Physics

Problem

A research satellite is to be placed in a circular orbit

400\,\text{km}

above Earth’s surface. Take Earth’s mass as

6.0\times10^{24}\,\text{kg}

, its radius as

6.4\times10^{6}\,\text{m}

, and the universal gravitational constant as

6.67\times10^{-11}\,\text{N\,m}^{2}\,\text{kg}^{-2}

. Neglect atmospheric drag. a. (i) Compute the orbital speed of the satellite at this altitude. b. (ii) Find the minimum speed required for the same satellite to escape from Earth when it is already at the height of

400\,\text{km}

. c. (iii) Compare the numerical ratio of your answers in (ii) and (i) with

\sqrt{2}

and state any conclusion.

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