Jupiter's four large moons - - Io, Europa, Ganymede, and Callisto - - were discovered by Galileo in 1610. Jupiter also has dozens of smaller moons. Callisto has a radius of about 2.40 106 m, and the mean distance between Callisto and Jupiter is 1.88 109 m. (a) If Callisto's orbit were circular, how many days would it take Callisto to complete one full revolution around Jupiter

Question

Jaylene Gallegos

Geography

15 April, 21:56

Jupiter's four large moons - - Io, Europa, Ganymede, and Callisto - - were discovered by Galileo in 1610. Jupiter also has dozens of smaller moons. Callisto has a radius of about 2.40 106 m, and the mean distance between Callisto and Jupiter is 1.88 109 m. (a) If Callisto's orbit were circular, how many days would it take Callisto to complete one full revolution around Jupiter

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Ava Waller · Answer 1

You would use

P^2 = (2π) ^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

P^2 = 39.5 * (6.65 x 10^27) / ((6.67 x 10^ - 11) (1.9 x 10^27)) = 2.07 x 10^12

P = 1,440,000 seconds = 16.66 days