28. Central Force Motion and the Kepler Problem

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• Syllabus
• Introduction to Mechanics

  • 1. Units and Dimensional Analysis
  • 2. Problem Solving and Estimation
• Mathematics: The Language of Science

  • 3. Cartesian Coordinates and Vectors
• Translational Kinematics

  • 4. One-Dimensional Kinematics and Free Fall
  • 5. One-Dimensional Kinematics: Non-Constant Acceleration
  • 6. Two-Dimensional Kinematics
• Force and Newton's Laws of Motion

  • 7. Concept of Force
  • 8. Applications of Newton's Second Law
• Circular Motion

  • 9. Circular Motion Kinematics
  • 10. Circular Motion Dynamics
• Conservation of Energy

  • 11. Work and Energy
  • 12. Work and the Dot Product
  • 13. Potential Energy
  • 14. Application of Energy Conservation
  • 15. Mechanical Energy and the Simple Harmonic Oscillator
• Momentum

  • 16. Momentum and Impulse
  • 17. Systems, Center of Mass, and Conservation of Momentum
  • 18. Collision Theory
  • 19. Continuous Mass Flow
• Two-Dimensional Rotational Motion

  • 20. Two-Dimensional Rotational Kinematics
  • 21. Two-Dimensional Rotational Dynamics
  • 22. Torque and the Simple Harmonic Oscillator
  • 23. Static Equilibrium
• Angular Momentum

  • 24. Angular Momentum
  • 25. Conservation of Angular Momentum
• Rotation and Translation

  • 26. Two-Dimensional Rotation and Translation Kinematics
  • 27. Two-Dimensional Rotation and Translation Dynamics
• Central Force Motion

  • 28. Central Force Motion and the Kepler Problem
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Learning Objectives

• Explain what is meant by a central force.
• Be able to solve problems involving the application of the conservation laws of energy and angular momentum to central force motion problems.
• Be able to explain how the two body Kepler problem can be reduced to a one body problem.
• Explain what is meant by a reduced mass.
• Describe how a one body problem in two dimensions and be interpreted as a one body problem in one dimension.
• Describe the meaning and origin of each term in effective potential energy.
• Be able to construct energy diagrams using the effective potential and describe different energy solutions.
• Be able to find the radius and energy associated with the lowest energy orbit using the effective potential energy.

Preparation

Course Notes

Notes: The Kepler Problem: Planetary Mechanics (PDF - 12MB)

Suggested Textbook Reading (Optional)

Chapter 12.1-12.5, 12.8. Young, Hugh D., Roger A. Freedman, and A. Lewis Ford. Sears and Zemansky's University Physics: with Modern Physics. 12th ed. San Francisco, CA: Addison-Wesley, 2007. ISBN: 9780805321876.

Lecture Video

Video Excerpts

Learning Activities

Guided Activities

Read through the class slides carefully. They explain all of the concepts from the module.

Slides: Central Force Motion and the Kepler Problem (PDF - 3.1MB)

Self-Assessment

Do the Concept Questions first to make sure you understand the main concepts from this module. Then, when you are ready, try the Challenge Problems. If you are struggling with the Challenge Problems, watch the Homework Help Session videos, which will give you tips on how to tackle problems of this type.

Concept Questions

Concept Questions (PDF)

Solutions (PDF)

Challenge Problems

Challenge Problems (PDF)

Solutions (PDF - 2.2MB)

Problem Solving Help

In the following videos Prof. Walter Lewin explains how to approach the Challenge Problems.

Help Session

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/central-force-motion/central-force-motion-and-the-kepler-problem/help-session/oE73MgGryj0.srt'}

Related Resources

There are countless resources available online to help you learn physics. Try these:

• Try out the My Solar System interactive simulation from PhET.
• Read about the Kepler Problem on Wikipedia.

Feedback

Did this course have everything you needed to learn the subject? Are there ways we could improve it? Let us know.

 

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