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Consider a celestial body, say the asteroid Didymos for example, with an elliptical orbit around the Sun. Now since the Sun has a huge gravitational pull and mainly because it is not at the center of Didymos's orbital; is this likely to create an imbalanced gravitational pull on the object at different locations on it's orbit, and as a result, will this eventually cause the Sun to slowly pull Didymos closer, each time Didymos moves along the path on it's orbital (from the side which is closer to the Sun).

Do orbits change over a period of time, especially when the Star is not at the center?

03-October-2019: Thank you all for answering my question. Just to confirm my understanding; if we consider only a two body system with no change in mass and distance, with the gravitational force being constant, there will be no major impact on the orbit unless the bodies are moving too close, but if there is a change in the distance between the two objects, the orbiting velocity will change. However, it is possible that other huge planetary bodies in the system, if they come close enough, may have some effect over a period of time due to irregularities in mass distribution.

Also I agree, there can be a seperate question with the title, how do orbits evolve over time. It is said that even a small change or disturbance in the mechanics or numbers, can lead to a chain of events and impact the entire planetary system.

It is fascinating to know how our beautiful, complicated and mysterious universe is protected and woven in delicate threads, in the fine fabric of dark matter which keeps everything together.

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    $\begingroup$ en.wikipedia.org/wiki/Elliptic_orbit $\endgroup$
    – Organic Marble
    Oct 1, 2019 at 16:54
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    $\begingroup$ Didymos is an unusual example because it's a binary asteroid, but I don't think that matters for the purposes of your question. See Keplerian orbit; the Sun is at one focus of the elliptical orbit, not the center, and in a simple orbit around a spherical Sun with no other planets and ignoring General Relativity, the orbit would stay the same over time. $\endgroup$
    – uhoh
    Oct 1, 2019 at 17:55
  • $\begingroup$ Scott Manley had a video where he talked about how satellites orbiting the moon will eventually crash. It's because of the irregular mass distribution, the moon's field is not spherically symmetric. The energy is conserved, as it must be, but the orbit becomes more elliptical over time and eventually intersects the surface. I confess I don't understand the physics, I can't give a nice explanation as to why that happens. If you're far enough away the orbit is stable, but then you're too far to study the moon. $\endgroup$
    – Greg
    Oct 1, 2019 at 19:48
  • $\begingroup$ Since you're pretty new to the site (and welcome!), if a posted answer fits your needs (and it sounds like it did), please accept it by clicking on the checkmark beside it. That formally shows the system that it answered the question, and rewards you and the answerer with some reputation points. $\endgroup$
    – Organic Marble
    Oct 3, 2019 at 15:45

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Considering only two bodies, if the closest approach of the two bodies is not too close, an elliptical orbit will remain perfectly* stable. An intuitive explanation for this that might help you is that as the bodies approach closer, they move faster, so they spend less time under the higher gravitational influence, and when they're further apart, they're moving slower, spending more time under a smaller gravitational influence. The wikipedia entries for Kepler orbit and elliptic orbit may also be informative (h/t Organic Marble and uhoh).

Once a third body enters the picture, or if the bodies get close enough together that irregularities in the mass distribution of one of the bodies come into play, the orbit will be unstable over a long period. In the real solar system, for example, the larger planets significantly distort the orbits of everything else in the system.

* As comments below point out, a number of factors including general relativity and GR's consequent gravitational waves make even simple 2-body orbits variable over the long term, but these issues would affect circular orbits as well as substantially elliptical ones.

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    $\begingroup$ Even with 2 bodies, the orbit will precess due to effects of GR, and even more subtly, decay due to emission of gravitational waves. But for an asteroid without a close approach, these effects will be almost unmeasurable. (The gravitational waves definitely unmeasureable with our current equipment) $\endgroup$
    – Quietghost
    Oct 2, 2019 at 2:40
  • $\begingroup$ And eluded to in this comment above if the central body is not spherical (e.g. oblate like the Sun (slightly J₂≅2E-07) or Earth (more J₂≅1E-03) or Jupiter (even more J₂≅1.5E-02)) the orbit will also precess and change in other ways as well. $\endgroup$
    – uhoh
    Oct 2, 2019 at 3:24
  • $\begingroup$ See this answer for an example of eccentricity oscillations, and nodal 1 and 2 and apsidal 3 precession. $\endgroup$
    – uhoh
    Oct 2, 2019 at 3:25
  • $\begingroup$ Also, unless the bodies are infinitely rigid, or in a mutual tidal lock with perfect equatorial circular orbit, the orbit will always evolve due to tidal forces. $\endgroup$
    – SF.
    Oct 2, 2019 at 5:39
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    $\begingroup$ I wonder if a separate question should be asked with an easy-to-find title for future readers, for example "what are all the (main) ways that a two body orbit can evolve over time?" or something to that effect. $\endgroup$
    – uhoh
    Oct 2, 2019 at 8:26

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