How do you calculate speed at an object's perihelion?

For example: The orbit of Halley's Comet around the sun is a long thin ellipse. At its aphelion the comet is 5.40 x 10^12m from the sun and moves with a speed of 13.0 km/s. What is the comet's speed at its perihelion where its distance from the sun is 8.60 x 10^10m.

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Feb 28, 2016

(perihelion speed / aphelion speed ) = ( 1 + eccentricity) / ( 1 $-$ eccentricity ) = (aphelion distance / perihelion distance)
So, the comet's perihelion speed = 816 km/s, nearly.

Explanation:

Perihelion speed = (5.40 x 10^12 / 8.60 x 10^10) X 13 km/s
In the usual notation, v^2 = $\mu$ (2/r $-$ 1/a ).
The other results follow from this.
Perihelion distance = a (1 $-$ e ) and aphelion = a ( 1 + e )

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