Hi Everyone,

This question came up as a review question. Any help with this would be greatly appreciated.

Thank You!

A comet is observed to have a speed $\displaystyle v$ when it is at a distance $\displaystyle r$ from the Sun, and its direction of motion makes an angle $\displaystyle \phi$ with the radius vector from the Sun. Show that the major axis of the elliptical orbit of the comet makes an angle

$\displaystyle \theta=\cot^{-1}(\tan\phi - \frac{2}{V^2R}\csc2\phi)$

with the initial radius vector of the comet where $\displaystyle V=\frac{v}{v_{E}}$ and $\displaystyle R=\frac{r}{a_{E}}$ are dimensionless ratios.

NOTE:$\displaystyle v_{E}$ and $\displaystyle a_{E}$ are the velocity and radius of Earth respectively. Assume the Earth's orbit about the Sun is circular.