Answer
The force of gravity between the moon and the sun is greater than that of the moon and the earth.
Work Step by Step
The force of gravity between the moon and the earth is given as
$F_{E,M}=G\frac{M_EM_M}{R_{EM}^2}$
We plug in the known values to obtain:
$F_{E,M}=6.67\times 10^{-11}\frac{(5.97\times 10^{24})(7.35\times 10^{22})}{(3.84\times 10^8)^2}=1.98\times 10^{20}N$.......eq(1)
Now the force of gravity between the moon and the sun is given as
$F_{S,M}=G\frac{M_SM_M}{(R_{SM})^2}$
We plug in the known values to obtain:
$F_{S,M}=\frac{(2.00\times 10^{30})(7.35\times 10^{22})}{(1.50\times 10^{11}+3.84\times 10^8)^2}=4.34\times 10^{20}N$...........eq(2)
By comparing eq(1) and eq(2), we can see that the force of gravity between the moon and the sun is greater than that of the moon and the earth.
