"For every action, there is an equal and opposite reaction." Newton's Third Law of Motion
Simply put, just push someone, and they move back as a response to the transferred kinetic energy before they fall. These laws of motion are the basis of all physical reactions in the known universe, before the theories of Einstein and other later physicists.
A kink is in the sheets, and this the "Three-Body Problem" which hampered by Newton's Laws of motion. Overall, when dealing with the three-body problem with problems that are hard to solve, but there is light at the end of the tunnel. This is courtesy of the Astrophysicist, Nicholas Stone from the Hebrew University of Jerusalem's, Racah Institute of Physics, with answers to this conundrum. Another key scientist is Nathan Leigh at Chile's La Universidad de Concepción, who also did clear up this problem with Nicholas Stone. Results of their studies were published in the latest edition of Nature.
To describe how the three-body equation works, it shows how the earth does orbit the sun and calculating the problem would be easy. Another wrangle to add would be, including the moon in the equation that makes it the three-body problem or equation. Normally, it will be easy to predict two bodies like the sun and earth are entangled in the same orbit. Include the moon, and there is another object going around the sun. This addition to two other celestial bodies needs more paradigms to consider too.
It starts with a center point of any group of two or three bodies, like the earth going around the sun with the moon. This is easily explainable using laws of motion set by Newton, next to come is the catch-22 of the premise. Chaos is now in play, if the celestial objects are the same size, how far from the center of the orbit of all of them. This condition will cause these three bodies to compete who pulls most, according to the gravity involved (like a gravity tug-o-war). Next is how the chaos and irregular orbits are not easy to calculate, with normal math methodology.
The three-body problem is now nearing resolution as one of the three bodies is outed and becomes two binary bodies instead. One example of this relationship is binary stars and other celestial objects. It was the key to solving the three-body problem.
As a model to predict any result, the chaos created by competing bodies is not a problem. Calculating the planets' movements as an example is done with classical mathematics for the equation. This produced a "high degree of expected results" that were accurate as predicted in computer models made to explain the phenom. No one anticipated the results would get good approximations too.
If three black holes are in orbit of each other, it introduces chaos until one is knocked from the common orbit. Only dual black holes will be left orbiting regularly now. By guessing the probable outcome, will be important to investigate what the pair will do in stabilized orbit.
For now, it will help solve the three-body problem, there will be better solutions and visualizations to come.
Related article: Researchers Crack Newton's Elusive '3-Body' Problem That Has Baffled Scientists for Centuries