Problem 1

A satellite of mass

m

moves uniformly in a circular orbit of radius

r

measured from the center of an isolated, spherically symmetric planet of mass

M

. Neglect drag and the satellite's effect on the planet;

G

is the gravitational constant. (a) Identify the force and state the condition for a circular orbit. (b) Derive the orbital speed

v

and period

T

. (c) Check their dependence on

m

and their dimensions.

problems.proof.stepOf

\frac{GMm}{r^2}=m\frac{v^2}{r}

problems.proof.analysis

Apply Newton's second law along the inward radius. Gravitational force must provide exactly the required centripetal acceleration.