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launching a rocket from the space station

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Rocket Propulsion. See attached file for full problem description.

A rocket is fired from a space station that is 1000 miles above the surface of the Earth. We take the radius of the Earth to be 4000 miles, so r = 5000 miles. Suppose that the rocket is fired "horizontally". That is, suppose at the time the rocket is launched.
a) With what speed must the rocket be launched so that it will never come back?
b) With what speed must it be launched to go into circular orbit?

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Solution Summary

The initial speed of launching a rocket from the space station is calcualted so that the rocket has a circular orbit.

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Please see the attached file.

Here is the answer.
1000 miles = 1609.344 Kilometer 4000 miles = 6437.376 Km
5000 miles =8046.72 Km.

It is given that, the rocket is fired from the space station, which is already at a height of 1000 miles above the surface ie 5000 miles above the centre of the earth.

In order to orbit round the earth, it must be projected with a speed equal to the orbital speed of the satellite. The orbital speed of ...

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