First slide

Motion of planets and satellites

Question

By what percent ,the energy of the satellite has to be increased to shift it from an orbit of radius ’r’ to ‘3r’

Easy

A

66.7%
B

33.3%
C

15%
D

20.3%

Solution

$T E = \frac{- G m m}{2 r}; Δ T E = \frac{G m m}{2} (\frac{1}{r_{1}} - \frac{1}{r_{2}}) T E % = \frac{Δ T E}{T E} \times 100 % = \frac{\frac{G m m}{2} (\frac{1}{r_{1}} - \frac{1}{r_{2}})}{\frac{G m m}{2 r_{1}}} \times 100 % = \frac{(\frac{1}{r} - \frac{1}{3 r})}{\frac{1}{r}} \times 100 % = \frac{(\frac{3 - 1}{3 r})}{\frac{1}{r}} \times 100 % = \frac{2}{3} \times 100 = 66.7 %$

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