Posted by Carlie on Sunday, April 19, 2009 at 8:30pm.
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.