How Can We Calculate The Mass Of A Planet?

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How do we know the mass of a planet originally appeared on Quora – the knowledge sharing network where compelling questions are answered by people with unique insights.
It’s actually pretty cool.
One of the things Sir Isaac Newton is most famous for is his theory of gravity. He established that the pull of gravity between any two objects can be calculated from the mass of the two objects, the square of the distance between them, and a gravitational constant. When you put an apple on a scale, you’re actually measuring the force between that apple and the earth. The weight depends on both masses; if the earth was a different mass, the apple would have a different weight on earth.

So, once we’ve measured the weight of the apple, we can work backward. We can easily convert the weight of the apple to find its mass. And we know the distance between the center of the apple and the center of the earth, because we know how big the earth is (how we first calculated that is another story, though a pretty interesting one). Given all that, the two things we don’t know are the mass of the earth and the gravitational constant. If we can find one, we can use Newton’s equation to figure out the other.
Enter Henry Cavendish.
Cavendish was a brilliant and wealthy but very shy and eccentric 18th century scientist. He made a number of groundbreaking scientific discoveries, and didn’t even bother to publish many of them. But one that he did publish was the gravitational constant. See, gravity means that there is an attractive force between all objects, not just planets and stars. So, if you take a big, heavy, metal ball and place it close to another big, heavy ball, there will be an attractive force between them. When dealing with 350 pound chunks of metal instead of planets, the force is very, very tiny, but it’s there. An amateur scientist/clergyman named John Michell invented an impressively delicate apparatus for measuring these tiny forces, and left it to Cavendish when he died. Cavendish, after much trial and error, managed to set up an experiment that used it to accurately measure the force between pairs of metal balls. Knowing that force, the mass of the balls, and the distance between them, Cavendish could accurately calculate the gravitational constant. (In case you’re curious, it’s 6.67*10^-11 cubic meters per kilogram-second squared).
With that number known, we can solve the mass equation for the whole world. Every time you step on a bathroom scale, you’re measuring the mass of the planet. If we know your mass and your distance from the center of the earth, then we can apply Newton’s equation of gravity and determine the mass of the planet you’re standing on. What’s more, once we know the mass of the earth, we can use orbital observations to calculate the mass of the moon and the sun, and we can use those to determine the mass of the other bodies in the solar system. All of which was first made possible by one guy fiddling with a delicate balance in his estate in England 200 years ago.
source:quora via forbes

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