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cpburris
Gold Member
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Homework Statement
A comet is going in a parabolic orbit lying in the plane of the earth’s orbit. Assuming that the earth’s orbit is a circle of radius a. The points where the comets orbits intersects the earth’s orbit are given by:
cos θ = −1 + 2p/a
where p is the perihelion distance of the comet defined as θ = 0.
Use this to show that the time that the comet remains within the earth’s orbit is given by:
[tex]\frac{2^{1/2}}{3\pi}(2p/a+1)(1-p/a)^{1/2}\tau_E[/tex]
where [tex]\tau_E[/tex] is the period of the Earth's orbit (i.e. 1 year).
The Attempt at a Solution
Well I used an expression for the angular momentum per unit mass and integrated to get theta in terms of t, set it equal to the intersection points, solved for t for each, and then took the difference. That yielded an answer, but not one that even remotely resembled what was asked for. I am just not sure what to do now.