You are an astronaut in the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it. (a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km? (b) By how much must you reduce your orbital radius to catch up in 7.0 hours? Mass of Earth: 5.98x1024 kg, radius of Earth: 6.38×10 m, Universal Gravitation Constant: 6.67x10-1'N•m²/kg?

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You are an astronaut in the space shuttle pursuing a satellite in need of repair. You are in a
circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km
behind it. (a) How long will it take to overtake the satellite if you
reduce
your
orbital
radius by 1.0 km? (b) By how much must you reduce your orbital radius to catch up in 7.0
hours? Mass of Earth: 5.98×1024 kg, radius of Earth: 6.38×10 m, Universal Gravitation
Constant: 6.67x10-l'N•m?/kg?
Transcribed Image Text:You are an astronaut in the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it. (a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km? (b) By how much must you reduce your orbital radius to catch up in 7.0 hours? Mass of Earth: 5.98×1024 kg, radius of Earth: 6.38×10 m, Universal Gravitation Constant: 6.67x10-l'N•m?/kg?
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