THE LAW OF UNIVERSAL GRAVITATION WITHOUT THE CONSTANT G, TAKING INTO ACCOUNT THE ACCELERATED EXPANSION OF THE UNIVERSE AND KEPLER'S LAWS OF PLANETARY MOTION

The force of universal gravitation is represented by a single physical law—Newton's law of universal gravitation, F = GMm/r². This law of gravitation includes the constant G, which is considered a fundamental constant. Newton's law of universal gravitation does not provide a complete and precise definition of the force of universal gravitation. It "sees" only the force of gravitational interaction between two bodies and does not take into account the gravitational attraction of other bodies in the universe. Many theorists believe that creating a consistent theory of gravity will require rethinking the very nature of gravity and, possibly, the status of G as a fundamental constant. The fundamental status of G has been questioned by many scientists. Is it possible to describe gravity without the constant G? Here we show that Newton's law, F = GMm/r², is not the only law of universal gravitation. Rejecting the concept of G leads to a new law of universal gravitation, more accurate than Newton's law. The new law of universal gravitation is expressed by the formula: FU = mR^3/(T^2)r^2+(mc^2)√Ʌ. The new law of gravitation without the constant G takes into account the accelerated expansion of the Universe and Kepler's laws of planetary motion. It shows the total force of universal gravitation, taking into account the gravitational interaction of all N bodies in the Universe. This law of gravitation is a solution to the inverse N-body problem for N = 2 and for N → ∞. It includes parameters available from observations.