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Standard XII

Physics

Satellites

Two satellite...

Question

Two satellites $A$ and $B$ of the same mass are orbiting the earth at altitudes $R$ and $3 R$ respectively,where $R$ is the radius of the earth. Taking their orbits to be circular obtain the ratios of their kinetic and potential energies.

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Solution

Kinetic energy of a satellite is given by

$K = \frac{1}{2} m v^{2} = \frac{1}{2} m {(\sqrt{\frac{G M}{R}})}^{2} = \frac{G M m}{2 R}$

Also, potential energy is given by

$U = - \frac{G M m}{R}$

Hence, the ratio is

$\frac{K_{1}}{K_{2}} = \frac{U_{1}}{U_{2}} = \frac{3 R + R}{R + R} = 2$

Answer is 2.

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Two satellites A and B of the same mass are orbiting the earth at altitudes R and 3R respectively,where R is the radius of the earth. Taking their orbits to be circular obtain the ratios of their kinetic and potential energies.

Kinetic energy of a satellite is given byK=12mv2=12m(√GMR)2=GMm2RAlso, potential energy is given byU=−GMmRHence, the ratio isK1K2=U1U2=3R+RR+R=2Answer is 2.

Two satellites $A$ and $B$ of the same mass are orbiting the earth at altitudes $R$ and $3 R$ respectively,where $R$ is the radius of the earth. Taking their orbits to be circular obtain the ratios of their kinetic and potential energies.