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

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

Problem

A satellite of mass

m

moves in a circular orbit around a planet of mass

M

. (a) Using an appropriate physical argument, derive an expression for the satellite’s orbital speed

v

in terms of

G

M

, and the orbital radius

r

. (b) Express the orbital period

T

in terms of

r

M

, and

G

. (c) Eliminate

r

to write the satellite’s total mechanical energy

E

exclusively in terms of

m

M

G

, and

T

. Show each algebraic step clearly. (d) A

250\,\text{kg}

satellite has an orbital period of

90.0\,\text{min}

around Earth. Using your expression from part (c), calculate its total mechanical energy.