Unit 7: Gravitation

Big Ideas:
1. Every mass exerts a force on every other mass.
2. Satellites in orbit follow Kepler’s Laws.
3. Satellites in uniform circular motion experience a gravitational force that acts centripetally.
4. The total energy of an orbiting satellite will determine its trajectory.

Learner Objectives (as published by the College Board):
1. Students should know Newton's Law of Universal Gravitation, so that they can:
A. Determine the force that one spherically symmetrical mass exerts on another.
B. Determine the strength of the gravitational field at a specified point outside a spherically symmetrical mass.
C. Describe the gravitational force inside and outside a uniform sphere, and calculate how the field at the surface depends on the radius and density of the sphere.

2. Students should understand the motion of an object in orbit under the influence of gravitational forces, so that for a circular orbit they can:
A. Recognize that the motion does not depend on the object’s mass; describe qualitatively how the velocity, period of revolution, and centripetal acceleration depend upon the radius of the orbit; and derive expressions for the velocity and period of revolution in such an orbit.
B. Derive Kepler’s Third Law for the case of circular orbits.
C. Derive and apply the relations among kinetic energy, potential energy, and total energy for such an orbit.

3. Students should understand the motion of an object in orbit under the influence of gravitational forces, so that for a general orbit they can:
A. State Kepler’s three laws of planetary motion and use them to describe in qualitative terms the motion of an object in an elliptical orbit.
B. Apply conservation of angular momentum to determine the velocity and radial distance at any point in the orbit.
C. Apply angular momentum conservation and energy conservation to relate the speeds of an object at the two extremes of an elliptical orbit.
D. Apply energy conservation in analyzing the motion of an object that is projected straight up from a planet’s surface or that is projected directly toward the planet from far above the surface.