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  1. #1
    Jun 2009

    An Orbit Problem

    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.
    Last edited by calculusfrk; Jul 25th 2009 at 07:36 AM.
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