A satellite moves in a circular orbit of radius around a planet of mass .

PHYSICS · Multi-part · CBSE · Physics · Gravitation · Gravitation

Problem

A satellite moves in a circular orbit of radius

r

around a planet of mass

M

. (a) Obtain an expression for the orbital speed

v_{\text{orb}}

of the satellite in terms of

G

M

and

r

. (b) Derive an expression for the escape speed

v_{\text{esc}}

of a body located at the same distance

r

from the planet’s centre. (c) Hence prove that

v_{\text{esc}} = \sqrt{2}\,v_{\text{orb}}

. (d) State the physical significance of the result obtained in part (c).