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Introductory Physics Homework Help
How much work is done when a satellite is launched into orbit?
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[QUOTE="tuki, post: 6127520, member: 656961"] [h2]Homework Statement [/h2] A Satellite is brought up into a geostationary orbit (altitude 35800km measured from the surface of the earth). Satellite weights 1000.0kg. How much work is required to bring satellite from a surface of the Earth to geostationary orbit? [h2]Homework Equations[/h2] Newton's law of universal gravitation $$ F = G \frac{m_1m_2}{r^2} $$ Work is defined as: $$ W \int F \cdot s ds $$ [h2]The Attempt at a Solution[/h2] I want to compute work done by Newton's law of universal gravitation when moving satellite from the surface of the Earth to the orbit. It should be done with:h0 is surface of the Earth (about 6371 km) h1 is geostationary orbit (about 6371 km + 35800 km = 42171km) m1 is mass of the satellite (about 1000 kg) m2 is mass of the Earth (about 5.972E24) $$ W = \int_{h_0}^{h_1} G \frac{m_1 m_2}{r^2} dr = - G \frac{m_1 m_2}{h_1} - (- G \frac{m_1 m_2}{h_0} $$ $$ = G m_1 m_2 (\frac{1}{h_1} - \frac{1}{h_0}) \approx 5.3108\cdot 10^{10} \text{ J} $$ However, our textbook suggests that the correct answer would be 5.77E10 Joules. I can't exactly spot out where the mistake is. [/QUOTE]
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How much work is done when a satellite is launched into orbit?
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