First slide

Motion of planets and satellites

Question

The gravitational force between two objects is proportional to 1/R (and not as 1/R²) where R is separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to

Moderate

A

$\frac{1}{R^{2}}$
B

$R^{0}$
C

$R^{1}$
D

$\frac{1}{R}$

Solution

$F_{G} = \frac{GMm}{R} (as F_{G} \propto \frac{1}{R} given)$
$So \frac{{mv}^{2}}{R} = \frac{GMm}{R} \Rightarrow v^{2} \propto R^{0}$

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