the Newton’s law of gravity that the

$$g_{\text{planet}} = \frac{GM}{R^2}$$ $$M = 4M_e$$ $$R = \frac{1}{2}R_e$$ $$g = \frac{GM_e}{R_e^2} = 9.8 \frac{m}{s^2}$$ $$G = 6.67 \cdot 10^{-11} \frac{m^3}{kg \cdot s^2}$$

$M_e$ is mass of the Earth, $R_e$ is radius of Earth.

From hence, gravitational acceleration at surface of planet is

$$g_{\text{planet}} = \frac{4GM_e}{R_e^2 / 4} = 16g = 156.8 \frac{m}{s^2}$$

Answer:

$$g_{\text{planet}} = 16g = 156.8 \frac{m}{s^2}$$