THE LAW OF GRAVITATION THAT TAKES INTO ACCOUNT THE ACCELERATED EXPANSION OF THE UNIVERSE AND KEPLER'S LAWS OF PLANETARY MOTION

The law of gravity FU = mR^3/(T^2)r^2+(mc^2)√Ʌ is investigated, which is considered as a relativistic version of the law of universal gravitation. The new law of gravitation 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 → ∞. The total force of universal gravitation consists of two components: the force of gravitational interaction of two bodies FH-K = mR^3/(T^2)r^2 and an additional cosmological force FCos = (mc^2)√Ʌ. A feature of this law of universal gravitation is that it does not include the gravitational constant G and mass M. It includes parameters available from observations. These are the parameters of the planets' orbits (R and T) and the cosmological constant Ʌ. The new law of gravitation shows that in addition to the force of gravitational interaction between two bodies, the bodies are acted upon by the cosmological force FCos = (mc^2)√Ʌ of the universe. The presence of the speed of light in the law of gravitation together with the cosmological constant Ʌ represents a relativistic version of the law of universal gravitation obtained within the framework of classical gravity. The additional cosmological force causes acceleration A0 = (c^2)√Ʌ=10.4922 x 10⁻¹⁰ m/s² close to the acceleration value (a₀ = 1.2 x 10⁻¹⁰ m/s²) predicted by MOND.