Question

How much work will be done to take a space draft orbiting at $200km$ above the surface of earth to an orbit at $4000km$ above the surface of the earth? Assume circular orbit. Mass of spacecraft equal to $2000kg.$

• A. $0.83\times {10}^{10}J$
• B. $1.23\times {10}^{10}J$
• C. $1.53\times {10}^{10}J$
• D. $1.83\times {10}^{10}J$

Answer 1

The correct option is D $1.83\times {10}^{10}J$

$W=\Delta PE+\Delta KE=P{E}_{final}-P{E}_{initial}+K{E}_{final}-K{E}_{initial}$

$=K{E}_{initial}-K{W}_{final}=\frac{GMm}{{10}^3\times }[\frac{1}{8400}-\frac{1}{10400}]$

$=\frac{6.67\times {10}^{-11}\times 6\times {10}^{24}\times 2000}{{10}^3}\left[\frac{2000}{8400\times 10400}\right]$

$=\frac{40\times {10}^{14}}{21\times {10}^4}=1.83\times {10}^{10}J$