Abstract
A novel method for the computation of the motion of multi-body systems is proposed against the traditional one, based on the dynamic exchange of attraction forces or using complex field equations, that hardly face two-body problems. The Newton gravitational model is interpreted as the emission of neutrino/gravitons from celestial bodies that combine to yield a cumulative flux that interacts with single bodies through a momentum balance. The neutrino was first found by Fermi to justify the energy conservation in β decay and, using his model; we found that the emission of neutrino from matter is almost constant independently from the nuclides involved. This flux can be correlated to Gauss constant G, allowing the rebuilding of Newton law on the basis of nuclear data, the neutrino weight and the speed of light. Similarly to nature, we can therefore separate in the calculations the neutrino flux, that represents the gravitational field, is dependent on masses and is not bound to the number of bodies involved, from the motion of each body that, given the field, is independent of the mass of bodies themselves. The conflict between exchanges of forces is avoided, the mathematics is simplified, the computational time is reduced to seconds and the stability of result is guaranteed. The example of computation of the solar system including the Sun and eight planets over a period of one to one hundred years is reported, together with the evolution of the shape of the orbits.
Highlights
Newton himself solved the problem of two interacting bodies, but he soon discovered that, for multiple bodies, his differential equations of motion did not predict some orbits correctly: the attracting forces do conform to his laws of motion and to the law of universal gravitation, but the many multiple interactions make any exact solution intractable
The problem of finding the general solution was considered very important and challenging: in the late 19th century King Oscar of Sweden, established a prize for anyone who could find the solution to the problem, The prize was awarded to Poincaré, even though he did not solve the original problem but a restricted three-body problem in which the third mass is negligible
The general n-body problem fell in the hand of mathematicians: the elegant Hamilton’s approach transforms the original Newtonian system of 3 n second order differential equations of motion in a system of 6n first order differential equations with 3n position coordinates and 3n momentum values; no analytical or numerical solution has been found
Summary
Newton himself solved the problem of two interacting bodies, but he soon discovered that, for multiple bodies, his differential equations of motion did not predict some orbits correctly: the attracting forces do conform to his laws of motion and to the law of universal gravitation, but the many multiple interactions make any exact solution intractable. After the extensive work of Poincare [1] [2], many proposals and models of Celestial Mechanics, both numerical and analytical or a mixture of the two, are present in the literature, and full books have been written. The fault is not of the Newton model, nor of mathematics, but of the way mathematic is applied For those that are interested in the relation between mathematics and physics we suggest the last recent book of Penrose [4] The Road to Reality. On the last page of the conclusion, he wisely invites the reader to open a different window for understanding the unknowns of the Universe
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