Ncert Exercises & Solutions

8.24 A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system? Mass of the space ship = 1000 kg; mass of the sun = 2×1030 kg; mass of mars = 6.4×1023 kg; radius of mars = 3395 km; radius of the orbit of mars = 2.28 ×108 km; G = 6.67×10-11 N m2 kg–2.

$T h e p o t e n t i a l e n e r g y o f s p a c e s h i p d u e t o s u n :$
$U = \frac{- G M m_{s}}{r}$
$T h e p o t e n t i a l e n e r g y o f s p a c e s h i p d u e t o m a r s h :$
$U' = \frac{- G M m_{m}}{R}$
$T o t a l e n e r g y o f s p a c e s h i p = U + U'$
$= \frac{- G M m_{s}}{r} + \frac{- G M m_{m}}{R}$
$H e n c e, t h e e n e r g y n e e e d t o l a u n c h t h e s p a c e s h i p :$
$= \frac{G M m_{s}}{r} + \frac{G M m_{m}}{R}$
$= 6.67 \times 10^{- 11} \times 10^{3} (\frac{2 \times 10^{30}}{2.28 \times 10^{11}} + \frac{6.4 \times 10^{23}}{3.395 \times 10^{6}})$
$= 6 \times 10^{11} J (A p p r o x .)$

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