Kepler’s Impossible Equation

Why is such a simple equation so difficult to solve? Head to https://www.kiwico.com/welchlabs and use code WELCHLABS for 50% off your first monthly club crate or 20% off your first Panda Crate. Welch Labs Imaginary Numbers Book! https://www.welchlabs.com/resources/imaginary-numbers-book Welch Labs Posters: https://www.welchlabs.com/resources How the Bizarre Path of Mars Reshaped Astronomy: https://youtu.be/Phscjl0u6TI Support Welch Labs on Patreon! https://www.patreon.com/welchlabs Special thanks to Patrons: Juan Benet, Ross Hanson, Yan Babitski, AJ Englehardt, Alvin Khaled, Eduardo Barraza, Hitoshi Yamauchi, Jaewon Jung, Mrgoodlight, Shinichi Hayashi, Sid Sarasvati, Dominic Beaumont, Shannon Prater, Ubiquity Ventures, Matias Forti, Brian Henry, Tim Palade, Petar Vecutin, Nicolas baumann Learn more about WelchLabs! https://www.welchlabs.com TikTok: https://www.tiktok.com/@welchlabs Instagram: https://www.instagram.com/welchlabs REFERENCES Colwell, P. (1993). Solving Kepler's Equation Over Three Centuries. United Kingdom: Willmann-Bell. Needham, T. (1997). Visual Complex Analysis. United Kingdom: Clarendon Press. Bate, R. R., Mueller, D. D., White, J. E. (1971). Fundamentals of Astrodynamics. Egypt: Dover Publications. Vallado, D. (2001). Fundamentals of Astrodynamics and Applications. Netherlands: Springer Netherlands. Borghi R. On the Bessel Solution of Kepler’s Equation. *Mathematics*. 2024; 12(1):154. https://doi.org/10.3390/math12010154 Tom Archibald, Craig Fraser, Ivor Grattan-Guinness, The History of Differential Equations, 1670–1950. Oberwolfach Rep. 1 (2004), no. 4, pp. 2729–2794 Francisco G. M. Orlando, C. Farina, Carlos A. D. Zarro, P. Terra; Kepler's equation and some of its pearls. Am. J. Phys. 1 November 2018; 86 (11): 849–858. Arthur A. Rambaut, M.A. A Simple Method of obtaining an Approximate Solution of Kepler's Equation. *Monthly Notices of the Royal Astronomical Society*, Volume 50, Issue 5, March 1890, Pages 301–302. Ben Coleman. How to Find the Taylor Series of an Inverse Function. https://randorithms.com/2021/08/31/Taylor-Series-Inverse.html 17 Recent papers on Kepler’s equation can be found in references 2-16 here: https://www.mdpi.com/2227-7390/12/1/154