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What is the relationship between the Newtonian laws of motion and gravity and the Keplerian laws of planetary motion?

In the Wikipedia article for "Kepler's laws of planetary motion," the article suggests that "Isaac Newton showed in 1687 that relationships like Kepler's would apply in the Solar System ...
Colin Pace's user avatar
6 votes
1 answer
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Is Koestler's ‘The Sleepwalkers’ still well regarded? Is there a more recent similar source?

Arthur Koestler's The Sleepwalkers is well-known as both a group biography of Copernicus, Brahe, Kepler and Galileo and an account of the revolutionary turn in astronomy that, in Koestler's phrasing, ...
Norman Gray's user avatar
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How did Kepler know that orbits are elliptical?

Suppose I was living in his time. How would Kepler explain that the orbits are elliptical? Since none of his 3 laws explain why orbits are elliptical, I assume he must have had other reasons to ...
FlightMuj's user avatar
2 votes
1 answer
187 views

Did Kepler influence Fermat?

On page 347 in his "Mathematical Thought, volume 1", Morris Kline writes: "The work on the third class of problems, finding the maxima and minima of functions, may be said to begin with an ...
Mikhail Katz's user avatar
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6 votes
1 answer
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Kepler's position with respect to Tycho Brahe's world system?

When Kepler was an assistant of Tycho Brahe, did Kepler in public declare his support for Copernicus' system or Brahe's system (the earth at rest, but the planets orbiting the sun) or was he undecided?...
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6 votes
3 answers
792 views

Did Kepler arrive at his planetary laws based on Mars's orbit alone?

Kepler apparently arrived at his first two laws based on the Tycho's data for Mars. But Mars has the largest eccentricity except for Mercury, so it is easier to tell the difference between a circle ...
wdlang's user avatar
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3 votes
2 answers
463 views

What was Galileo's opinion of Kepler's work?

They were contemporaries. Kepler lived from 1571 to 1630, and Galileo lived from 1564 to 1642. The former's life span was contained in that of the latter. So, did Galileo hear of Kepler's work and ...
S. Kohn's user avatar
  • 530
3 votes
1 answer
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How did Kepler make his discovery?

It is often said that he used Tycho's data. But the apparent motion of a planet is chaotic, right? The reason is simply that we are living on and observing from the earth, but not the sun. So, how ...
John's user avatar
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2 votes
0 answers
270 views

Is it true that Johannes Kepler thought that the earth was hollow?

I was researching a little about the hollow earth theory, I know that many Scientist's back up this theory, namely Euler and Edmond Halley. I would like to know what was the theory that Johannes ...
neo33's user avatar
  • 121
8 votes
3 answers
1k views

How did Newton and Kepler (actually) do it?

Today if I want to calculate an elliptical orbit of some object due to the gravity of another, I use Runge-Kutta integration, and I can see the individual steps I use shown in that article. Back "...
uhoh's user avatar
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3 votes
2 answers
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Was "Kepler's third law" deduced from the Galilean moons, or from planetary motion?

I have read that Galileo was able to start observing the four large satellites of Jupiter in 1610. Did he ever attempt to estimate the relative sizes of the four orbits, and their periods? I made a ...
uhoh's user avatar
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8 votes
2 answers
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How did Kepler infer three-dimensional positions from Tycho Brahe's data?

This has bugged me for some time. Tycho Brahe's data on planetary observations, presumably, consisted of the direction in which a planet was observed at a given date and time, but not the distance to ...
Emilio Pisanty's user avatar
21 votes
3 answers
2k views

How did Kepler "guess" his third law from data?

It is amazing that Kepler determined his three laws by looking at data, without a calculator and using only pen and paper. It is conceivable how he proved his laws described the data after he had ...
user avatar
2 votes
0 answers
908 views

Was Kepler aware of the following golden relationship between the planets?

Was Kepler aware that Venus and Mars have a golden section relationship other than that he attributed to them in his 5 perfect solids model of the Solar System? The dodecahedron and the icosahedron, ...
John Shanahan's user avatar
8 votes
1 answer
492 views

What was the reaction to Kepler's *Somnium* when it was published?

Kepler's Somnium ("The Dream") is a work of fiction that is sometimes regarded as the first example of science fiction (e.g. by Carl Sagan). In it, Kepler describes a journey to the Moon and various ...
winwaed's user avatar
  • 2,070
19 votes
2 answers
551 views

What data did Kepler work out his laws from?

It's well known that Kepler worked out his laws by fitting curves to Tycho Brahe's data on the trajectories of planets through the sky. What was this data? How does one record the trajectory of a ...
Jack M's user avatar
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