Masses
Once you know how far away a planet is, you can use the orbital periods (
P
) of moons circling a
planet and how far the moons are from the planet (d) to measure the planet's mass. You measure
the angular separation between the moon and the planet and use basic trigonometry to convert
the angular separation into distance between the planet and moon. That conversion, though, first
requires that the distance
to
the planet and moon be known.
Isaac Newton used his laws of motion and gravity to generalize Kepler's third law of planet
orbits to cover any case where one object orbits another. He found for any two objects orbiting
each other, the sum of their masses, planet mass + moon mass = (4
π
2
/G) × [(their distance
apart)
3
/(their orbital period around each other)
2
]. Newton's form of Kepler's third law can,
therefore, be used to find the combined mass of the planet and the moon from measurements of
the moon's orbital period and its distance from the planet.
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 Fall '10
 EmilyHoward
 Astronomy, Moons, Solar System, Planet

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