A satellite of mass is required to be shifted from an initial circular orbit of…

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

Problem

A satellite of mass

m

is required to be shifted from an initial circular orbit of radius

r_1

about a planet of mass

M

to a higher circular orbit of radius

r_2

(

r_2>r_1

). (a) Derive an expression for the work that must be done on the satellite to accomplish this transfer, expressing your answer in terms of

G

M

m

r_1

and

r_2

. (b) Using the derived expression, calculate the work needed to move a

200\,\text{kg}

satellite from an orbit of radius

8.0\times10^{6}\,\text{m}

to an orbit of radius

1.2\times10^{7}\,\text{m}

around Earth, taking

G=6.67\times10^{-11}\,\text{N m}^2\text{kg}^{-2}

and

M_{\oplus}=6.0\times10^{24}\,\text{kg}

. (c) Based on your calculation, comment on whether the required work is more sensitive to the initial or to the final orbital radius.