Kepler's laws of planetary motion (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Kepler's laws of planetary motion" in English language version.

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  • Robert Small, An account of the astronomical discoveries of Kepler (London: J Mawman, 1804), pp. 298–299.
  • Robert Small, An account of the astronomical discoveries of Kepler (London: J. Mawman, 1804).
  • In his Astronomia nova, Kepler presented only a proof that Mars' orbit is elliptical. Evidence that the other known planets' orbits are elliptical was presented only in 1621.
    See: Johannes Kepler, Astronomia nova ... (1609), p. 285. After having rejected circular and oval orbits, Kepler concluded that Mars' orbit must be elliptical. From the top of page 285: "Ergo ellipsis est Planetæ iter; ... " (Thus, an ellipse is the planet's [i.e., Mars'] path; ... ) Later on the same page: " ... ut sequenti capite patescet: ubi simul etiam demonstrabitur, nullam Planetæ relinqui figuram Orbitæ, præterquam perfecte ellipticam; ... " ( ... as will be revealed in the next chapter: where it will also then be proved that any figure of the planet's orbit must be relinquished, except a perfect ellipse; ... ) And then: "Caput LIX. Demonstratio, quod orbita Martis, ... , fiat perfecta ellipsis: ... " (Chapter 59. Proof that Mars' orbit, ... is a perfect ellipse: ... ) The geometric proof that Mars' orbit is an ellipse appears as Protheorema XI on pages 289–290.
    Kepler stated that every planet travels in elliptical orbits having the Sun at one focus in: Johannes Kepler, Epitome Astronomiae Copernicanae [Summary of Copernican Astronomy] (Linz ("Lentiis ad Danubium"), (Austria): Johann Planck, 1622), book 5, part 1, III. De Figura Orbitæ (III. On the figure [i.e., shape] of orbits), pages 658–665. From p. 658: "Ellipsin fieri orbitam planetæ ... " (Of an ellipse is made a planet's orbit ... ). From p. 659: " ... Sole (Foco altero huius ellipsis) ... " ( ... the Sun (the other focus of this ellipse) ... ).
  • Johannes Kepler, Harmonices Mundi [The Harmony of the World] (Linz, (Austria): Johann Planck, 1619), book 5, chapter 3, p. 189. From the bottom of p. 189: "Sed res est certissima exactissimaque quod proportio qua est inter binorum quorumcunque Planetarum tempora periodica, sit præcise sesquialtera proportionis mediarum distantiarum, ... " (But it is absolutely certain and exact that the proportion between the periodic times of any two planets is precisely the sesquialternate proportion [i.e., the ratio of 3:2] of their mean distances, ... ")
    An English translation of Kepler's Harmonices Mundi is available as: Johannes Kepler with E. J. Aiton, A. M. Duncan, and J. V. Field, trans., The Harmony of the World (Philadelphia, Pennsylvania: American Philosophical Society, 1997); see especially p. 411.
  • Roy Porter (1992). The Scientific Revolution in National Context. Cambridge University Press. p. 102. ISBN 978-0-521-39699-8.
  • Caspar, Max (1993). Kepler. New York: Dover. p. 304. ISBN 9780486676050.
  • Caspar, Max (1993). Kepler. New York: Dover. p. 286. ISBN 9780486676050.

books.google.com

  • In 1621, Johannes Kepler noted that Jupiter's moons obey (approximately) his third law in his Epitome Astronomiae Copernicanae [Epitome of Copernican Astronomy] (Linz ("Lentiis ad Danubium"), (Austria): Johann Planck, 1622), book 4, part 2, pages 554–555. From pp. 554–555: " ... plane ut est cum sex planet circa Solem, ... prodit Marius in suo mundo Ioviali ista 3.5.8.13 (vel 14. Galilæo) ... Periodica vero tempora prodit idem Marius ... sunt maiora simplis, minora vero duplis." (... just as it is clearly [true] among the six planets around the Sun, so also it is among the four [moons] of Jupiter, because around the body of Jupiter any [satellite] that can go farther from it, orbits slower, and even that [orbit's period] is not in the same proportion, but greater [than the distance from Jupiter]; that is, 3/2 (sescupla) of the proportion of each of the distances from Jupiter, which is clearly the very [proportion] as is used for the six planets above. In his [book] The World of Jupiter [Mundus Jovialis, 1614], [Simon Mayr or] "Marius" [1573–1624] presents these distances, from Jupiter, of the four [moons] of Jupiter: 3, 5, 8, 13 (or 14 [according to] Galileo) [Note: The distances of Jupiter's moons from Jupiter are expressed as multiples of Jupiter's diameter.] ... Mayr presents their time periods: 1 day 18 1/2 hours, 3 days 13 1/3 hours, 7 days 2 hours, 16 days 18 hours: for all [of these data] the proportion is greater than double, thus greater than [the proportion] of the distances 3, 5, 8, 13 or 14, although less than [the proportion] of the squares, which double the proportions of the distances, namely 9, 25, 64, 169 or 196, just as [a power of] 3/2 is also greater than 1 but less than 2.)
  • Godefroy Wendelin wrote a letter to Giovanni Battista Riccioli about the relationship between the distances of the Jovian moons from Jupiter and the periods of their orbits, showing that the periods and distances conformed to Kepler's third law. See: Joanne Baptista Riccioli, Almagestum novum ... (Bologna (Bononia), (Italy): Victor Benati, 1651), volume 1, page 492 Scholia III. In the margin beside the relevant paragraph is printed: Vendelini ingeniosa speculatio circa motus & intervalla satellitum Jovis. (Wendelin's clever speculation about the movement and distances of Jupiter's satellites.) From p. 492: "III. Non minus Kepleriana ingeniosa est Vendelini ... & D. 7. 164/1000. pro penextimo, & D. 16. 756/1000. pro extimo." (No less clever [than] Kepler's is the most keen astronomer Wendelin's investigation of the proportion of the periods and distances of Jupiter's satellites, which he had communicated to me with great generosity [in] a very long and very learned letter. So, just as in [the case of] the larger planets, the planets' mean distances from the Sun are respectively in the 3/2 ratio of their periods; so the distances of these minor planets of Jupiter from Jupiter (which are 3, 5, 8, and 14) are respectively in the 3/2 ratio of [their] periods (which are 1.769 days for the innermost [Io], 3.554 days for the next to the innermost [Europa], 7.164 days for the next to the outermost [Ganymede], and 16.756 days for the outermost [Callisto]).)
  • Bruce Stephenson (1994). Kepler's Physical Astronomy. Princeton University Press. p. 170. ISBN 978-0-691-03652-6.
  • In his Astronomia nova, Kepler presented only a proof that Mars' orbit is elliptical. Evidence that the other known planets' orbits are elliptical was presented only in 1621.
    See: Johannes Kepler, Astronomia nova ... (1609), p. 285. After having rejected circular and oval orbits, Kepler concluded that Mars' orbit must be elliptical. From the top of page 285: "Ergo ellipsis est Planetæ iter; ... " (Thus, an ellipse is the planet's [i.e., Mars'] path; ... ) Later on the same page: " ... ut sequenti capite patescet: ubi simul etiam demonstrabitur, nullam Planetæ relinqui figuram Orbitæ, præterquam perfecte ellipticam; ... " ( ... as will be revealed in the next chapter: where it will also then be proved that any figure of the planet's orbit must be relinquished, except a perfect ellipse; ... ) And then: "Caput LIX. Demonstratio, quod orbita Martis, ... , fiat perfecta ellipsis: ... " (Chapter 59. Proof that Mars' orbit, ... is a perfect ellipse: ... ) The geometric proof that Mars' orbit is an ellipse appears as Protheorema XI on pages 289–290.
    Kepler stated that every planet travels in elliptical orbits having the Sun at one focus in: Johannes Kepler, Epitome Astronomiae Copernicanae [Summary of Copernican Astronomy] (Linz ("Lentiis ad Danubium"), (Austria): Johann Planck, 1622), book 5, part 1, III. De Figura Orbitæ (III. On the figure [i.e., shape] of orbits), pages 658–665. From p. 658: "Ellipsin fieri orbitam planetæ ... " (Of an ellipse is made a planet's orbit ... ). From p. 659: " ... Sole (Foco altero huius ellipsis) ... " ( ... the Sun (the other focus of this ellipse) ... ).
  • Holton, Gerald James; Brush, Stephen G. (2001). Physics, the Human Adventure: From Copernicus to Einstein and Beyond (3rd paperback ed.). Piscataway, NJ: Rutgers University Press. pp. 40–41. ISBN 978-0-8135-2908-0. Retrieved December 27, 2009.
  • Holton, Gerald James; Brush, Stephen G. (2001). Physics, the Human Adventure: From Copernicus to Einstein and Beyond (3rd paperback ed.). Piscataway, NJ: Rutgers University Press. pp. 40–41. ISBN 978-0-8135-2908-0. Retrieved December 27, 2009.
  • Johannes Kepler, Harmonices Mundi [The Harmony of the World] (Linz, (Austria): Johann Planck, 1619), book 5, chapter 3, p. 189. From the bottom of p. 189: "Sed res est certissima exactissimaque quod proportio qua est inter binorum quorumcunque Planetarum tempora periodica, sit præcise sesquialtera proportionis mediarum distantiarum, ... " (But it is absolutely certain and exact that the proportion between the periodic times of any two planets is precisely the sesquialternate proportion [i.e., the ratio of 3:2] of their mean distances, ... ")
    An English translation of Kepler's Harmonices Mundi is available as: Johannes Kepler with E. J. Aiton, A. M. Duncan, and J. V. Field, trans., The Harmony of the World (Philadelphia, Pennsylvania: American Philosophical Society, 1997); see especially p. 411.
  • Wilbur Applebaum (2000). Encyclopedia of the Scientific Revolution: From Copernicus to Newton. Routledge. p. 603. Bibcode:2000esrc.book.....A. ISBN 978-1-135-58255-5.
  • Victor Guillemin; Shlomo Sternberg (2006). Variations on a Theme by Kepler. American Mathematical Soc. p. 5. ISBN 978-0-8218-4184-6.
  • Gerald James Holton, Stephen G. Brush (2001). Physics, the Human Adventure. Rutgers University Press. p. 45. ISBN 978-0-8135-2908-0.

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hyperphysics.phy-astr.gsu.edu

  • "Kepler's Laws". hyperphysics.phy-astr.gsu.edu. Archived from the original on 2022-12-13. Retrieved 2022-12-13.

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  • "Kepler's Laws". hyperphysics.phy-astr.gsu.edu. Archived from the original on 2022-12-13. Retrieved 2022-12-13.
  • "Orbits and Kepler's Laws". NASA Solar System Exploration. 26 June 2008. Archived from the original on 2022-12-13. Retrieved 2022-12-13.
  • "Planetary Motion: The History of an Idea That Launched the Scientific Revolution". earthobservatory.nasa.gov. 2009-07-07. Archived from the original on 2022-12-13. Retrieved 2022-12-13.
  • "Nicolaus Copernicus". history.com. 9 November 2009. Archived from the original on 2022-12-13. Retrieved 2022-12-13.
  • Bryant, Jeff; Pavlyk, Oleksandr. "Kepler's Second Law Archived 2019-09-11 at the Wayback Machine", Wolfram Demonstrations Project. Retrieved December 27, 2009.
  • Schwarz, René. "Memorandum № 1: Keplerian Orbit Elements → Cartesian State Vectors" (PDF). Archived (PDF) from the original on 5 January 2019. Retrieved 4 May 2018.
  • Müller, M (1995). "Equation of Time – Problem in Astronomy". Acta Physica Polonica A. Archived from the original on 14 November 2017. Retrieved 23 February 2013.

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