Question

A comet is in an elliptical orbit around the Sun. Its closest approach to the Sun is a distance of 4.8 × 1010 m (inside the orbit of Mercury), at which point its speed is 9.2 × 104 m/s. Its farthest distance from the Sun is far beyond the orbit of Pluto. What is its speed when it is 6 × 1012 m from the Sun? (This is the approximate distance of Pluto from the Sun.)

speed = ??

Answer 1

We will apply the principal of conservation of energy.

According to the conservation law, sum of the kinetic and potential energy of the comet+Sun must be equal at both positions.

Let m1 and m2 be the mass of the comet and sun and respective distances when it is close and far be r1 and r2.

Then applying the conservation principle,

v's denote the velocity of the comet and sun respectively.

Putting the values,