1. Read pages 401 – 403, 413 – 419 (the green “outlined” sections)

2.  Energy that is “stored” in an object’s gravitational field.  Work must be done in order to change the position of a second mass from an infinitely far away point in space to a position relatively near the first mass.  Remember: Work-Energy Theorem ◦ The amount of work done on an object is equal to the change in energy of that object. ◦ In this case, the energy change is all potential.

4.  Work is done when moving the mass from a distance infinitely far from the source of a gravitational field to some distance R from the source  This work is stored in the gravitational field between the two masses: Gravitational Potential Energy

5.  Graph of gravitational potential energy as a function of distance from a planet’s surface

6.  A field, defined at every point in space, but a scalar quantity  Defined as: ◦ The work done per unit mass to bring a small point mass (m) from infinity to a point P.

7.  Total energy, as usual, is the sum of the orbiting object’s gravitational potential and kinetic energies:  However, we can simplify this…

8.  Solve for v 2 using Newton’s laws:  Substitute into energy equation:

9.  Defined as: the velocity required for an object of mass m to be launched so that it escapes from the pull of the larger mass, M, and will move very far away from it. (assume that “very far away” means that the distance approaches infinity) ◦ Imagine that a satellite, when it is sitting at the surface of the Earth, is modeled as something sitting at the bottom of an infinitely deep “potential well” ◦ In order to escape the “well”, it must gain enough energy in order to get higher than the depth of the well…

11.  The “depth” of the potential well is:  If the satellite (mass = m) gets enough potential energy to raise it out of the well, it will have  The satellite really isn’t at “infinity”, but it is far enough away that it is no longer affected by the gravitational force

12.  The change in potential energy is equal to the change in kinetic energy…  For Earth: ( where g 0 = 9.81 m·s -2 …)