How do you weigh something as enormous as a planet, when there's no scale big enough and you can't even get there? The clever answer is to watch its moon. Gravity ties a moon to its planet, and the heavier the planet, the harder it pulls — so to keep from being dragged in, the moon of a heavy planet has to whip around really fast. A lighter planet pulls more gently, so its moon can take its time. That means if you measure how fast a moon is circling and how far out it is, you can work backward and figure out exactly how heavy the planet must be to hold it like that. Astronomers have weighed every planet in the solar system this way. In the simulator, drag the moon's distance and speed and watch the planet's mass appear.
Most people think you would need the moon's own weight to work out the planet's mass. In fact the moon's mass cancels out of the equation entirely, so only its speed and distance matter.
What's actually happening
Weighing a planet sounds like an impossible task. There is no scale vast enough, and you certainly can't pop one onto a balance. Yet we know the masses of all the planets to remarkable precision, including ones no human has ever visited. The secret is that you don't weigh the planet directly at all. You weigh it by spying on something it holds captive: a moon.
The physics rests on a single, elegant balance. A moon in orbit is being pulled inward by the planet's gravity, and that inward pull is exactly what bends its path into a circle instead of letting it fly off in a straight line. Write that balance down and something wonderful happens — the moon's own mass cancels right out of the equation, and you're left with the planet's mass equal to the moon's speed squared, times its orbital distance, divided by the gravitational constant G. In plain terms: measure how fast the moon is moving and how far out it orbits, and the planet's mass simply falls out. A heavy planet pulls hard, so it can only hold a moon that's moving fast; a light planet pulls weakly, so its moon ambles along. The moon is a gauge, and its motion reads off the mass of whatever it circles.
This is exactly how it has always been done. In 1610 Galileo pointed his telescope at Jupiter and saw four little points of light shuttling back and forth beside it night after night — its largest moons. Timing how long each took to circle and how far out it sat was enough, once Newton supplied the law, to weigh Jupiter: about 318 times the mass of Earth. The same method gives us Saturn, Mars, and the rest, and it scales right down — when a spacecraft swings past an asteroid, mission controllers watch how its path bends and deduce the asteroid's mass from that alone. We even weigh distant stars by watching the planets and companion stars that orbit them. No giant scale, no visit, no contact. Just a stopwatch, a careful eye on something going round, and one clean equation.
Watching how fast and far a moon orbits hands you the planet's mass through M = v²r / G, letting us weigh worlds we can never touch.
- 1Tie a small weight to a string and whirl it in a circle overhead, keeping the radius the same. Notice how fast you must spin it just to keep it up.
- 2Now grip the string a little harder and pull it in slightly while spinning — to hold the tighter, faster orbit you have to supply a stronger inward pull, exactly as a heavier planet would.
- 3A heavier planet is like your stronger pull: it forces its moon into a faster orbit. Read that backward and a fast-orbiting moon means a heavy planet — the very logic astronomers use.
Common questions
In the orbit equation the moon's mass cancels out completely. That is why a tiny captured asteroid and a huge moon both reveal their planet's mass equally well — only the speed and distance count.
Galileo, in 1610, after spotting four moons shuttling beside Jupiter. Once Newton supplied the law of gravity, timing those orbits weighed Jupiter at about 318 times the mass of Earth.
Yes. When a spacecraft swings past an asteroid, controllers measure how much the asteroid's gravity bends the probe's path and back out its mass, weighing a rock in deep space without ever landing.