Question

Calculate the magnitude of the acceleration due to gravity on the surface of Earth due to the Moon.

Answer 1

Answer:

$g'_h=1.096\times 10^{-5}\ m.s^{-2}$

Explanation:

We know that the gravity on the surface of the moon is,

• $g'=\frac{g}{6}$

• $g'=1.63\ m.s^{-2}$

Gravity at a height h above the surface of the moon will be given as:

$g'_h=\frac{G.m}{(r+h)^2}$ ..........................(1)

where:

G = universal gravitational constant

m = mass of the moon

r = radius of moon

We have:

• $G=6.67\times 10^{-11}\ m^3.s^{-2}.kg^{-1}$

• $m=7.35\times 10^{22}\ kg$

• $r=1.74\times 10^6\ m$

• $h=384.4\times 10^6\ m$ is the distance between the surface of the earth and the moon.

Now put the respective values in eq. (1)

$g'_h=\frac{6.67\times 10^{-11}\times 7.35\times 10^{22}}{(1.74\times 10^6+384.4\times 10^6)^2}$

$g'_h=1.096\times 10^{-5}\ m.s^{-2}$ is the gravity on the moon the earth-surface.