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Someone weighing the same as you would have to sit the same distance from the center (or the fulcrum) of a teeter-totter to have that teeter-totter balance. But you'd have to sit twice as far from the fulcrum as someone twice your weight to have the teeter-totter balance -- or three times as far as someone three times your weight, and so on and so forth.
Heavenly bodies that revolve around one another work the same way. They orbit around a "shared center of mass," a center that astronomers call a barycenter instead of a fulcrum. Regardless, it's the same idea.
It's really more accurate to say that the Moon and Earth revolve around a barycenter (shared center of mass) than to say that the Moon revolves around the Earth. But with Earth being some 81 times more massive than the Moon, that means the Moon is 81 times further away from the barycenter. Or to put it differently: since the Moon resides 81 times further, it must have 1/81 the mass of the Earth.
Does that mean you'd weigh 1/81 as much on the Moon as you do on Earth? Yes, if the Moon were the Earth's same size. But since the Moon's radius is about 1/3.5 the Earth's radius, that means you are closer to the Moon's center -- which increases the influence of the Moon's gravity. To find out how much more, first square 3.5 to get 12.25, then multipy 12.25 x 1/81 to find that you weigh about 12.25/81 or 0.15 as much.
Next month, we'll find your weight on a white dwarf star.
|Your Weight on Jupiter||Your Weight on White Dwarf||Your Weight on Neutron Star|
|March Feature: Asteroid Vesta|