Question

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

Answer 1

`g'_h=1.096* 10^(-5)\ m.s^(-2)`

Step-by-step explanation:

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

• 
  `g'=(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=(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* 10^(-11)\ m^3.s^(-2).kg^(-1)`

• 
  `m=7.35* 10^(22)\ kg`

• 
  `r=1.74* 10^6\ m`

• 
  `h=384.4* 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=(6.67* 10^(-11)* 7.35* 10^(22))/((1.74* 10^6+384.4* 10^6)^2)`

`g'_h=1.096* 10^(-5)\ m.s^(-2)` is the gravity on the moon the earth-surface.