7 votes
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How did Newton and Kepler (actually) do it?

Goldstine, A History of Numerical Analysis from the 16th through the 19th Century (1977), describes Kepler's approach (p. 47), which may be found in Kepler's Epitome Astronomiae Copernicanae (1618), ...
Michael E2's user avatar
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7 votes
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What calculation did Halley or anyone else do to estimate the effects of Jupiter and Saturn on Halley's comet's return in 1758/9?

Alexis Clairaut designed and led the detailed calculations of planetary perturbations to estimate the return-date in 1759 of what then became known as Halley's comet. The most detailed account of the ...
terry-s's user avatar
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5 votes

How did scientists (or researchers ) discover prograde and retrograde burns?

It was a theoretical invention. A special case, optimal elliptic transfer between two circular orbits, a.k.a. the Hohmann transfer, was described by Hohmann in The Attainability of Heavenly Bodies (...
Conifold's user avatar
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5 votes

How did Kepler make his discovery?

The movement of planets is not "chaotic". Otherwise prediction would be impossible. The planets move according to Kepler Laws, with very good accuracy. Strictly speaking the description of the motion ...
Alexandre Eremenko's user avatar
5 votes

How did Newton and Kepler (actually) do it?

Kepler's Proofs will get you started on your quest. This article mentions 987 folio pages of arithmetic; you should also look at the tables and methods of Copernicus.
Peter Diehr's user avatar
4 votes
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Did the principles of celestial mechanics affect the development of electromagnetism?

General references on the subject are Whittaker's History of the Theories of Aether and Electricity and Timeline Of History Of Electricity. Newton's persuasive evidence for the inverse square law of ...
Conifold's user avatar
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4 votes
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What are epicycles, deferents, eccentrics, equants, etc.?

All these words are from astronomy, used to describe the motion of the Sun, Moon and planets. The simplest model is this. Suppose that Earth is the center of a circle. This circle is called deferent. ...
Alexandre Eremenko's user avatar
4 votes

Was "Kepler's third law" deduced from the Galilean moons, or from planetary motion?

Kepler's third law was discovered on the basis of comparison of periods and distances of the planets. This was in 1619. Only in 1621 Kepler noticed that Galileo moons of Jupiter also satisfy this law. ...
Alexandre Eremenko's user avatar
4 votes
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Was "Kepler's third law" deduced from the Galilean moons, or from planetary motion?

The Wikipedia article on Harmonices Mundi states that Kepler gave only the conclusion. Since he had taken all of Brahe's observations, the presumption is that he used this data, for he was very ...
Peter Diehr's user avatar
3 votes

How did Newton and Kepler (actually) do it?

At the time of Kepler, not only Runge-Kutta, but the very notion of the differential equation was not avalailable:-) If you really would like to see how Kepler calculated the orbits, why don't you ...
Alexandre Eremenko's user avatar
3 votes

Poincaré's last geometric theorem

Poincaré was studying the circular restricted three-body problem, where two bodies in a binary system revolve around their barycenter and a third test mass moves in some orbit around them. Birkhoff ...
HDE 226868's user avatar
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3 votes
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What monograph on celestial mechanics did Jürgen Moser coauthor the 2nd and considerably expanded English language edition of with Carl Ludwig Siegel?

Siegel's original monograph of 1956 is available as Vorlesungen uber Himmelsmechanik (Grundlehren der mathematischen Wissenschaften), Springer, June 11, 1956. The expanded 1971 edition, authored with ...
nwr's user avatar
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2 votes

How did Alexis Bouvard calculate the orbits of Jupiter, Saturn and Uranus

Perturbation theory begins with Newton who tried to explain the motion of the Moon (this is the object in the solar system whose motion deviates most from Keplerian orbits). Newton essentially failed, ...
Alexandre Eremenko's user avatar
2 votes

Laplace's Treatise of celestial mechanics

In An IX du calenedrier republicain (1801) Jean-Baptiste Biot published his Analyse du traité de mécanique céleste de P.S. Laplace To develop the relationships existing between movements and forces ...
sand1's user avatar
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2 votes
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Did Newton find geodesics on curved surfaces in Principia?

You are on to something here. Section X of Book 1 of Principia discusses the motion of particles constrained to curves or surfaces under the action of central forces (that is forces directed towards a ...
Conifold's user avatar
  • 76k
1 vote
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Who was the first to understand the concept of outer-space?

As it almost always happens it is impossible to tell exactly "who was the first". But Hellenistic scientists certainly knew this. The moon has visible parallax, so that they could prove that Moon is ...
Alexandre Eremenko's user avatar

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