Abstract
The new branch of mathematics called fluxions by Newton and differential and integral calculus by most others allowed astronomers to calculate orbits of celestial bodies and led to a flowering of physics in the following 18th and 19th centuries when also new planets, Uranus and Neptune, were discovered. The Solar System with its planets, minor planets, and comets became a succesful testing ground for celestial mechanics based on Newton’s laws.
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Notes
- 1.
Bode was an amateur astronomer in Hamburg who wrote a popular book on “Starry Heavens.” In its second edition in 1772 he added an empirical law of planetary distances, originally found by Titius. He sent a copy to Johann Lambert (see Chap. 20) who replied, and as the result of the correspondence that followed, Bode was invited to take a position of a calculator in the Berlin Academy of Sciences. Bode started working as an assistant to the astronomer Johann III Bernoulli. One of Bode’s most eminent students was Johann Pfaff (1765–1825), a precursor of the German school of mathematical thinking. Pfaff’s student Carl Friedrich Gauss (Chap. 15) and followers were influential in determining the lines of development of mathematics in the nineteenth century. Another one of Pfaff’s students was Johann Bartels (1769–1836), who became professor of mathematics at the University of Kazan where he taught, among others, Nikolai Lobachevski (Chap. 15).
- 2.
Lexell’s work in St. Petersburg was continued by his younger associate Nicolaus Fuss (1755–1826) from Switzerland, and Nicolaus’ son Georg Fuss (1806–1856). The latter was an assistant to Wilhelm Struve in Tartu Observatory while Struve’s son Otto Struve (1819–1905) was a student there. Later both moved to Pulkovo Observatory which started in 1839 near St. Petersburg under Wilhelm Struve’s directorship. From there Lexell’s scientific family tree continues through Gylden and Swedish astronomer Oskar Backlund (1846–1916) to Karl Sundman mentioned below.
- 3.
If Tombaugh had missed Pluto, it would have been found later by Yrjö Väisälä of Turku University during minor planet searches in 1935–1945 (about Väisälä in Chap. 22).
- 4.
Leonhard Euler was one of the greatest mathematicians in history. He is remembered for the identity that links five fundamental mathematical constants:
$${\text{e}}^{i\pi } + 1 = 0$$Can you recognize them? Euler entered university of Basel at the age of thirteen and received a Master’s degree three years later in natural philosophy. He became a student of the famous Swiss mathematician Johann Bernoulli, himself a student of his older brother Jacob. Johann’s son Daniel had obtained a position at the Imperial Academy of Sciences at St. Petersburg, and he invited Euler to join him. Euler settled there during 1727–1741. Then for the next 25 year he worked at the Berlin Academy, but in 1766 returned to St. Petersburg. One of Euler’s many students was Italian Joseph-Louis Lagrange in Turin, whom he supervised by correspondence. Euler was so impressed by Lagrange that he invited the latter to come to Berlin to work with him. Lagrange initially declined the offer, but went there later for twenty years, at the time when Euler had already left. Apparently he was worried about being overshadowed of his former teacher. Lagrange finally settled in Paris where he was a member of the French Academy of Sciences.
- 5.
In a nonlinear system , a change in the state of the system depends on its present state. For example, y = kx + b is a linear deterministic law for which the derivative dy/dx = k does not depend on x. But the simple quadratic law y = kx2 + b is nonlinear; its derivative dy/dx = 2kx depends on the value of x.
- 6.
Lalande was a student of Joseph-Nicolas Delisle (1688–1768), a French astronomer and cartographer. He had studied under Jacques Cassini (Chap. 9).
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Teerikorpi, P., Valtonen, M., Lehto, K., Lehto, H., Byrd, G., Chernin, A. (2019). Celestial Mechanics. In: The Evolving Universe and the Origin of Life. Springer, Cham. https://doi.org/10.1007/978-3-030-17921-2_11
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