The law of motion discovered by Newton can explain every movement in terms of force, mass and acceleration in principle.

This perspective also gives us generalization of physical motions. For instance, you can explain an apple falling and attraction between the earth and the sun with the same laws. The laws enable us to describe and predict any of motions in the universe.

OK. With this gravitational law, let’s apply it to a general situation. Suppose there are two spheres with identical masses. Then, they are attracted each other due to gravity.

In fact, the motion of two objects can be reduced into a motion of one object, assuming that they are rotating and balancing with each other like the sun and the earth.

In other words, two objects can be regarded as the motion of the center of gravity. That means, you can just look at the center of gravity of two objects. The solution to the equation can be written in a mathematical form. It is nothing difficult.

Now, let’s add an object to this system. It is exactly the same sphere. You can imagine that these three objects attract each other due to gravitational force.

You may think it is easy to solve because there are only three. However, in general, it is impossible to write down in a simple mathematical formulas that was proved by a mathematician quite a while ago.

There are a lot of motions involving three or more agents in the universe. Of course, you can use a computer to represent the whole movement as numerical values; however, only a part of the world can be expressed as exact mathematical expressions.