Physics

Problem

A satellite of mass

m

is to be transferred from a circular orbit of radius

r_1

to a higher circular orbit of radius

r_2

(

r_2 > r_1

) around the Earth. Neglect any change in kinetic energy during the transfer. a. (i) Derive an expression for the external work

W

that must be done on the satellite in terms of

G

M

m

r_1

and

r_2

(

M

is the mass of the Earth). b. (ii) Using

G = 6.67 \times 10^{-11}\,\text{N m}^2\text{kg}^{-2}

M = 6.0 \times 10^{24}\,\text{kg}

and

R_E = 6.4 \times 10^{6}\,\text{m}

, calculate the work needed to move a

500\,\text{kg}

satellite from an initial orbit of radius

2R_E

to a final orbit of radius

3R_E

. Express your answer in joules.