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?)
Links to materials
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
Bradley S. Ambrose
Department of Physics
118 Padnos Hall
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)
Creative Commons License
Kepler’s First Law
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
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:
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•Tutorials in Introductory Physics, L.C. McDermott P.S. Shaffer, and the Physics Education Group at the University of Washington (Prentice Hall, 2002)
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•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)