Ncert Exercises & Solutions

8.19 A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth’s gravitational influence? Mass of the satellite = 200 kg; mass of the earth = 6.0×1024 kg; radius of the earth = 6.4 × 106 m; G = 6.67 × 10–11 N m2 kg-2.

T o t a l e n e r g y o f t h e s a t e l l i t e = \frac{1}{2} m v^{2} + (\frac{- G M_{e} m}{R_{e} + h}) . . . . . . (i)

a n d, v_{o} = \sqrt{\frac{G M_{e}}{R_{e} + h}} . . . . . . . . (i i)

F r o m (i) a n d (i i),

T o t a l e n e r y o f s a t e l l i t e = - \frac{1}{2} (\frac{G M_{e} m}{R_{e} + h})

E n e r g y e x p e n d e d t o r o c k e t = \frac{1}{2} (\frac{G M_{e} m}{R_{e} + h})

= \frac{1}{2} \times (\frac{6.67 \times 10^{- 11} \times 6 \times 10^{24} \times 200}{6.4 \times 10^{6} + 0.4 \times 10^{6}})

= 5.9 \times 10^{9} J

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