In 1610, Galileo discovered the first four moons of Jupiter. One of them, Ganyme
ID: 2097358 • Letter: I
Question
In 1610, Galileo discovered the first four moons of Jupiter. One of them, Ganymede, is actually the largest moon in the solar system. It has a diameter of 3270 miles. It is larger than Mercury and almost 3/4 the size of Mars. To a good approximation, you can consider Ganymede to move in uniform circular motion about Jupiter, with an orbital radius of rG = 1 Times 109m. The mass of Jupiter is 300 times that of Earth. You can assume the Earth's radius to be RE = 7 Times 106 m and the acceleration of gravity at the surface of the Earth to be g = 9.8 m/s2. Also, assume that Ganymede and Jupiter are spheres. How long does it take (in Earth days) for Ganymede to make one complete revolution about Jupiter? (There are 86400 seconds in one Earth day). t =Explanation / Answer
P^2 = (2?)^2(D^3)/((G)(M))
where P is the orbital period in seconds, D is the distance in meters, M is the mass in kilograms of Jupiter, and G is the 6.67 x 10^ -11 m^3/ kg sec^2
M Jupiter = 1.9 x 10^27 kg, D = 1.88 x10^9 meters