First slide

Gravitaional potential energy

Question

Energy required to transfer a 400 kg satellite in a circular orbit of radius 2R to a circular orbit of radius R, where R is the radius of the earth :
[Given : g = 9.8 ms^-2 ,R = 6.4 x 10⁶m]

Easy

A

1.65 x 10⁹ J
B

3.13 x 10⁹ J
C

6.26 x 10⁹ J
D

4.80 x 10⁹ J

Solution

Energy required
$\begin{array}{l} = \{\frac{- {GM}_{e} m}{2 (4 R)}\} - \{\frac{- {GM}_{e} m}{2 (2 R)}\} = \frac{{GM}_{e} m}{R} [\frac{1}{4} - \frac{1}{8}] \\ = mgR [\frac{1}{8}] = \frac{400 \times 9 .8 \times 6 .4 \times 10^{6}}{8} = 3 .13 \times 10^{9} J \end{array}$

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