Question

A comet orbiting the Sun has a perihelion distance of 1 AU. At aphelion, it is at 69 AU. What is the ratio of its speed at perihelion to its speed at aphelion?

Answer 1

69

Explanation:

v = `sqrt`(`mu`(2/r `-` 1/a).
Perihelion = a( 1 `-` e) and aphelion = a( 1 + e). Required ratio simplifies to the ratio aphelion/perihelion.
For the Earth, this ratio is 1.03399.