# PHYS 2211 Module 12.3

## Gravitational Potential Energy and Total Energy

12.3 Gravitational Potential Energy and Total Energy

### Learning Objectives

By the end of this section, you will be able to:

• Determine changes in gravitational potential energy over great distances
• Apply conservation of energy to determine escape velocity
• Determine whether astronomical bodies are gravitationally bound

### Gravitational Potential Energy beyond Earth

Recall from Module 8 that we defined the change in potential energy as the negative work done by a conservative force:

When we calculated the change in gravitational potential energy, we assumed that the force of gravity was a constant force:

This was valid for objects moving near the surface of Earth because the force of gravity is very close to constant for small changes in height.

But now we need to consider how the gravitational potential energy is affected when objects with mass are moved farther apart or closer together, with distances that are large.

Discuss!

A student is studying the potential energy change of a 50 kg object raised 90 km above Earth’s surface. What will be the percentage error if she simply used the approximate relation ΔU = mgΔy?

Practice!

### Bound and Unbound Systems

Practice!

The formula for energy conservation only involves v2, so angle does not matter.

Discuss!

If a planet has the same surface gravity as the earth (that is, the same value of g at the surface), what is its escape speed?

A planet orbiting a distant star has a radius 3.24 x 106 m.  The escape speed for an object launched from this planet’s surface is 7.65 x 103 m/s.  What is the acceleration due to gravity at the surface of the planet?