The discussion revolves around the challenge of demonstrating that planets follow elliptical orbits around the sun using Newton's theory. Participants explore the relationship between Newton's laws and Kepler's laws of planetary motion, particularly focusing on the derivation of elliptical orbits.
Participants express differing views on the ease of deriving elliptical orbits using Newton's laws. While some believe it is straightforward and standard in textbooks, others highlight the limitations regarding initial conditions and the historical context of Kepler's work.
The discussion touches on the dependence on initial conditions for applying Newton's laws, which remains unresolved. There is also a mention of the historical development of the laws of planetary motion, indicating a potential gap in understanding the transition from observational data to theoretical formulation.
The part of the Wiki page you linked to shows the three Keplers laws, one of which, namely the first law, states that the planets follow elliptic orbits. Newtons laws should let us see why that happens.fresh_42 said:Wikipedia has it
I haven't checked the English version, the German does exactly this. Try the second alternative, either by reading just the formulas or translate the page. It worked reasonably well here (translated by Google chrome). A few sentences remained untouched, but it worked sufficiently.kent davidge said:Newtons laws should let us see why that happens.
kent davidge said:So one should be able to arrive at the equation of the ellipse presented in the Wiki page, by means of Newtons laws.
https://en.wikipedia.org/wiki/Kepler_orbit#Johannes_Kepler said:n 1601, Johannes Kepler acquired the extensive, meticulous observations of the planets made by Tycho Brahe. Kepler would spend the next five years trying to fit the observations of the planet Mars to various curves. In 1609, Kepler published the first two of his three laws of planetary motion. The first law states:
"The orbit of every planet is an ellipse with the sun at a focus."
That's standard fare in the first-semester mechanics class. It's in Kleppner and Kolenkow; and I'd expect to find it any comparable textbook. Googling for "derive Kepler's" brings up many promising-looking links.kent davidge said:Is it difficult to show that planets follow elliptic orbits around the sun, using Newton's theory?