Kepler's equation (English Wikipedia)

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

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"Mihi ſufficit credere, ſolvi a priori non poſſe, propter arcus & ſinus ετερογενειαν. Erranti mihi, quicumque viam monſtraverit, is erit mihi magnus Apollonius." Hall, Asaph (May 1883). "Kepler's Problem". Annals of Mathematics. 10 (3): 65–66. doi:10.2307/2635832. JSTOR 2635832.
Pfleger, Thomas; Montenbruck, Oliver (1998). Astronomy on the Personal Computer (Third ed.). Berlin, Heidelberg: Springer. ISBN 978-3-662-03349-4.

books.google.com

Aaboe, Asger (2001). Episodes from the Early History of Astronomy. Springer. pp. 146–147. ISBN 978-0-387-95136-2.
Colwell, Peter (1993). Solving Kepler's Equation Over Three Centuries. Willmann-Bell. p. 4. ISBN 978-0-943396-40-8.
North, John (2008-07-15). Cosmos: An Illustrated History of Astronomy and Cosmology. University of Chicago Press. ISBN 978-0-226-59441-5.
Livingston, John W. (2017-12-14). The Rise of Science in Islam and the West: From Shared Heritage to Parting of The Ways, 8th to 19th Centuries. Routledge. ISBN 978-1-351-58926-0.
It is often claimed that Kepler's equation "cannot be solved analytically"; see for example here. Other authors claim that it cannot be solved at all; see for example Madabushi V. K. Chari; Sheppard Joel Salon; Numerical Methods in Electromagnetism, Academic Press, San Diego, CA, USA, 2000, ISBN 0-12-615760-X, p. 659

doi.org

Swerdlow, Noel M. (2000). "Kepler's Iterative Solution to Kepler's Equation". Journal for the History of Astronomy. 31 (4): 339–341. Bibcode:2000JHA....31..339S. doi:10.1177/002182860003100404. S2CID 116599258.
Dutka, J. (1997-07-01). "A note on "Kepler's equation"". Archive for History of Exact Sciences. 51 (1): 59–65. Bibcode:1997AHES...51...59D. doi:10.1007/BF00376451. S2CID 122568981.
"Mihi ſufficit credere, ſolvi a priori non poſſe, propter arcus & ſinus ετερογενειαν. Erranti mihi, quicumque viam monſtraverit, is erit mihi magnus Apollonius." Hall, Asaph (May 1883). "Kepler's Problem". Annals of Mathematics. 10 (3): 65–66. doi:10.2307/2635832. JSTOR 2635832.
Colwell, Peter (January 1992). "Bessel Functions and Kepler's Equation". The American Mathematical Monthly. 99 (1): 45–48. doi:10.2307/2324547. ISSN 0002-9890. JSTOR 2324547.
Boyd, John P. (2007). "Rootfinding for a transcendental equation without a first guess: Polynomialization of Kepler's equation through Chebyshev polynomial equation of the sine". Applied Numerical Mathematics. 57 (1): 12–18. doi:10.1016/j.apnum.2005.11.010.
Odell, A. W.; Gooding, R. H. (1986). "Procedures for solving Kepler's equation". Celestial Mechanics. 38 (4). Springer Science and Business Media LLC: 307–334. Bibcode:1986CeMec..38..307O. doi:10.1007/bf01238923. ISSN 1572-9478. S2CID 120179781.

e-rara.ch

Kepler, Johannes (1609). "LX. Methodus, ex hac Physica, hoc est genuina & verissima hypothesi, extruendi utramque partem æquationis, & distantias genuinas: quorum utrumque simul per vicariam fieri hactenus non potuit. argumentum falsæ hypotheseos". Astronomia Nova Aitiologētos, Seu Physica Coelestis, tradita commentariis De Motibus Stellæ Martis, Ex observationibus G. V. Tychonis Brahe (in Latin). pp. 299–300.
Kepler, Johannes (1621). "Libri V. Pars altera.". Epitome astronomiæ Copernicanæ usitatâ formâ Quæstionum & Responsionum conscripta, inq; VII. Libros digesta, quorum tres hi priores sunt de Doctrina Sphæricâ (in Latin). pp. 695–696.
"Mihi ſufficit credere, ſolvi a priori non poſſe, propter arcus & ſinus ετερογενειαν. Erranti mihi, quicumque viam monſtraverit, is erit mihi magnus Apollonius." Hall, Asaph (May 1883). "Kepler's Problem". Annals of Mathematics. 10 (3): 65–66. doi:10.2307/2635832. JSTOR 2635832.

harvard.edu

ui.adsabs.harvard.edu

Swerdlow, Noel M. (2000). "Kepler's Iterative Solution to Kepler's Equation". Journal for the History of Astronomy. 31 (4): 339–341. Bibcode:2000JHA....31..339S. doi:10.1177/002182860003100404. S2CID 116599258.
Dutka, J. (1997-07-01). "A note on "Kepler's equation"". Archive for History of Exact Sciences. 51 (1): 59–65. Bibcode:1997AHES...51...59D. doi:10.1007/BF00376451. S2CID 122568981.
Odell, A. W.; Gooding, R. H. (1986). "Procedures for solving Kepler's equation". Celestial Mechanics. 38 (4). Springer Science and Business Media LLC: 307–334. Bibcode:1986CeMec..38..307O. doi:10.1007/bf01238923. ISSN 1572-9478. S2CID 120179781.

adsabs.harvard.edu

Swerdlow, Noel M. (2000). "Kepler's Iterative Solution to Kepler's Equation". Journal for the History of Astronomy. 31 (4): 339–341. Bibcode:2000JHA....31..339S. doi:10.1177/002182860003100404. S2CID 116599258.

jgiesen.de

It is often claimed that Kepler's equation "cannot be solved analytically"; see for example here. Other authors claim that it cannot be solved at all; see for example Madabushi V. K. Chari; Sheppard Joel Salon; Numerical Methods in Electromagnetism, Academic Press, San Diego, CA, USA, 2000, ISBN 0-12-615760-X, p. 659

jstor.org

"Mihi ſufficit credere, ſolvi a priori non poſſe, propter arcus & ſinus ετερογενειαν. Erranti mihi, quicumque viam monſtraverit, is erit mihi magnus Apollonius." Hall, Asaph (May 1883). "Kepler's Problem". Annals of Mathematics. 10 (3): 65–66. doi:10.2307/2635832. JSTOR 2635832.
Colwell, Peter (January 1992). "Bessel Functions and Kepler's Equation". The American Mathematical Monthly. 99 (1): 45–48. doi:10.2307/2324547. ISSN 0002-9890. JSTOR 2324547.

nasa.gov

ntrs.nasa.gov

Stumpff, Karl (1 June 1968). "On The application of Lie-series to the problems of celestial mechanics". NASA Technical Note D-4460. {{cite journal}}: Cite journal requires |journal= (help)

semanticscholar.org

api.semanticscholar.org

Swerdlow, Noel M. (2000). "Kepler's Iterative Solution to Kepler's Equation". Journal for the History of Astronomy. 31 (4): 339–341. Bibcode:2000JHA....31..339S. doi:10.1177/002182860003100404. S2CID 116599258.
Dutka, J. (1997-07-01). "A note on "Kepler's equation"". Archive for History of Exact Sciences. 51 (1): 59–65. Bibcode:1997AHES...51...59D. doi:10.1007/BF00376451. S2CID 122568981.
Odell, A. W.; Gooding, R. H. (1986). "Procedures for solving Kepler's equation". Celestial Mechanics. 38 (4). Springer Science and Business Media LLC: 307–334. Bibcode:1986CeMec..38..307O. doi:10.1007/bf01238923. ISSN 1572-9478. S2CID 120179781.

winemantech.com

Keister, Adrian. "The Numerical Analysis of Finding the Height of a Circular Segment". Wineman Technology. Wineman Technology, Inc. Retrieved 28 December 2019.

worldcat.org

search.worldcat.org

Colwell, Peter (January 1992). "Bessel Functions and Kepler's Equation". The American Mathematical Monthly. 99 (1): 45–48. doi:10.2307/2324547. ISSN 0002-9890. JSTOR 2324547.
Odell, A. W.; Gooding, R. H. (1986). "Procedures for solving Kepler's equation". Celestial Mechanics. 38 (4). Springer Science and Business Media LLC: 307–334. Bibcode:1986CeMec..38..307O. doi:10.1007/bf01238923. ISSN 1572-9478. S2CID 120179781.