* As the operation is repeated, the error may be expanded due to the limitation of the decimal operation.

* If your computer is outside of the limits that it can handle (overly large or small numbers), it may freeze.

Two-body problem

In classical mechanics, the two-body problem is a mathematical problem of how two bodies are moving after a certain amount of time, given their mass, current speed, and direction of motion.It is assumed that both objects move only by gravity.

\[F=G\frac { { m }_{ 1 }{ m }_{ 2 } }{ { r }^{ 2 } } \]

Satellites that orbiting planets, and binary star systems are two-body problems.

Representative two-body problems

Three Body Problem

The three-body problem is a mathematical problem of how the three bodies are moving after time when they know the mass, current speed, and direction of movement.

The two-body problem is solved easily by simple equations, while the Three Body Problem does not have a perfect mathematical solution. All the solutions presented historically are only approximate solutions.

The three-body problem began with the question of the orbits of the three bodies of the Sun, Earth, and Moon. Isaac Newton, in his book Principia, deals with the case of three moving bodies in gravity. However, he couldn’t explain mathematically why the three heavenly bodies had a stable orbit. Since then, many have failed to solve the three body problem. In 1890 Henri Poincaré proved impossible to obtain a general solution to the three body problem, which later became the basis of chaos theory.

Many-body problem

The many-body problem is the problem of finding the motion state after giving the mass, initial position, and initial velocity of several objects.

Many-body problems can only be solved approximately.