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.