Kepler's equation

In orbital mechanics, Kepler's equation relates various geometric properties of the orbit of a body subject to a central force.

It was derived by Johannes Kepler in 1609 in Chapter 60 of his Astronomia nova,^[1]^[2] and in book V of his Epitome of Copernican Astronomy (1621) Kepler proposed an iterative solution to the equation.^[3]^[4] This equation and its solution, however, first appeared in a 9th-century work by Habash al-Hasib al-Marwazi, which dealt with problems of parallax.^[5]^[6]^[7]^[8] The equation has played an important role in the history of both physics and mathematics, particularly classical celestial mechanics.

^ 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.
^ Aaboe, Asger (2001). Episodes from the Early History of Astronomy. Springer. pp. 146–147. ISBN 978-0-387-95136-2.
^ 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.
^ 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.
^ Colwell, Peter (1993). Solving Kepler's Equation Over Three Centuries. Willmann-Bell. p. 4. ISBN 978-0-943396-40-8.
^ 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.
^ 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.

[1] 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.

[2] Aaboe, Asger (2001). Episodes from the Early History of Astronomy. Springer. pp. 146–147. ISBN 978-0-387-95136-2.

[3] 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.

[kep-iter-4] 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.

[5] Colwell, Peter (1993). Solving Kepler's Equation Over Three Centuries. Willmann-Bell. p. 4. ISBN 978-0-943396-40-8.

[6] 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.

[7] North, John (2008-07-15). Cosmos: An Illustrated History of Astronomy and Cosmology. University of Chicago Press. ISBN 978-0-226-59441-5.

[8] 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.

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