Comet Speed at 6x10^12 m from Sun

[ohheytai]

A comet is in an elliptical orbit around the Sun. Its closest approach to the Sun is a distance of 4.7x10^10 m (inside the orbit of Mercury), at which point its speed is 9.6x10^4 m/s. Its farthest distance from the Sun is far beyond the orbit of Pluto. What is its speed when it is 6x10^12 m from the Sun? (This is the approximate distance of Pluto from the Sun.)



I have no idea how to do this can someone please help?

 

[willem2]

conservation of energy. You know the potential energy and the kinetic energy at the closest point to the sun, and the potential energy at 6*10^12 m. All energies will contain the mass of the comet, but you can cancel that. You'll have to look up the mass of the sun.