Extension of Newton's classical theory of gravitation to the Universe: new law of cosmological force as an addition to Newton's law of gravitation

A new law of gravitational interaction is derived as an addition to Newton's law of gravitation. The additional force, which follows from the new law of gravitational interaction, refers to the Universe. This force is not given by the formula of Newton's law of gravitation. Newton's law is applicable to describe the gravitational interaction of point masses. The new law of cosmological force is applicable to describe the gravitational interaction of bodies with the Universe beyond the applicability of Newton's law of gravitation. The coupling constant in the law of cosmological force is the cosmological constant Ʌ. The new law of cosmological force complements Newton's law of classical gravitation. The law of cosmological force shows that in addition to the Newtonian two-body gravitational force, the gravitational force of the universe acts on all bodies. On small scales, the additional cosmological force is much smaller than the Newtonian force. On the scale of the Universe it is huge and has a theoretical limit equal to the Planck force c4/G. The Newtonian force of gravitational interaction between two bodies together with the cosmological gravitational force gives the total gravitational force. The Law of universal gravitation is presented in a new form. The Law of universal gravitation contains two laws: Newton's law of gravitation and the law of cosmological force. The Law of universal gravitation in classical representation and the quantum Law of universal gravitation are given. The law of cosmological force gives a very close force value to the Pioneer anomaly and indicates the gravitational nature of the Pioneer anomaly.