The nature of the problem

Toggle Background

The correlation problem or many-body problem is one of the major issues of theoretical physics. Consider the system of the sun and earth:

Due to gravity the earth is attracted by the sun (and vice versa) and due to the speed of the earth it will keep orbiting around sun. Using simple mathematics we may calculate the exact period of a year as well as the position x(t), velocity v(t) and acceleration a(t) of the earth. Now we add another planet. Say Venus:

Although this seems to be a minor change of the system it will prohibit the assembly of an exact mathematical solution. Every body attracts any other. The attraction between earth and Venus complicates things extremely. In an approximation one may neglect this attraction and the problem is once again soluble (if we assume the sun to be much much heavier than Venus and earth). However, this solution remains an approximation and will deviate from the real orbits after a sufficiently long period of time.