Speed update of a comet in an ELLIPTICAL orbit

[shnav34]

A comet is in an elliptical orbit around the Sun. Its closest approach to the Sun is a distance of 5e10 m (inside the orbit of Mercury), at which point its speed is 9e4 m/s. Its farthest distance from the Sun is far beyond the orbit of Pluto. What is its speed when it is 6e12 m from the Sun? (This is the approximate distance of Pluto from the Sun.)

Homework Equations

Ug(r) = -G(m1*m2)/r
this is a guess, the problem is i don't know what equations to use

i tried to solve it with an incorrect method and got a speed of 3500 something m/s

 

[ideasrule]

Have you tried the conservation of energy?

 

[shnav34]

that's the problem, everyone says that and i have no idea what is needed equations are needed to figure that out what the conservation of energy is