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

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

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

    NOTE: v_{E} and 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 08:36 AM.
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