Undergrad Focus of Earth's elliptical orbit

[avito009]

If the orbit of the Earth has only one focus which is the Sun then why can't 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?

 

[BvU]

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

 

[jbriggs444]

If the orbit of the Earth has only one focus which is the Sun

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.

 

[avito009]

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

 

[jbriggs444]

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

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.

 

[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.

 

[David Lewis]

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

 

[Tom.G]

Here is a link that should give enough info for you to calculate the answer.
http://www.starhop.com/library/pdf/studyguide/high/brsp-9ellipse.pdf
Also see the links at the end of that paper and look at:
https://www.reddit.com/r/askscience/comments/1iygt9/is_the_nonsun_foci_of_Earth's_orbit_within_the/

 

[collinsmark]

[...] then why can't it move in a circular path.

[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.)