Abstract
If Kepler’s laws applied to planets revolving around the Sun, perhaps it was due to some as-yet (in 1619) undiscovered force that caused such motions. Kepler was convinced that such a force originated in the Sun, operating at one focus of the ellipses described by the planets. He speculated that the Sun’s force might be akin to magnetism. Civilization would have to wait another 70 years before Isaac Newton would unveil his theory of gravitation.
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Notes
- 1.
Florian Cajori [1], (Short title) Principia.
- 2.
Ibid., Book I, Proposition II, Theorem II, 42.
- 3.
Ibid., Book III, Proposition VIII, Theorem VIII, 414.
- 4.
Principia, 13–14.
- 5.
The Committee on Data for Science and Technology (CODATA) maintains standards for international uses. See http://physics.nist.gov/cuu/Constants/international.html. The full value for G given by CODATA is 6.67384 x 10−11. http://physics.nist.gov/cgi-bin/cuu/Value?bg|search_for=G. m3 kg−1 s−2.
- 6.
Principia, Book III, Proposition VII, Theorem VII, 414–15.
- 7.
Recall that in the angular notation for acceleration, a = ω 2 r is equivalent to a = v 2/r.
- 8.
The precise length of an astronomical unit is 149,597,870.691 km. See http://neo.jpl.nasa.gov/glossary/au.html.
Reference
Cajori (1949) Principia in modern English: Sir Isaac Newton’s mathematical principles of natural philosophy. Book I, Proposition I, Theorem I (Motte’s Translation Revised). University of California Press, Berkeley, p 40
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MacDougal, D.W. (2012). Newton’s Master Stroke: The Universal Law of Gravitation. In: Newton's Gravity. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5444-1_8
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