# Potential Energy After Escape Velocity

1. Sep 29, 2008

I'm not quite sure I'm understanding potential energy correctly. Let's say we have a runaway planet in deep space which is going in a perfectly straight line. The planet is perfectly spherical and doesn't have an atmosphere. If an object on the surface spontaneously (for the sake of simplicity as it's not the point) acquires a high upward velocity, it's kinetic energy should gradually be converted to potential energy as gravity slows it down, right? Well let's say that when the object was launched it had achieved escape velocity and eventually escapes the planet's gravity and drifts away from the planet. Let's say the object never gets caught in the planet's field of gravity again. Since it's not going to go near the planet again, where did all of that potential energy go? Energy can't be created or destroyed so the potential energy can't just simply disappear... I'm confused X_X

2. Sep 29, 2008

### vanesch

Staff Emeritus
It went into its freedom :-)
Consider this: you have a debt. You also have an income. Your income is used to pay back that debt, so at a certain point, you've paid back everything. Your debt doesn't exist anymore. Where did all the money of your income go ?

What happens is that gravitationally (or otherwise) bound systems have a *negative* potential energy as compared to free systems. They must first pay back their debt of binding energy before they can be free. Otherwise they remain bound.

3. Sep 29, 2008

### olgranpappy

the kinetic energy of the launched object is initially some positive number and the potential energy (relative to infinity) is some negative number. When the rocket is far away (never to be seen by the planet again) the kinetic energy is some smaller positive number and the potential energy is zero. The sum of the kinetic and potential energy is constant throughout the process.

4. Sep 29, 2008