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

You are an astronaut in the space shuttle pursuing a satellite in need of repair. You find yourself in a circular orbit of the same radius as the satellite, but 30 km behind it. (a) How long will it take to reach 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 8.0 hrs?

What is the purpose of differentiating in part (a)? I understand that the change in radius is small compared to overall radius, but what does differentiating do for us?

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