Oort Cloud Parabolic Comet

A comet in the Oort cloud falls towards the Sun. As it picks up speed from the Sun's gravity, it accidentally picks up a very tiny extra velocity boost from a nearby object in the solar system, so that its trajectory is now a true parabola. It eventually whips around the Sun and begins to travel back out into the far reaches of space.

Let θ\theta be the angle POA,\angle POA, where point OO is the center of the Sun, point PP is where the comet has come closest to the Sun, and point AA is where it is on the trajectory outward.

The radial velocity of the comet relative to the Sun is the speed in which the comet is moving away from the Sun in the direction of the line OAOA. For what angle θ\theta is this radial velocity the greatest?

Express your answer to the nearest degree.

Note: Kepler orbits are commonly described by the polar equation r(θ)=a(1e2)1+ecos(θ),r(\theta)=\dfrac{a(1-e^2)}{1+e \cos(\theta)}, where aa is the semi-major axis, and ee is the eccentricity. For a circle, e=0;e=0; for an ellipse, 0<e<1;0<e<1; for a parabola, e=1;e=1; for a hyperbola, e>1e>1. Also, you may want to look up Kepler's laws and vis-viva equation.


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