Besides the forces described by Newtonian dynamics, there is an additional cosmological force in the Universe, which is observed in experiments, but does not follow from Newton's law of gravitation. The additional cosmological force was not represented in Newtonian dynamics. The law of cosmological force Fcos = (mc^2)√Ʌ is derived. The law of cosmological force makes it possible to obtain the extended law of universal gravitation. The extended law of universal gravitation includes two laws of gravitation: Newton's law of gravitation and the law of cosmological force. The extended law of universal gravitation does not have the limitations of Newton's law of gravitation. It describes the full force of gravitational interaction both on small scales and on the scale of the Universe. The coupling constants in the extended law of universal gravitation are two constants: the Newtonian constant of gravitation G and the cosmological constant Ʌ. The equation of the extended law of universal gravitation without using the gravitational constant G is given. The extended law of universal gravitation gives an explanation of the Galaxy rotation curve and the Pioneer anomaly. Extended Newtonian dynamics is able to provide solutions to the problems of astrophysics and cosmology without expecting (and instead of) quantum gravity.