Teaching Modern Physics - QuarkNet - Fermilab

Newton’s Universal Law of Gravitation
and Kepler’s Laws of Planetary Motion
(Chapter 7b)
I. Teacher’s Notes:
These two topics fall under the larger topic we’ve been working through recently, which is
Simple Harmonic Motion (SHM). Just like an oscillating pendulum, a mass oscillating on the end
of a spring, or an object moving in a circle, planets orbiting the sun or satellites orbiting the
Earth have a measurable period of oscillation. This group of topics together make up a sizable 6
percent of the AP exam, so work to become comfortable with these ideas.
II. Student Objectives:
Students should:
A. Know Newton’s Law of Universal Gravitation so they can:
1. Determine the force that one spherically symmetrical mass exerts on another.
2. Determine the strength of the gravitational field at a specified point outside a
spherically symmetrical mass.
B. Understand the motion of a body in orbit under the influence of gravitational forces so
they can, for a circular orbit:
1. Recognize that the motion does NOT depend on the body’s mass.
2. Describe qualitatively how the velocity, period of revolution, and centripetal
acceleration depend upon the radius of the orbit.
3. Derive expressions for the velocity and period of revolution in such an orbit.
C. Understand the motion of a body in orbit under the influence of gravitational forces so
they can, for a general (not necessarily circular) orbit:
1. Apply conservation of angular momentum to determine the velocity and radial
distance at any point in the orbit.
2. Apply angular momentum conservation and energy conservation to relate the speeds
of a body at the two extremes of an elliptical orbit.
III. Activities and Assignments:
A. READ CHAPTER 7, sections 7.7 - 7.8 (a very nice intro. to the topics)
B. Gravitational interactions activity
1. Brainstorm, “What CAUSES gravity?”
2. Worksheet, “Gravitational Interactions”
3. Where does “g” = 9.8 m/s 2 come from??
C. Interactive Physics Simulation 32, “Solar System”
D. Problem Set #1, Chapter 7, pages 202-211
1. CQ: 14, 19
2. P: 8a, 41, 42, 47, 49
E. Kepler’s Laws of Planetary Motion
1. Lecture/Demo
a. First Law—elliptical orbits
b. Second Law—equal areas in equal times
c. Third Law—mathematically relates orbital periods and radii
d. Seasons and speeds w/planet dance
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