A planet has mass M and radius R. A satellite is placed just above the planet’s surface in a circular orbit.
a. (i) Derive an expression for the orbital speed of the satellite in terms of G, M and R.
b. (ii) Derive an expression for the minimum speed required by a projectile to escape from the planet’s surface.
c. (iii) Show that the ratio of the escape speed to the orbital speed obtained in parts (i) and (ii) is a constant, and calculate its numerical value.