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Euler’s Legacy to Astronautics

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Leonhard Euler and the Foundations of Celestial Mechanics

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Abstract

Euler returned to St. Petersburg in 1766, beckoned by Catherine II, the new Russian empress. At that time, the monarch was implementing many educational reforms based on what she believed were the highest European standards. Euler would help her cause. He was fifty-nine, soon to become completely blind, but his mind was vigorous, full of ideas that were yet to give much fruit. This chapter chronicles Euler’s personal struggles during his last years of life, and concludes with an overview of his most important contributions to mathematics, physics, and astronomy, ending with the unpublished Astronomia mechanica, his embryonic analysis of celestial mechanics. Therein lies the first formal definition: Astronomia mechanica est scientia motus corporum coelestium ex viribus, quibus sollicitantur, determinandi.

In darkness I saw clearly the universe’s divine revolutions, and I calculated the motions of dazzling celestial bodies …. Now I follow the eternal light through a path of stars, guiding me to the most magnificent heavens …

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Notes

  1. 1.

    Euler (1768) (E. 343, E. 344, E. 417).

  2. 2.

    Klyve (2010).

  3. 3.

    Fellmann (2007).

  4. 4.

    Ibid., p. 57.

  5. 5.

    Lagrange (1892, tome 14); Correspondance de Lagrange avec Euler, p. 219.

  6. 6.

    Fellmann (2007, p. 119).

  7. 7.

    Diderot (1749).

  8. 8.

    Euler (1772) (E. 418).

  9. 9.

    Fellmann (2007).

  10. 10.

    Euler (1772) (E. 418).

  11. 11.

    Verdun (2015, pp. 360–368).

  12. 12.

    Euler (1778) (E. 504).

  13. 13.

    Fellmann (2007, p. 119).

  14. 14.

    William Herschel discovered Uranus in 1781. While measuring the directions and brightness of stars, Herschel found a fuzzy spot that moved among the stars. This was Uranus, the first planet that was not known to the ancients.

  15. 15.

    Anders Lexell computed the orbit and concluded that the new cosmic object was probably planetary.

  16. 16.

    Éloge de M. Léonard Euler, lu à l’Académie impériale des sciences, dans son assemblée du 23 octobre 1783, par M. Nicolaus Fuss.

  17. 17.

    Gindikin (2007, p. 172).

  18. 18.

    Musielak (2014). This article provides insights regarding the life of the princess and reviews the material covered in the letters.

  19. 19.

    Calinger (2007).

  20. 20.

    Posthumous works in mathematics and physics.

  21. 21.

    Verdun (2015) studied and translated Astronomia Mechanica from the original Latin into German. Consult in particular pp. 544–549, 883–908.

  22. 22.

    Euler (1862, pp. 177–316) (E. 834).

  23. 23.

    Ibid., p. 177.

  24. 24.

    Verdun (2015, pp. 458, 884).

  25. 25.

    Euler (1768, p. 230) (E. 343).

  26. 26.

    Laplace (1799, p. 1).

  27. 27.

    This phrase is attributed to Laplace. Cf. Fellmann (2007, p. 136).

  28. 28.

    Euler (1757) (E. 226).

  29. 29.

    Euler (1736) (E. 15).

  30. 30.

    Ibid., Part 2, § 832.

  31. 31.

    Euler (1752) (E. 177).

  32. 32.

    Ibid.

  33. 33.

    Euler (1767) (E. 336).

  34. 34.

    Wilson (2003, p. 315).

  35. 35.

    This relation does not appear in this form in Euler’s manuscripts but it became known as “Euler’s identity.”

  36. 36.

    Hakfoort (1995).

  37. 37.

    Euler (1759) (E. 239).

  38. 38.

    Euler (1780) (E. 502).

  39. 39.

    NASA Exoplanet Archive records exoplanet discoveries that appear in peer-reviewed, scientific papers. These exoplanets have been confirmed using multiple detection methods or by analytical techniques.

  40. 40.

    Euler (1768) (E. 343), Letter LIX.

  41. 41.

    Apollo 11 was America’s program that landed the first two humans on the Moon. The spacecraft was launched by a Saturn V rocket from Kennedy Space Center in Florida, on July 16 at 9:32 a.m. EDT (13:32 UTC) and was the fifth crewed mission of NASA’s Apollo program.

  42. 42.

    Celestial mechanics, a translation of Laplace’s Mécanique Céleste, is concerned with the perturbations on the motion of a body orbiting a larger one by a third body.

  43. 43.

    The term “classical mechanics” was coined in the early twentieth century to describe the system of mathematical physics begun by Isaac Newton. It was improved by Euler, Lagrange, and others after them.

  44. 44.

    The asteroid 5540 Smirnova was named in her honor.

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  1. Department of Physics, University of Texas, Arlington, TX, USA

    Dora Musielak

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Musielak, D. (2022). Euler’s Legacy to Astronautics. In: Leonhard Euler and the Foundations of Celestial Mechanics. History of Physics. Springer, Cham. https://doi.org/10.1007/978-3-031-12322-1_8

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