12 votes
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What data did Kepler work out his laws from?

Today, sky coordinates are measured as "Right Ascension" (RA) and declination. These are similar to the angular coordinates we use for the Earth's surface but are measured on the celestial sphere ...
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  • 2,048
10 votes

What 19th century developments contributed to the General theory of Relativity?

There are several major ideas that went into general relativity: finite speed of gravity propagation, not necessarily Euclidean geometry of space, identification of inertia and gravity, mechanics as ...
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10 votes

What data did Kepler work out his laws from?

At the time of Brahe and Kepler they did not use the right ascention and declination to record the movement of planets. These coordinates are related to the Earth, and it is known since the times of ...
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7 votes
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Why did scientists think the orbit of Mars had the shape of a limaçon in the geocentric model?

The right hand side picture shows qualitatively what you obtain from Ptolemy's model. The actual curve is a cycloid, in the first approximation. It uses rigorous mathematics. Moreover it describes ...
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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), ...
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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 ...
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  • 3,044
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 (...
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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 ...
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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.
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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 ...
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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. ...
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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. ...
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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 ...
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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 ...
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3 votes

Poincare's last geometric theorem

Poincare 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 ...
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3 votes

What happened in astronomy between Hipparchus and Ptolemy?

Actually, I've found some sources that suggest that Apollonius applied epicycles to planetary motion: From here: Apollonius also was an important person in founding Greek mathematical astronomy. ...
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3 votes

Why does JPL at NASA give two different values in astronomical units for planetary distances?

I believe the question is asking about the following tables, one for the period 1800 AD to 2050 AD, the other two for 3000 BC to 3000 AD. Note that in these tables, "EM Bary" refers to the Earth-Moon ...
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3 votes
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Did Archimedes use epicycles in his planetarium?

Let me try to summarize this long discussion to an "answer". All that we know about epicycle theory comes from Ptolemy. Ptolemy credits Apollonius (262-190 BC) with one mathematical theorem (which ...
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3 votes

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 ...
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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 ...
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2 votes

What happened in astronomy between Hipparchus and Ptolemy?

You can look in Wikipedia for the list of astronomers between Hipparchus and Ptolemy, or for more detail consult Neugebauer. (Or Ptolemy himself:-) The problem is that 90% of our knowledge about ...
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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 ...
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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 ...
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