1. Gravitational Potential Energy Consider an object a distance r from the center of the Earth. Where would the object need to be so that the gravitational potential energy of the object – Earth system is zero? What is the gravitational potential energy of an object at a distance r from the center of the Earth?

2. Gravitational Potential Energy What is the gravitational potential energy of an object at a distance r from the center of the Earth?

3. Gravitational Potential Energy What is the gravitational potential energy of an object at a distance r from the center of the Earth? Gravitational Potential Energy Notice that since we have defined E g = 0 at ∞ any finite separation r is below ∞ and is therefore negative. As in our uniform gravitation field strength definition near the surface of the Earth the E g is smaller (more negative) as the separation decreases.

4. Escape Speed Escape Speed – the initial speed for a projectile of mass m to completely escape from the gravitational force of a planet or system. This means that the projectile would move upward forever, coming to rest only at infinite. Mechanical Energy At ∞, both E k and E g = 0. Hence, E Tf = E kf + E gf = 0

5. Escape Speed Escape Speed – the initial speed for a projectile of mass m to completely escape from the gravitational force of a planet or system. Where M = mass of the planet or system Escape Speed Law of Conservation of Energy

6. Escape Speed What is the escape speed from the Earth?