Background: The n-body problem describes the motion of any "n" objects when under each others gravitational field. As described by Brittanica: "In the general n-body problem, all bodies have arbitrary masses, initial velocities, and positions; the bodies interact through Newton's law of gravitation, and one attempts to determine the subsequent motion of all the bodies." This theoretical equation is closely linked with the motion of celestial bodies, leading to centuries of research and testing to find a general solution. Although many approximations have been found (such as restricted 3-body problems of Jupiter's effect on asteroids), an exact general equation has yet to be discovered.

(Source: Brittanica: The n-body problem)

Newton's Law of Gravitation is the fundamental equation that describes the force of attraction between two objects. It is defined as:

where F is the force of attraction, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the two objects. This equation is the basis for the n-body problem, as it describes the force of attraction between any two objects in the system.

However, the n-body problem contains multiple objects, so this problem is unsolvable due to the nature of how unstable this system would be. The n-body problem is unsolvable because there is no general solution to explain the motion of the $n$ bodies.