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