A comet moves about the Sun in an elliptical orbit with its

A comet moves about the Sun in an elliptical orbit, with its closest approach to the Sun being about 0.615 AU and its greatest distance from the sun being 37.0 AU (1 AU = the Earth-Sun distance). If the comet\'s speed at closest approach is 54.0 km/s, what is its speed when it is farthest from the Sun? (The gravitational force exerted by the Sun on the comet is parallel to the moment arm, so exerts no torque. Therefore, angular momentum of the comet around the Sun is conserved.)

Solution

Conservation of angular momentum

L = L
mv x r = mV x R
v x r = V x R

given that the comet\'s path is perpendicular to the sum at the closests and most distant points, the cross product is simply:

v *r = V*R

v = V R/r

v = 54 km/s * .615 au/ 37 au
v = .8975 km/s