At the University of North Carolina at Asheville (UNC-A) we have used Kepler's third law in a liberal-arts conceptual astronomy course to help students sharpen their quantitative skills without using a calculator. Doing quantitative physics without a calculator represents one of the many ways we can study the physical world. Furthermore, it is fun.
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A way to visualize this is to draw the usual ellipse with a string looped around the foci with a taut pull. By definition of the ellipse, the average of the lengths of the two string sections from each focus to a point on the ellipse is equal to the semimajor axis. Consider these as “conjugate” lengths. Then, each point on the planet's orbit can be paired up with a “conjugate” point elsewhere on the orbit. The average of these two conjugate distances from the Sun (left focus) is always equal to the length of the semimajor axis.
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Manfred
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Jerry B. Marion and Stephen T. Thornton, Classical Dynamics of Particles and Systems, 4th ed. (Saunders College Publishing, Fort Worth, 1995), p. 309. Walter Hohmann, a German pioneer in space travel, proposed his transfer orbit in 1925.
15.
Michael Zeilik and Stephen A. Gregory, Introductory Astronomy & Astrophysics, 4th ed. (Saunders College Publishing, Fort Worth, 1998), p. 32. I first encountered the least-energy analysis (Earth to Jupiter) when I was fresh out of graduate school. Since I was embarking on teaching astronomy for the first time, I attended a two-day astronomy workshop for teachers at the University of North Carolina at Chapel Hill. The Voyager spacecrafts had just arrived at Jupiter. The simplicity and power of the approach left a lasting impression on me since training in advanced mathematical techniques offered little assistance here.
16.
See EPAPS Document E-PHTEAH-42-010409.
This document may be retrieved via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html)or from ftp.aip.org in the directory/epaps/in the phys_teach folder. See the EPAPS homepage for more information.
17.
For example, Eugene Hecht, Physics: Algebra/Trig, 3rd ed. (Brooks/Cole Publishing, Pacific Grove, CA, 2003), p. 160; James S. Walker, Physics (Prentice Hall, Upper Saddle River, NJ, 2002), p. 359.
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Robert H.
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See EPAPS Document E-PHTEAH-42-010409.
This document may be retrieved via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html) or from ftp.aip.org in the directory/epaps/in the phys_teach folder. See the EPAPS homepage for more information.
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© 2004 American Association of Physics Teachers.
2004
American Association of Physics Teachers
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