First slide

Keplers 3 Laws

Question

A satellite can be in a geo stationary orbit around a planet at a distance r from the centre of the planet. If the angular velocity of the planet about its axis doubles, a satellite can now be in a geostationary orbit around the planet if its distance from the centre of the planet is

Moderate

A

$\frac{r}{2}$
B

$\frac{r}{2 \sqrt{2}}$
C

$\frac{r}{{(4)}^{\frac{1}{3}}}$
D

$\frac{r}{{(2)}^{\frac{1}{3}}}$

Solution

$T^{2} \propto r^{3} \Rightarrow {(\frac{2 π}{ω})}^{2} \propto r^{3}$
$∴ {(\frac{r^{'}}{r})}^{3} = {(\frac{ω}{ω_{1}})}^{2} = {(\frac{1}{2})}^{2} \Rightarrow r^{'} = \frac{r}{{(4)}^{\frac{1}{3}}}$

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