You are an astronaut in the space shuttle pursuing a satellite in need of repair. You

Chapter 5, Problem 85GP

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QUESTION:

Problem 85GP

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?

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QUESTION:

Problem 85GP

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?

ANSWER:

Solution 85GP

Step 1 of 5

(a)

Here we have to calculate the time taken to overtake the satellite when the orbital radius is reduced by 1 km.

The orbital speed for the objects in the orbit around the earth is related to the orbital radius as given below,

                                ………..1

Where  is universal gravitational constant, is the mass of the earth and is the orbital radius.

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