I carefully read the Wikipedia article Discovery of Neptune, and I don't get what the irregularity of Uranus orbit was that lead to the discovery of Neptune. Years ago, I watched some educational film that schematically showed the irregularity as follows. When the two planets were "near" each other Neptune's gravity would temporarily pull Uranus out of its orbit and then Uranus would be somehow pulled back and continue orbiting along an elliptical orbit as if nothing happened. So Uranus' orbit would be perfectly elliptical except some rather short arc where it would be bent outwards.
This doesn't make sense – if there's some external force that "pulls" (even slightly) Uranus out of its orbit how would it get back into orbit? I suppose its orbit must have permanently (yet slightly) changed. So as time passes, successive deviations must accumulate each time Neptune passes Uranus and Uranus' orbit must get bigger (further from the Sun) and since Neptune is also attracted to Uranus by the very same gravity Neptune orbit must get smaller (closer to Sun).
What exactly is the irregularity and why is Uranus' orbit not permanently changed each time Neptune passes by?
Best Answer
Orbits are funny things really The key thing is the distance from the object that they are orbiting, and the speed at which they are going.
Spacecraft routinely speed up/ slow down their orbital speed, to affect where they are orbiting around a particular spacecraft.
So, the real answer is, Neptune pulls Uranus closer when it is ahead of it in orbit, and slows it down when it is behind it in orbit. The net effect is to almost cancel each other out. But you are right, over a very long period of time, it can have an affect. The same is true of all planets, they affect each other over a long period of time. It actually was part of the irregularity discussed previously (See the article The Discovery of the Outer Planets).