What does perturb mean? This is recorded in a change in the motion, else it would be a meaningless term. I could say the planets harumpf, but give no evidence of this, and none would agree. Therefore, perturb gives evidence, and this evidence is a slowing or speeding up, or a wider orbit or closer orbit, but it most certainly does not mean no change. Given that the planets change when they are perturbed, they should stay changed, according to man's theory. If an orbit swings wide to move toward a giant it is passing, should not the orbit stay wide then? If a planet slows slightly due to a giant's gravity attraction behind it, should it not stay slower? Human astrophysics has two discomfiting notions they use as guides in this situation. They can't put these notions together, so like two passengers in the back seat of a car who can't talk to each other, they stare out opposite windows and pretend the other doesn't exist.
There are several problems for humans here, none of which are addressed due to the discomfort factor. While the larger planet is slowing to pull toward the smaller planet, on its approach, the smaller planet finds the larger coming to meet it and increases its speed toward the larger somewhat due to this. The point of passage is not equidistant in the perturbation swath, it is placed toward the early part of the drama, due to this, with the rush to meet being quicker and taking place in a shorter period of time than the lingering exiting phase. Since the two planets are traveling in the same direction, they spend more time together during the exiting phase than the approach.
If either the larger or smaller planet were standing still, the human argument that the speed of orbit is compensated upon approach and exit might be valid, but as they are both moving, the perturbation is not equal on both sides. Net - the smaller planet should be slowed overall in its orbital speed, as it has the larger planet in close proximity behind it for a longer period of time. This is due to the larger planet tagging along behind the smaller planet. Net - the larger planet should be sped up overall in its orbital speed, as it is being encouraged to chase the smaller planet now aheadof it for a longer period of time. This should be intuitively obvious to humans, who find the car slows more, overall, the longer the brakes are applied. To state that the length of time is irrelevant would be absurd.
More than the speed of the orbit is affected when orbiting planets perturb each other, the shape of the orbits is also affected. Given a smaller planet passing on an inside track and orbiting at a faster speed, the smaller planet will pull outward toward the larger during passage. Thus, its orbit has been changed, as for a period of time it is tracking along in a wider curve, at a greater distance from its sun. According to the human explanation for orbits - that they represent an equilibrium between the planets forward motion and the gravity tug from the sun such that the forward motion has been bent into a curve, and that the equilibrium is maintained by centrifugal force caused by the continuing tug of the forward motion - this new orbit shape should be maintainable with no need for the planet to return to its pre-perturbation state.
We have asserted that the equilibrium of orbits is maintained by a combination of not only the gravity tug from the sun but also by the repulsion force that has been generated between the planet and its sun, and the planets being swept ahead of rotating energy fields thrown out from the sun like long sweeping arms. That the perturbed planets return to their pre-perturbation state is in line with our explanation, not the human explanation for orbits. Nevertheless, our explanation is called wacky and the dictates of the gods of science whom childish humans cling to in their desperate need for security in an uncertain world once again perpetuate the Dark Ages of Astronomy, which are with mankind still.