One way to encourage interest in students of introductory, general education astronomy courses is to explore how some of the topics can relate to other subjects. Many students have experience with music, having participated in band or choir in high school, with some still doing so in college. Many such students enjoy hearing about Kepler’s attempts to relate his study of planetary orbits to musical notes and scales.

1.
A.
Robinson
, “
Johannes Kepler’s pursuit of harmony
,”
Phys. Today
73
,
36
42
(
2020
).
2.
P.
Pesic
, Music and the Making of Modern Science (
The MIT Press
,
Cambridge, MA
,
2014
), pp.
80
82
.
3.
Fig. 1 prepared by A. Lai, Instructor of Music, Henry Ford College, based on an image from J. Kepler
, Harmonices Mundi (1619).
4.
For more detail how musical intervals and scales relate to frequency ratios, see HyperPhysics
, http://hyperphysics.phy-astr.gsu.edu/hbase/Music/mussca.html.
5.
Although these equations apply for circular orbits, and do not apply for an arbitrary point on an elliptical orbit, at the two extreme points of the elliptical orbit, the radial velocity is zero, so the motion is instantaneously identical to the motion associated with a circular orbit of that radius—the “kissing circle” tangent to the ellipse at the extreme radius
.
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