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Introductory Physics Homework Help
Satellite in orbit losing speed
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[QUOTE="Karol, post: 4864845, member: 20512"] [h2]Homework Statement [/h2] A satellite is put into a stationary orbit around earth, i.e. it stays above one point, then it passes through a cloud and looses 10% of it's kinetic energy. it is stabilized again in a new orbit, what's the new radius. [h2]Homework Equations[/h2] Attraction force: ##F=\frac{GMm}{R^2}## Acceleration: ##a=\frac{V^2}{R}## Relation of speed with period: ##2\pi R=V\cdot T## [h2]The Attempt at a Solution[/h2] Finding the initial speed by finding the initial radius: The initial period is 24 hours, the period is ##24\cdot 3600=86,400## $$\frac{GMm}{R^2}=\frac{V^2}{R}=\frac{4\pi^2 R^2}{T^2}$$ $$R^3=\frac{6.67E-11\cdot 6E24\cdot 86,400^2}{4\pi^2}\rightarrow R=35,904 km$$ The initial speed is: $$S=VT\rightarrow 42,303,864=V\cdot 86,400\rightarrow V=3076$$ The initial kinetic energy: $$\frac{1}{2}m\cdot 3076^2=4,257,799$$ The final velocity after deducing 10%: $$4,257,799\cdot 0.9 \cdot m=\frac{1}{2}m\cdot V^2\rightarrow V^2=8,515,598$$ $$R=\frac{GM}{V^2}=\frac{6.67E-11\cdot 6E24}{8,515,598}=46,996 km$$ It should be R=40,500 km [/QUOTE]
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Satellite in orbit losing speed
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