# I Focus of Earth's elliptical orbit

1. Jul 25, 2016

### avito009

If the orbit of the earth has only one focus which is the Sun then why cant it move in a circular path. Since a circle has only one focus and that is at the centre. Why is the sun the only focus when the path of earth is an ellipse?

2. Jul 25, 2016

### BvU

The sun is a focus.
Excentric orbits have to do with angular momentum conservation. Check out Kepler

3. Jul 25, 2016

### jbriggs444

The orbit of the Earth is an ellipse and has two foci, one of which is located at the sun.

Edit: A moment too late.

4. Jul 25, 2016

### avito009

Does this have any relation to the fact that the smallest distance in space time is an ellipse? its not a straight line?

5. Jul 25, 2016

### jbriggs444

An ellipse in three space and a geodesic in four dimensional space-time are not the same thing. There is a relationship, but it would be far better to understand the classical model first before trying to tackle the model according to general relativity.

6. Jul 25, 2016

### Khashishi

A random orbit is much more likely to be an ellipse than a circle. That's because there are many more ellipses than circles, and any slight perturbation will change a circle into an ellipse.

One focus is in the sun. The other focus is in space.

7. Jul 26, 2016

### David Lewis

One focus of the Earth's orbit is located at the Earth-Sun barycenter.

8. Jul 26, 2016

### Tom.G

Last edited by a moderator: May 8, 2017
9. Jul 27, 2016

### collinsmark

[In case this concept was lost somewhere in the rest of the posts]

A circle is a special case of an ellipse. In other words, all circles are ellipse, just a special ones where both foci happen to be in the same place.

Earth's orbit (in particular) is not about to become completely circular any time soon; it would take a lot of energy to change its orbit significantly. But as far as Earth's orbit goes, it's not too terribly far from being circular, meaning it already has a pretty low eccentricity, comparatively speaking.

But there is nothing that says an orbit of a body, generally speaking, cannot be circular*. Orbits can be circular. Of the infinitely many eccentricities an orbit can have, a circle is one possibility (hence why it is called a "special case").

*(I'll restrict this statement to a "two-body problem" such one star and one planet in the system, and such that the gravitation of any other bodies can be ignored.)