N-body problem solved

The solution to the oldest enigma of physics: the 300 year old n-body problem solved

The solution to the n-body problem is best demonstrated at its origin: our solar system. The well known law: "A force of gravity on an extended object acts through its center of mass; hence, this point is sometimes called the center of gravity. " says that the combined forces of all planets act concentrated in the barycenter (this law can be found in every physics textbook, so the links should suffice as reference). This law is wrong. This becomes imediatedly obvious if you reduce our solar system to a tree body system earth-sun-jupiter. Earth rotates without any doubt (and by all measurements etc..) around the center of mass of the system earth-sun, which is in this case really nearly identical with the center of mass of the sun, because the mass proportions of the two bodies are extremely different. This makes clear that every planet and the sun form barycenters of their own. This doesn't touches the correctness of the general formulation of Newtons law: "The vector sum of all forces in a solar system constitute the combined force which acts on the central star (and all other objects)."

(picture not true scale!)

Now it becomes comprehensible why more than 300 years the greatest mathematical geniuses of their times couldn't find a solution: mathematics refused to prove a law which was based on wrong facts. Now if you try to simulate in computers the first law above, you get similar wrong solutions as described in literature to the n-body problem. Quite contrary if you simulate according to the general formulation of Newtons law you get the correct orbits of the planets and! the sun. Hopefully it doesn't take another 300 years now that this is accepted by the physics community.

This was readable on sunorbit.net from day one (and easily verifiable on my old pages on archive.org). I removed it later in the hope that the conventional description with a common barycenter would enhance the acceptance. This was not the case. Quite contrary since again only the phenomenological part of my explanation was seen by most, now even wronger explanations are given in the net. I hope you understand that I give no links here to these wrong descriptions, you can search by yourself for "center of mass".

And finally: While there are many "scientific" simulations of very authoritative institutions (no, no links..) out there which obviously never have heard anything about the n-body problem or simply didn't care about any theoretical foundations, the 'mainstream' scientific astro physics community found the chaos theory while investigating the n-body problem: "During all the attempts to analytically solve the n-body problem, the foundations were laid for chaos theory." or here: "Poincaré's work on the restricted three-body problem was the foundation of deterministic chaos theory." Poor old Poincaré shell be responsible for chaos theory of 1960! Hic! Or here: Simply put, anything more than two bodies in a system, and the solution can very quickly turn into one best exemplified by chaos theory. If you need more citations like this, search for yourself for "n-body chaos theory", you find sources of all kinds of authority.

But the real background of all these citations is nothing else than that all problems in physics that use the first law above automatically lead to chaotic solutions!

Has anyone ever seen Jupiter move chaotically? Or the Earth? Or Saturn? Or Venus? No, the simple truth is that from generation to generation a false law was passed on in physics textbooks. And whats more astonishing: this law can be deduced as wrong by simple reasoning! You only must not follow the conventional ways of thinking! But quite naturally, the final prove in this case you can only give with computers!

And one thing should be sure: if Newton or Gallilei would have had access to computers this law would have disappeared 300 or 400 years ago from physics textbooks!

Placed in the net 25.1.2010 (german) 31.1.2010 (english)

Some links to the n-body problem and it's history:

http://www.scholarpedia.org/article/Three_body_problem (short and main details)

http://www.gap-system.org/~history/PrintHT/Orbits.html or http://www-history.mcs.st-and.ac.uk/HistTopics/Orbits.html

http://adsabs.harvard.edu/full/1930JRASC..24..347B