Showing that planets follow elliptical orbits

  • #1
933
56
Is it difficult to show that planets follow elliptic orbits around the sun, using Newton's theory?

I have seen the equations showing it, but from General Relativity, considering the Newtonian limit.

How to arrive at them using only Newton?
 

Answers and Replies

  • #3
933
56
Wikipedia has it
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.

So one should be able to arrive at the equation of the ellipse presented in the Wiki page, by means of Newtons laws.
 
  • #4
fresh_42
Mentor
Insights Author
2021 Award
16,461
15,542
Newtons laws should let us see why that happens.
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.
 
  • Like
Likes kent davidge
  • #5
anorlunda
Staff Emeritus
Insights Author
10,429
7,656
So one should be able to arrive at the equation of the ellipse presented in the Wiki page, by means of Newtons laws.

There is one thing you can't get from Newton's Laws; the initial conditions. I mean the position, and momentum at the time you start applying Newton's Laws.

With Newton's Laws, an orbit could be elliptical or (nearly) circular. Kepler predated Newton,

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."
 
  • Like
Likes kent davidge
  • #6
Nugatory
Mentor
13,858
7,259
Is it difficult to show that planets follow elliptic orbits around the sun, using Newton's theory?
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.
 
  • Like
Likes kent davidge

Related Threads on Showing that planets follow elliptical orbits

  • Last Post
Replies
4
Views
746
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
7
Views
15K
Replies
3
Views
2K
  • Last Post
Replies
8
Views
2K
Replies
2
Views
3K
Replies
11
Views
1K
  • Last Post
Replies
21
Views
6K
  • Last Post
Replies
2
Views
5K
Top