Question

Io, one of the moons of Jupiter, circles Jupiter once every 1.77 days. The radius of its orbit is 4.22 X 108 m. If this orbit is circular, what is the mass of Jupiter?

Answer 1

m=mass of satellite, M=mass of Jupiter
R=4.22•10^8 m, T= 1.74 days=1.74•24•3600 seconds,
G =6.67•10^-11 N•m²/kg²,

F= G•M•m /R²
Centripetal acceleration
a=v²/R =(2•π•R/T)² /R=4• π²•R/T². (1)
Newton’s 2Law
F=m•a = G•M•m /R².
a= G•M /R² (2)
Equate (1) and (2)
4• π²•R/T² = G•M /R²
M= 4• π²•R³/T²•G = ...