INVERSE N-BODY PROBLEM

Newton's law of gravity F = GMm/r^2 shows the force of gravitational interaction of two bodies. The solution of the inverse problem of two bodies (Bertrand problem) also leads to Newton's law of gravity. However, the solution of the direct and inverse problems of two bodies does not lead to a physical law that is capable of giving the full force of gravitational interaction of N-bodies. Newton's law of gravity does not take into account that all bodies of the Universe participate in gravitational interaction simultaneously. The fundamental law of gravity for N bodies has not been discovered. The obstacle was the unsolved gravitational problem of N bodies. The inverse problem of N-bodies, as a problem of obtaining a formula for the gravitational force, 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.