Tutorials on orbital mechanics and central forces

Angular momentum and Kepler’s Second Law

Pretest (.pdf)

Tutorial (.pdf)

Homework (.pdf)

Exam questions (.docx)

Instructor notes (.pdf)

All materials (~2.3MB .zip,

.docx and .pdf)

Tutorial title

Emphasis (what do students do?)

Review angular momentum concept in context of point particles; derive relationship between torque and time rate-of-change of angular momentum

Deduce that gravitational forces conserve angular momentum

Gravitation and conservation of energy

Contact information for co-PIs

Department of Physics

Grand Valley State University

Allendale, MI 49401

Tel.:  616-331-2524

FAX:  616-331-3740

Email:  ambroseb@gvsu.edu

Michael C. Wittmann

Department of Physics and Astronomy

5709 Bennett Hall

University of Maine

Orono, ME  04401-5709

Tel.:  207-581-1237

FAX:  207-581-3410

Email:  wittmann@umit.maine.edu

Use Newton’s law of gravitation to derive function for gravitational potential energy

Apply conservation of energy to open two-body systems (e.g., escape velocity) and elliptical orbits (e.g., total energy as determining factor for semi-major axis)

Kepler’s First Law

Tutorial (.pdf)

Homework (.pdf)

All materials (~1MB .zip,

.docx and .pdf)

Express angular momentum in polar coordinates; relate latus rectum, semi-major axis, and eccentricity

Perform guided derivation of polar equation of ellipse using Newton’s 2nd law and Kepler’s 2nd law

Tutorial (.pdf)

Homework (.pdf)

All materials (~1MB .zip,

.docx and .pdf)

Energy and angular momentum for
closed orbits

Review relationships between (1) semi-major axis and total energy and (2) latus rectum and angular momentum

Gain practice in using energy and angular momentum arguments to solve orbit transfer problems

Pretest (.pdf)

Tutorial (.pdf)

Homework (.pdf)

Exam questions (.docx)

Instructor notes (.pdf)

All materials (~1.2MB .zip,

.docx and .pdf)

Sponsored in part by NSF grants DUE-0441426 and DUE-0442388

Intermediate Mechanics Tutorials are modeled after:

1. Tutorials in Introductory Physics, L.C. McDermott P.S. Shaffer, and the Physics Education Group at the University of Washington (Prentice Hall, 2002)

1. Activity-Based Tutorials, M.C. Wittmann, R.N. Steinberg, E.F. Redish, and the University of Maryland Physics Education Research Group (Wiley, 2004 and 2005)