How do I use Kepler's Third Law to calculate the mass of Jupiter from the motion of its moons?

Answer by  willard (874)

You can determine the mass using Newton's generalization of Keplers third law. The mass of the planet is (4(Pi)^2/G) times (orbital radius cubed)/divided by the orbital period squared. G is Newton's gravitational constant.

Answer by  Brandon55 (1719)

First, measure the time period for each of Jupiter's satellites to fully orbit. Second, write down each satellites distance from the planet. Finally, use Kepler's Third Law to calculate the mass of the planet. Mathematically it is written as M=(a^2/p^2)*(4(pie)^2/G). In the equation, remember that G is the gravitational constant applied by Newton.