- A probe of mass m has landed on the equator of a rotating asteroid of mass M and radius R. 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(GM/R² – ω²R). [2]
(b) Deduce that the probe will remain on the asteroid surface only if ω ≤ √(GM/R³). [1]
(c) Another probe orbits the Sun.
(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. [2]
(ii) Estimate the equilibrium temperature of the probe assuming it behaves as a black body. [2]