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The space shuttle is in a 250-km-high circular orbit. It
Chapter 13, Problem 46P(choose chapter or problem)
Problem 46P
The space shuttle is in a 250-km-high circular orbit. It needs to reach a 610-km-high circular orbit to catch the Hubble Space Telescope for repairs. The shuttle’s mass is 75,000 kg. How much energy is required to boost it to the new orbit?
Questions & Answers
QUESTION:
Problem 46P
The space shuttle is in a 250-km-high circular orbit. It needs to reach a 610-km-high circular orbit to catch the Hubble Space Telescope for repairs. The shuttle’s mass is 75,000 kg. How much energy is required to boost it to the new orbit?
ANSWER:
Step 1 of 1
We have to find the energy required to boost the space shuttle from a \(250-\mathrm{km}-\mathrm{high}\) circular orbit to a circular orbit of \(610 \mathrm{~km}\)
The work done by the thrusters of the space shuttle to change the orbit can be found using the law of conservation of energy.
\(W_{\text {Thruster }}=\Delta E_{\text {mech }}\)
\(=\frac{1}{2} \Delta U_{g}\)
\(=\frac{1}{2}\left(\frac{-G M_{e} m}{r_{f}}-\frac{-G M_{m} e m}{r_{i}}\right)\)
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