Question

A comet moves in a Parabolic orbit with the sun as focus when the comet is $2\times {10}^7$ km from the sun, the line from the sun to it makes an angle $\frac{\pi }{2}$ with the axis of the orbit. Find how near the comet comes to the sun.

Answer 1

The equation of this parabola is given by $r=\frac{p}{1-\cos \theta }$

when $\theta =\pi /2$, $r=\frac{p}{1-\cos \frac{\pi }{2}}=p$

But $r=2\times {10}^{7}km$

so, $p=2\times {10}^{7}km$

Nearest distance between comet and sun is $\frac{p}{2}$ [from figure]

$={10}^{7}km$