How much less would you weigh on the Moon than on Earth?

The Deep Space Climate Observatory (DSCOVR) captured this image of the Moon and Earth in July 2015. Due to its smaller mass — and therefore, lower gravitational pull — you would weigh less on the Moon than Earth. Credit: NASA/NOAA

If you weigh a certain amount on Earth, how much less or more would you weigh on the Moon?

Makayla
Arkansas

The short answer is that you would weigh roughly one-sixth your Earth weight on the Moon. So if your bathroom scale reads 180 pounds (81.6 kilograms) on Earth, it would read 30 pounds (13.6 kg) on the Moon. Though actually, your mass — expressed in kilograms — never changes, and your scale (built only for use on Earth) would be lying to you in metric. More on that in a moment.

And we can figure this out for any planet! Good old Isaac Newton gave us an equation for figuring out the force of gravity almost 350 years ago. Gravity exists and works the same everywhere in the cosmos, but how strongly we feel it (i.e., its force) varies depending on how much mass is around.

The force of gravity between two objects, according to Newton, is equal to GMm/r², where G is the gravitational constant, a number that never changes. Newton figured this number out through lots of experimentation, which we’ve since refined in labs. Your mass (call it m), the amount of stuff you are made of, also doesn’t change. (Well, it does if you win a hot-dog-eating contest, but not because of what planet you’re on.) So that leaves us with M (the mass of the planet) and r (its radius, assuming you’re standing on its surface). 

NASA provides us with a list of planets’ masses and radii — you’ll find it at https://nssdc.gsfc.nasa.gov/planetary/factsheet/ — and then you just need a calculator to figure out the rest!

By the way, we use kilograms and pounds interchangeably on Earth, because no matter what country you’re in, Earth’s gravity doesn’t change. But that doesn’t work once you leave the ground. Out in space, a kilogram is still a kilogram, because it’s a measure of mass — how much stuff you’re made of. But a pound is actually a measure of force — how hard the planet’s gravity is tugging. So if you’re planet-hopping, you really want to compare pounds and Newtons (the latter of which is in units of kilograms x meters/second²).

Korey Haynes
Contributing Editor