Why does the Earth revolve with the Sun at one of its foci? Does the other focus do nothing? Why is there this asymmetry in our solar system?
Asked
Active
Viewed 600 times
8
Qmechanic
- 201,751
Swapnanil Saha
- 777
-
"Does the other focus do nothing" what do you expect it to do? – Yrogirg Aug 30 '12 at 16:35
-
1Well, I don't know, but the same thing happens if you take a planar cut, at an angle, through a cone. The curve you get is an ellipse, and the center of the cone is one focus of the ellipse. – Mike Dunlavey Aug 30 '12 at 16:50
-
@ Yrogirg : Anything, but just not be the way it is. – Swapnanil Saha Sep 01 '12 at 13:30
-
1Related: http://physics.stackexchange.com/q/4731/ – dmckee --- ex-moderator kitten May 13 '13 at 20:22
-
@MikeDunlavey Note that that is incorrect. The centre of the cone is the centre of the ellipse. The foci are the touching points of the largest spheres that touch both the cone and the plane in either region. – Emilio Pisanty Apr 10 '14 at 12:33
-
1@EmilioPisanty: Thanks. You're right - except that the center of the cone is not the center of the ellipse, except for a circle. Easiest way to see that is to cut the cone on a plane almost, but not quite, parallel to the edge, so as to create an ellipse of very high eccentricity. – Mike Dunlavey Apr 10 '14 at 12:45
2 Answers
16
I'm almost certain there used to be an answer to this question, but it seems to be gone, I'll write another one. The Earth and Sun both orbit their mutual barycenter (disregarding any other objects of course). That one point is a focal point of both ellipses, and all three focal points are collinear.
It may appear asymmetric because the Sun's motion is so small, which comes from the asymmetry in the masses. Imagine smoothly scaling the Sun down to an Earth mass. As you did so, the ellipses would approach each other in size, and your missing symmetry would be restored. The key is to notice that there are three, not just two, foci in the system.
3
The other focus fixes the solution: it selects a particular ellips out of the infinite solutions that could revolve around the first focus.
Note that the law of equal areas only depends of the central force, this is the focus where the Sun is.
arivero
- 1,943