What does this have to do with chemistry?

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Replace the sun by a nucleus of charge +2 as earth and Venus by electrons: You end up with the helium atom. Of course that is not real chemistry so far but if you add more "suns" that are nuclei and more planets that are electrons you end up with a molecule. Unfortunately, in the case of chemistry there are two additional complications:

1. Electrons are small and light so we must use quantum mechanics instead of usual mechanics to describe them.
2. Electrons are "indistinguishable".

The latter two facts turn out to be rather strange to the human mind but nature at small scales (as at high velocities) is in fact strange... It is impossible to give a brief introduction into quantum mechanics. However, we shall resume that the central goal is to solve the so called "Schrödinger equation" containing the many-body problem. What is the Schrödinger equation? It describes the evolution of the probability of finding a particle at a certain place at a certain time. It is the quantum world replacement of the equations of motion of classical mechanics. (The latter is for example: You drive in your car at a certain speed. Then you may predict your position at any time.) The Schrödinger equation is a so called "partial differential equation" and the solution is a so called "wavefunction" because it behaves with respect to many aspects like usual (water)waves. While solving the Schrödinger equation for the wavefunction one gets the desired energy of the system.