The reason for the limitations of Newton's classical theory of gravitation is that classical gravitation remained an unfinished theory. Newton's formula FN = GMm/r^2 gives the force of gravitational interaction between two bodies. Accordingly, Newton's law formula gives only part of the force of universal gravitation and does not apply to the universe. In classical gravitation the additional cosmological force of gravitational interaction of bodies with the mass of the Universe remained undiscovered. The additional cosmological force is represented by a new law of gravitation, different from Newton's law. The law of cosmological force is presented using the cosmological constant Ʌ: FCos = mu2022c^2u2022√Ʌ. The cosmological force has a linear dependence on the mass of the body and does not obey the law of inverse squares. On small scales, the additional cosmological force is much smaller than the Newtonian force. On the scale of the Universe, the cosmological force exceeds the Newtonian force and has a theoretical limit equal to the Planck force FP = c^4/G = 1.21027u202210^44 N. This large force was not represented in the law of universal gravitation. A new mathematical formula for the law of universal gravitation is given. The law of universal gravitation is represented by two equations, Newton's law FN = GMm/r^2 and the law of cosmological force FCos = mu2022c^2u2022√Ʌ. The law of universal gravitation admits a quantum description of the gravitational interaction. It is shown that extended classical gravity has a high heuristic potential. The law of universal gravitation in extended form explains the mystery of galaxy rotation curves and the Pioneer Anomaly without involving the dark matter hypothesis.