How Fast is a Comet at Pluto's Distance?

[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.)

Homework Equations

G*M*((1/ri) - (1/rf)) = (1/2)*((vi)^2 - (vf)^2)

The Attempt at a Solution

i got 4.2103e4 m/s is this right? someone please help i plugged it into that eqaution if it isn't can someone show me how? thanks

 

[lippyka]

! Yes, your answer is correct. The equation you used is:G*M*((1/ri) - (1/rf)) = (1/2)*((vi)^2 - (vf)^2)where G is the gravitational constant (6.67x10^-11), M is the mass of the Sun (2x10^30 kg), ri is the initial distance (4.7x10^10 m), rf is the final distance (6x10^12 m), vi is the initial velocity (9.6x10^4 m/s), and vf is the final velocity (4.2103e4 m/s).