The Moon’s gravity stretches Earth, which causes Earth’s tides. How much stronger is the force of the Moon’s gravity on a 1 kg mass on the side of Earth closest to the Moon compared to the force of the Moon’s gravity on a 1 kg mass on the side of Earth farthest from the Moon. Compare the forces as a ratio.

Question

Can anyone help me with this problem, and show the steps.
Thanks in advance!

Answer 1

let the two distances be r and R, where R=r+D, with D being earth's diameter.
If the two forces are F and f, with F being the force on the far-side mass, then
f/F = (GMm/r^2) / (GMm/R^2) = R^2/r^2 = ((r+D)/r)^2 or (1+D/r)^2