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Kepler's Third Law Without a Calculator
1.Karen Bouffard, “Fermi questions,” Phys. Teach. 37, 314 (May 1999) and
1.Karen Bouffard, “More Fermi questions,” Phys. Teach. 37, 364–365 (Sept. 1999).
2.John Sherfinski, “Let's introduce more ‘Mental Math,’” Phys. Teach. 39, 184–185 (March 2001).
3.Steven D. Doty and Sandra L. Doty, “Dielectric breakdown of air as order-of-magnitude physics,” Phys. Teach. 36, 6–9 (Jan. 1998).
4.Jeff Hester et al., 21st Century Astronomy (W.W. Norton & Co., New York, 2002), p. 59.
5.James Metz, “Finding Kepler's third law with a graphing calculator,” Phys. Teach. 38, 242 (April 2000).
6.Annie B. Elliott, Stephen D. Murray, and Richard A. Ward, “Spreadsheet-based exercises for introductory laboratories,” Phys. Teach. 41, 18–19 (Jan. 2003).
7.Harold Cohen, “Testing Kepler's laws of planetary motion,” Phys. Teach. 36, 40–41 (Jan. 1998).
8.Xiong-Skiba Pei, “Using Interactive Physics in planetary motion,” Phys. Teach. 36, 42–43 (Jan. 1998).
9.Manfred Bucher, “Kepler's third law: Equal volumes in equal times,” Phys. Teach. 36, 212–214 (April 1998).
10.Jay M. Pasachoff, Astronomy: From the Earth to the Universe (Saunders College Publishing, Fort Worth, 1998), p. 31.
11.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.
12.Manfred Bucher and Duane P. Siemens, “Average distance and speed in Kepler motion,” Am. J. Phys. 66, 88–89 (Jan. 1998).
13.Alfred Romer, “Halley's comet” Phys. Teach. 22, 488–493 (Nov. 1984).
14.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 . 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. [Supplementary Material]
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.
18.Robert H. Romer, “The answer is forty-two — Many mechanics problems, only one answer,” Phys. Teach. 41, 286–290 (May 2003).
19.See EPAPS Document . 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. [Supplementary Material]
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