INVERSE N-BODY PROBLEM

The solution of the two-body gravitational problem led to the discovery of Newton's law of gravitation F = GMm/r^2. The solution of the inverse two-body problem (Bertrand problem) also leads to Newton's law of gravitation. However, the solution of the direct and inverse two-body problems does not provide a complete description of gravity. The law of gravitation for N bodies is missing. The fundamental law of gravitation for N bodies has not been discovered. The obstacle was the unsolved gravitational problem of N bodies. The inverse problem of N-bodies has not been studied in physics. Here we present a new method for finding the law of gravitational force for N bodies. The method is based on reducing the gravitational problem of N bodies to the two-body problem, where the central body is a system of N bodies. The problem of an N-body system is the inverse problem of the N-body problem. This is the problem of finding the law of gravitational force from the known integral characteristics of the N-body system. The solution of the inverse problem of N bodies gives a new law of gravitation F = (mc^2)√Ʌ. Instead of the gravitational constant G, the new law of gravity includes the cosmological constant Ʌ. The new law of gravity F = (mc^2)√Ʌ allows us to overcome the limitations inherent in Newton's law of gravity F = GMm/r^2 and leads to a new law of universal gravitation.