Io, one of jupiter’s moons, is about the size of earth’s moon. io has a radius of about 1.85 x 106 m, and the mean distance between io and jupiter is 4.22 x 108 m. jupiter has a mean radius of 7.15 x 107m, and a mass of 1.90 x 1027kg. if io’s orbit is circular, what is its orbital speed?

Io is in a circular orbit so there is a centripetal force acting on it. This centripetal force is the gravitational force Jupiter exerts on it.
Fg=Fc
G(M*m)/r^2 = m*ac,

where G is the universal constant of gravitation = 6.67*10^(-11) [m^3*kg^.1*s^-2],
M is Jupiter's mass,
m is Io's mass,
r is the distance between Io and Jupiter,
and ac is the centripetal acceleration which equals v^2/r, where v is the linear Io's speed and r is the radius of the orbit, in this case the distance between Io and Jupiter.

Substituting ac=v^2/r in the formula above and rearranging gives v=√(GM/r).
Plug in numbers to find v=17329.4 m/s.

therefore, the efficiency is: