Focus of Earth's elliptical orbit

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Discussion Overview

The discussion revolves around the nature of Earth's elliptical orbit around the Sun, specifically addressing the concept of foci in elliptical orbits and the relationship between circular and elliptical paths. Participants explore theoretical implications, mathematical properties, and connections to broader concepts in physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question why Earth's orbit cannot be circular if it has one focus at the Sun, suggesting a misunderstanding of the relationship between circular and elliptical orbits.
  • Others clarify that while the Sun is a focus of the elliptical orbit, the orbit itself has two foci, with the other focus located in space.
  • One participant mentions that excentric orbits relate to angular momentum conservation and references Kepler's laws.
  • There is a discussion about the relationship between ellipses in classical mechanics and geodesics in four-dimensional space-time, with some arguing that understanding classical models is essential before tackling general relativity.
  • Another point raised is that random orbits are statistically more likely to be elliptical rather than circular due to the greater number of possible elliptical configurations.
  • One participant notes that Earth's orbit is not likely to become circular without significant energy input, emphasizing that it currently has a low eccentricity.
  • Links to external resources are provided for further exploration of the topic.

Areas of Agreement / Disagreement

Participants express differing views on the nature of orbits, particularly regarding the implications of having one versus two foci. While some points are clarified, the discussion remains unresolved on several aspects, particularly the relationship between elliptical and circular orbits.

Contextual Notes

Some limitations include potential misunderstandings of the definitions of foci in elliptical orbits and the implications of energy requirements for changing orbital shapes. The discussion also touches on complex concepts that may require further clarification.

avito009
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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?
 
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The sun is a focus.
Excentric orbits have to do with angular momentum conservation. Check out Kepler
 
avito009 said:
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.
 
Does this have any relation to the fact that the smallest distance in space time is an ellipse? its not a straight line?
 
avito009 said:
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.
 
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.
 
One focus of the Earth's orbit is located at the Earth-Sun barycenter.
 
avito009 said:
[...] 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.)
 

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