A probe of mass m has landed on the equator of a rotating asteroid of mass M and radius R.
diagram not to scale
The asteroid rotates with angular speed ω.
(a) By drawing a free-body diagram for the probe, show that the normal force, N, on the probe from the asteroid is given by N=m(R2GM−ω2R).
(b) Deduce that the probe will remain on the asteroid surface only if ω≤R3GM.
(c) Another probe orbits the Sun.
(c.i) The distance between the probe and the Sun is 4 times the distance between the Earth and the Sun. Show that the intensity of the solar radiation at the surface of the probe is 85 W m−2.
(c.ii) Estimate the equilibrium temperature of the probe assuming it behaves as a black body.