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?
An elliptical orbit is a type of orbit in which an object, such as a planet or satellite, follows an oval-shaped path around another object, such as a star. This path is called an ellipse, and it is characterized by two focal points, with the object orbiting around one of them.
The discovery of elliptical orbits is credited to Johannes Kepler, a German astronomer, in the early 17th century. He observed the movements of the planets and noticed that their orbits were not perfectly circular, as previously believed, but instead followed an elliptical shape.
There are several pieces of evidence that support the idea of planets following elliptical orbits. One is the observation of the planets' positions in the sky, which can be accurately predicted using Kepler's laws of planetary motion. Another is the shape of the orbits themselves, which have been confirmed through observations and mathematical models.
The shape of a planet's elliptical orbit is primarily influenced by two factors: the planet's mass and its distance from the object it is orbiting, typically a star. The more massive the planet, the more it will affect the shape of its orbit. The farther the planet is from the object it is orbiting, the more elongated its orbit will be.
While planets generally follow elliptical orbits, there are certain factors that can cause deviations. These include the gravitational pull of other nearby objects, such as other planets or moons, and the effects of relativity. However, these deviations are generally small and do not significantly alter the overall elliptical shape of a planet's orbit.