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 m2kg–2.

Asked by Sudhanshu | 1 year ago |  137

##### Solution :-

Mass of the spaceship, ms =1000 kg
Mass of the Sun, M=2×1030kg
Mass of Mars, mm =6.4×1023kg
Radius of orbit of Mars, R=2.28×1011 m
Universal gravitational constant, G=6.67×10−11Nm2kg−2

The potential energy of the spaceship due to the gravitational attraction of the Sun,

Us =$$\dfrac{−GMm_s}{R}$$

Potential energy of the spaceship due to the gravitational attraction of Mars,

Um=$$\dfrac{−Gm_mm_s}{r}$$

Total energy of the spaceship, E= Um+Us

=[$$\dfrac{−GMm_s}{R}$$]+[$$\dfrac{−Gm_mm_s}{r}$$]

The negative sign indicates that the satellite is bound to the system. Energy required to launch the spaceship out of the solar system

=−(total energy of the spaceship)

– E = [$$\dfrac{−GMm_s}{R}$$]+[$$\dfrac{−Gm_mm_s}{r}$$]

= Gms($$\dfrac{M}{R}$$ + $$\dfrac{m_m}{r}$$)

=  $$6.67 \times 10^{-11}\times 10^{3}$$

$$\times \left ( \dfrac{2\times 10^{30}}{2.28\times 10^{11}}+\dfrac{6.4 \times 10^{23}}{3.395\times 10^{6}} \right )$$

= 5. 91 x 1011 J

Answered by Sudhanshu | 1 year ago

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