Physics

Problem

An astronaut of mass

72\,\text{kg}

orbits the Earth in a circular satellite path at an altitude of

200\,\text{km}

. Assume

g = 9.8\,\text{m s}^{-2}

and

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

. a. (i) Derive an expression for the orbital speed

v

required for a circular orbit at altitude

h

in terms of

g

R

, and

h

. b. (ii) Using the value of

v

obtained in part (i), establish an expression for the actual gravitational force acting on the astronaut at that altitude. c. (iii) Compute the numerical value of this force for

h = 200\,\text{km}

. d. (iv) Compare the result of part (iii) with the astronaut’s weight on the Earth’s surface and comment on the apparent weightlessness experienced inside the satellite.

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