First slide

Motion of planets and satellites

Question

Two identical satellites are at R and 7 R away from earth surface, the wrong statement is (R = Radius of earth)

Difficult

A

Ratio of total energy will be 4
B

Ratio of kinetic energies will be 4
C

Ratio of potential energies will be 4
D

Ratio of total energy will be 4 but ratio of potential and kinetic energies will be 2

Solution

Orbital radius of satellites, $r_{1} = R + R = 2 R$
$\begin{array}{l} r_{2} = R + 7 R = 8 R \\ U_{1} = \frac{- GMm}{r_{1}} and U_{2} = \frac{- GMm}{r_{2}} \\ K_{1} = \frac{GMm}{2 r_{1}} and K_{2} = \frac{GMm}{2 r_{2}} \\ E_{1} = \frac{GMm}{2 r_{1}} and E_{2} = \frac{GMm}{2 r_{2}} \\ ∴ \frac{U_{1}}{U_{2}} = \frac{K_{1}}{K_{2}} = \frac{E_{1}}{E_{2}} = 4 \end{array}$

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