Question

A comet of mass m travels around the Sun in a very large elliptical orbit. At closest approach, the comet is a distance r from the Sun and has a velocity v. How fast is the comet moving at its farthest point from the Sun at a distance d away?

a) vd/r
b) vr/d
c) vrd
d) Zero

Answer 1

To determine the comet's speed at its farthest point from the Sun, the conservation of angular momentum is used, and the speed can be found with the formula vr/d, where v is the velocity at closest approach, r is the distance at closest approach, and d is the farthest distance.

Step-by-step explanation:

The question you've asked is about determining the velocity of a comet at its farthest point from the Sun, given its velocity at its closest approach. According to Kepler's laws of planetary motion, in particular the conservation of angular momentum, a comet will travel faster when it is nearer to the Sun and slow down as its distance from the Sun increases. This is because the angular momentum must remain constant, so the velocity and distance are inversely proportional.

Given that the comet has a velocity v at a distance r at its closest approach, and at its farthest point it is a distance d away, we can set the conservation of angular momentum equation mv₁r₁ = mv₂r₂. Solving for v₂ (the velocity at the farthest point), we get v₂ = vr/d. Therefore, the comet's velocity at its farthest point from the Sun will be vr/d.