Energy needed for a velocity change?

[Mecia22]

Homework Statement

I figured out the escape speed from the sun, and the speed the spaceship was already going. So how much energy would that velocity take?

The Attempt at a Solution

This is how I did it:
E=(1/2mv(escape speed)^2-1/2m27777(current speed)^2)+Gm1m2/rSo did I do that right?

 

[voko]

It is unclear what you are trying to determine.

The energy required to change velocity does not depend on the distance from the Sun. It is merely the difference between the kinetic energies at the two velocities.

However, if you also change the position, there is a change in the potential energy, and that must be accounted for.

The keyword is "change" in both cases.