A research satellite of negligible mass is placed in a circular orbit at an altitude…

PHYSICS · Multi-part · CBSE · Physics · Gravitation · Gravitation

Problem

A research satellite of negligible mass is placed in a circular orbit at an altitude of

300\,\text{km}

above Earth’s surface. The radius of Earth is

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

and Earth’s mass is

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

. The universal gravitational constant is

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

. (1) Calculate the speed of the satellite in its orbit, expressing your answer to three significant figures with appropriate units. (2) Determine the orbital period of the satellite. Express your answer in minutes. (3) Compute the ratio

\dfrac{K}{|U_g|}

of the satellite’s kinetic energy

K

to the magnitude of its gravitational potential energy

U_g

while in orbit, and interpret the physical meaning of the value you obtain. (4) Qualitatively describe how the orbital speed would change if the satellite were instead placed in a circular orbit at an altitude of

600\,\text{km}

above Earth’s surface, citing relevant physical relationships in your explanation.

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