# Q & A: elliptical orbits

Q:
why orbits are always elliptical(like earths orbit around sun)?
- vishal sharma (age 23)
patiala,punjab,india
A:
Real orbits actually aren't quite elliptical. Pure elliptical orbits arise when
1. There are just two objects around.
2. The attractive force between them follows the inverse square law, like Newton's gravity.
3. There are no other forces around.
4. The objects are perfectly spherical.
5. Newton's laws are valid in a Euclidean space.

All of these conditions are pretty nearly true for planetary motion.
1. Although there are several planets, they usually aren't close enough to each other to exert strong forces.
2. and 5 are excellent approximations for our solar system, though measurably not quite right.
3. Is a  very good approximation, since electromagnetic forces are relatively unimportant for planets.
4. Is a fairly good approximation, although the Sun's non-spherical shape (caused by its rotation) does affect the orbits of inner planets.

Anyway, given the simple inverse-square force in a simple space, Newton was able to derive the elliptical shape of the orbits by pure math. The derivation is not especially simple- I always forget it and have to struggle to recreate it. There's a nice version in one of Feynman's books.

Mike W.

(published on 10/22/2007)

## Follow-Up #1: elliptical orbits

Q:
What is elliptical orbits?
- Amber (age 18)
balitmore md
A:
Elliptical orbits are orbits that are shaped like ellipses. An ellipse is a stretched-out circle.

The elliptical orbits produced by gravity around the Sun have a special feature. The Sun is at one 'focus' of the ellipse. The two foci of ellipses are two points which have this property: the sum of the distances to these two points are the same for all the points on the ellipse.

The fact that the planetary orbits were elliptical was discovered by Kepler using astronomical data collected by the Danish astronomer Tycho Brahe.  Isaac Newtons great contribution was to calculate that the orbits should be elliptical using the inverse square force law of universal gravitation.

Mike W.

Lee H

(published on 10/22/2007)

## Follow-Up #2: gravity and elliptical orbits

Q:
Does gravity causes elliptical orbits? If it is true,please explain it.
- Niharika Reddy (age 19)
India
A:
Yes, gravity does cause elliptical orbits. Specifically, two properties of gravity lead to the ellipse:
1. It always points toward a fixed point
2. The strength goes inversely with the square of the distance from that point.

(These are not unique to gravity. An electrical force can give the same shape of orbit.)

Although Newton demonstrated this mathematically over 400 years ago, it still remains hard to show. I didn't ever go through the argument in detail until well into adulthood. Even in compact form, it's too long for this site, and at any rate it's always hard for me to reproduce it.

Here's a link to a version of the argument, which the author picked up from Feynman.

Mike W.

(published on 07/03/2011)