Question

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

• A. 0.83× 10¹⁰ J
• B. 1.23 × 10¹⁰J
• C. 1.53 × 10¹⁰J
• D. 1.83 × 10¹⁰

Answer 1

Answer: (D)

1.83 × 10¹⁰

Answer 2

W = ∆PE + ∆KE = PE_final – PE_initial + KE_final - KE_initial

= KE_initial – KE_final =

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

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