Abstract
The German mathematician Johannes Kepler (1571–1630) worked tirelessly for years trying to make sense the data of his employer Tycho Brahe, a Danish nobleman-astronomer. Tycho was a meticulous observer. From his self-financed and constructed observatory in Denmark, Tycho in the late 1500s had gathered an enormous set of positional data on the movements of the planets, including Mars. Later (in 1600) Tycho hired Kepler to be his assistant in Prague, in the court of Rudolph II, ruler of the Holy Roman Empire. Though Kepler was Tycho’s able assistant, Tycho was not generous with sharing his data with Kepler. This frustration ended upon Tycho’s death, Kepler succeeded to his position as imperial mathematician, and inherited all of Tycho’s precious notes. Tycho’s data on Mars in particular was thorough and precise, far more accurate than any observations in the history of astronomy.
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Notes
- 1.
This data can be found at the NASA Jet Propulsion Laboratory website: http://ssd.jpl.nasa.gov/txt/p_elem_t1.txt.
- 2.
An astronomical unit (AU) is the mean Earth-Sun distance, the astronomers’ standard yardstick.
- 3.
- 4.
The data on masses and sidereal periods were taken from the Jet Propulsion Laboratory website http://ssd.jpl.nasa.gov/?planet_phys_par and the distances from the Sun were derived from http://ssd.jpl.nasa.gov/txt/p_elem_t1.txt. The ellipsis after some numbers indicates truncation (not rounding).
- 5.
Perihelion is nowadays often denoted by the letter q.
- 6.
Aphelion is often denoted by the letter Q, which we will use later to avoid confusing it with period P of a body in orbit.
- 7.
See Chap. 3 for a discussion of radian measure.
- 8.
The derivation of the conic equation is standard in many textbooks, but the approach here was inspired by the particularly concise treatment given by Peter van de Kamp [3].
- 9.
See the JPL Orbital Dynamics website, http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=1P%26orb=1#top
- 10.
The information may be found at the Minor Planet Center, website, http://www.minorplanetcenter.net/iau/Ephemerides/Comets/and from Elements and Ephemeris for 73P-C/Schwassmann-Wachmann at http://ubasti.cfa.harvard.edu/~cgi/ReturnPrepEph?d = c&o = 0073P for epoch October 6, 2011.
References
Koestler A (1985) The watershed: a biography of Johannes Kepler. University Press of America, Lanham, Md.
Rufus WC (1931) Johann Kepler, History of science society, Special publication no. 2. Waverly Press, Baltimore, pp 17–22
van de Kamp P (1964) Elements of astromechanics. W. H. Freeman, San Francisco, pp 8–9
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MacDougal, D.W. (2012). The Geometry of the Solar System: Kepler’s Laws of Planetary Motion. In: Newton's Gravity. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5444-1_4
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