# Europa is one of Jupiter's moons. This moon is in a circular orbit of 6.71x10^8 meters within a period of 3.55 days. What is the mass of Jupiter?

1. Europa is one of Jupiter's moons. This moon is in a circular orbit of 6.71x10^8 meters within a period of 3.55 days. What is the mass of Jupiter?

The time it takes a satellite to orbit a central body, its orbital period, can be calculated from

T = 2(Pi)sqrt[a^3/µ]

where T is the orbital period in seconds, Pi = 3.1416, a = the semi-major axis of an elliptical orbit = (rp+ra)/2 where rp = the perigee (closest) radius and ra = the apogee (farthest) radius from the center of the earth, µ = the central bodies gravitational constant = GM, the gravitational constant times the mass of the central body. In the case of a circular orbit, a = r, the radius of the orbit.

You have T, r, and G = 6.67259x10^-11m^3/kg.sec.^2. Solve for M.

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