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Math Help - Central Force Motion on elliptical orbit

  1. #1
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    Central Force Motion on elliptical orbit

    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}\csc(2\phi)) with the initial radius vector of the comet, where V=\frac{v}{v_{E}} and R=\frac{r}{a_{E}} are the dimensionless ratios. Use the numerical values that we used for the eccentricity calculation to now calculate a value for the angle \theta.

    Thanks a lot~.
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  2. #2
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    Where v_{E} is the speed of Earth, and a_{E} is the orbital radius. Then the eccentricity calculation of the comet is \varepsilon=\sqrt{1+(V^2-\frac{2}{R})(RVsin\phi)^2)}

    And the numerical values we used here is \phi=30, R=4 and V=1/2 so that \varepsilon=0.866

    These are the given values and konwn formulas
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