by

filosofo

on Apr 16, 2008

## McDonald’s Spaced Out

This is McDonald’s idea of making their Happy Meals educational. (That I took this photograph may also be proof of bad parenting on our part, but let’s overlook that.)

I think what they mean is that you can jump six times as high on the Moon.

In case you were wondering, that’s because the surface gravity of the Moon is 1/6 that of the Earth’s. It’s *not* because the moon has 1/6 the mass or the diameter of the Earth, as you might suspect. In fact, as you can see here, the mass of the Moon is 1.23% of the Earth’s, and its radius is 27.25%.

Surface gravity can be expressed like so:

`( Surface gravity of the Moon/Surface gravity of the Earth ) = ( Mass of Moon/Mass of the Earth ) / ( Radius of Moon / Radius of Earth ) `^{2}

Plug in the numbers, and you get the following:

`( Surface gravity of the Moon/Surface gravity of the Earth ) = ( 0.07349 x 10`^{24} kg/5.9736 x 10^{24} kg ) / ( 1738.1 km / 6378.1 km ) ^{2}

Which ends up as `Surface gravity of the Moon/Surface gravity of the Earth = 0.1656 ~ 1/6`