callisto is a moon of jupiter (mass = 1.90 x 10^27 kg), which orbits the planet with a period of 16.9 days. what is the radius of its orbit?

Question

[?] x 10^ [?] m

Coefficient: ?

Exponent: ?

Answer 1

GmM/r² = mv²/r, where G is gravitaional constant, M is Jupiter mass, m is mass of Callisto, v = 2πr/T,

r is radius of orbit, T is period. From here GM/r = 4π²r²/T²; r = (GMT²/(4π²))^1/3_;

r = (6.6743·10^·-11kg^-1m³s^-2·1.90·10²⁷kg·(16.9·24·3600)²s²/(4π²))^1/3 = 1.9·10⁹ m