Ever wondered why it takes a tremendously huge rocket to launch people from the earth, but the Apollo astronauts managed to launch from the moon in a comparatively tiny lunar module? Easy, the whole thing was faked and NASA forgot to come up with a plausible explanation!

Wow, it was almost physically painful to type that even as a joke. The real reason is some very easy but still pretty cool physics. Shall we take a look?

For a given object, the gravitational potential energy per kilogram with respect to distant space is given by this easy little equation:

So to pick up one kilogram of mass from the earth and remove it from the earth’s gravitational influence requires energy given by that formula. Plugging in values for the mass of the earth and the radius of the earth gives U = 6.25 x 10^{7} J/kg.

But the moon? Use the same equation and plug in the mass and radius of the moon. I get U = 2.8 x 10^{6} J/kg.

You might remember that the surface gravity of the moon is about 1/6 that of the earth. But the potential energy of an object at the moon’s surface is (from the above equations) only about 1/23 that of the same object at the earth’s surface. It’s much, much easier to launch from the surface of the moon than it is from the surface of the earth. And since it’s so much easier, you don’t have as many kilograms of fuel and rocket to move to orbit in the first place. This is why it takes one of these to launch people from the earth into deep space:

And only one of these to launch from the moon: