Three identical science satellites

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

Problem

Three identical science satellites, each of mass

1200\,\text{kg}

, orbit Mars in separate circular paths of radii

r_{A}=4.0\times10^{6}\,\text{m}

r_{B}=5.0\times10^{6}\,\text{m}

, and

r_{C}=7.0\times10^{6}\,\text{m}

, measured from the planet’s center. Mars has mass

M_{\!M}=6.42\times10^{23}\,\text{kg}

and radius

R_{\!M}=3.39\times10^{6}\,\text{m}

. (a) Rank the satellites’ total mechanical energy per unit mass

E/m

from most negative to least negative. Justify your ranking without performing detailed calculations. (b) For satellite B, calculate its orbital speed

v

, kinetic energy

K

, gravitational potential energy

U

, and total mechanical energy

E

. (c) Determine the escape speed

v_{\text{esc}}

for an object located at radius

r_{B}

from Mars’ center. Then compute the ratio

v_{\text{esc}}/v

for satellite B. (d) Explain the physical significance of the ratio obtained in part (c) and discuss what it implies about the additional energy needed for satellite B to escape Mars’ gravity.

Related theory

Browse the problem library