A research satellite orbits Earth at an altitude of above the planet’s surface

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A research satellite orbits Earth at an altitude of

400\,\text{km}

above the planet’s surface. Relevant constants (use exact values given): •

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

•

M_{\!E}=5.97\times10^{24}\,\text{kg}

• Earth’s mean radius

R_{\!E}=6.37\times10^{6}\,\text{m}

(a) Determine the orbital radius

r

of the satellite measured from Earth’s center. (b) Calculate the satellite’s orbital speed

v

. (c) Compute the satellite’s kinetic energy per unit mass,

K/m

. (d) Compute the gravitational potential energy per unit mass,

U/m

. (e) Determine the total mechanical energy per unit mass,

E/m

, for the satellite in this orbit.