Question

If a planet were suddenly stopped in its orbit supposed to be circular, show that it would fall into , where T is the time period of revolution. the sun in a time $T\times \left(\frac{\sqrt{2}}{8}\right)$

Answer 1

By Kepler's law

$\frac{T^1}{T}=(\frac{r^{\prime }}{r}{)}^{\frac{3}{2}}$ Time taken by planet to revolve around the sum of radius r= T

$[r^1=\frac{1}{2}r]$

$\Rightarrow T^1=T(\frac{1}{2}{)}^{\frac{3}{2}}$ Time period of planet to reach sum in an elliptied path $2t^1=T^1$

$t^1=\frac{\sqrt{2}}{8}T$