exupero's blog

Jumping higher when the sun and moon are overhead

In the previous post we worked out how much higher one can jump when the sun is directly overhead. The natural question to ask next is how much having the moon directly overhead can add:

In this case g works out to 9.814 m/s², the same as before, at least to three decimal places; the difference doesn't show up until the hundred thousands place. With a 1-foot jumping height, having the sun overhead added 0.1905 millimeters; having both the sun and moon overhead adds 0.1917 millimeters above one foot, That is, the moon only adds 1.2 microns.

That's a little surprising given than the moon is much closer than the sun and gravitational pull fades as a square of distance, but the difference comes from the fact that while the sun is 400 times further from the Earth than the moon, it's almost 30 million times more massive. Thirty million is a lot more than 400 squared, making the moon's influence a lot less than the sun's.