A student notices that the escape velocity from the surface of a planet is related to the orbital velocity of a close-to-surface satellite by a constant factor.
Answer the following questions to analyse this observation:
(i) Explain, in terms of energy considerations, why a body needs additional kinetic energy to escape completely from the planet’s gravitational field compared with the energy required to stay in a circular orbit at the same radius.
(ii) Using suitable reasoning (without performing a full numerical derivation), account for the appearance of the factor 2 in the relation between escape velocity and orbital velocity measured at the same radius.
(iii) Describe qualitatively how the difference between the two velocities would change, if at all, when the satellite is in a higher circular orbit instead of skimming the planet’s surface.