It is well known that the Kepler constant R^3/T^2 is a constant of celestial mechanics. It is shown here that the ratio of the cube of the distance to the square of time is a constant for many physical objects and is of a universal nature. The cosmological equation GMUTU 2 =RU 3 is obtained, which includes the constant RU^3/TU^2 as a ratio of the parameters of the Universe. The cosmological equation combines 4 parameters of the Universe: mass MU, radius RU, time TU and the Newtonian constant of gravitation G. In the cosmological equation, the constant RU^3/TU^2 is a constant of the Universe. The electrodynamic equation e 2 t0 2 =mere 3 4πε0 is obtained, which includes the constant re^3/t0^2 as a ratio of the parameters of the electron. The equation combines 4 parameters of the electron: mass me, classical radius of the electron re, characteristic time t0, electric charge e. In the equation containing the electron parameters, the constant re^3/t0^2 is a constant of electromagnetism. These equations show that the limits of applicability of Kepler's ratio R^3/T^2 go far beyond planetary mechanics. Ratio R^3/T^2 is a constant not only of celestial mechanics, but also a constant of the Universe and even a constant of the electron.

The article explores the relationship between the masses of elementary particles and the fine-structure constant α. In addition to the Koide formula, a new formula is proposed, which is as accurate as the Koide formula. The new formula demonstrates the connection between the masses of four elementary particles (electron, proton, tau lepton, and muon) with the fine-structure constant α: Considering the high precision of the fine-structure constant and the accurate experimental values of the electron, proton, and muon masses, the new formula provides a significantly more accurate value for the mass of the tau lepton compared to the current experimental value: m τ /m e =3477.0298… (1776.7586… MeV) The obtained value of the tau lepton mass (1776.7586... MeV/c 2) is within the range of the experimental value but does not coincide with the result obtained by the Koide formula (1776.9688... MeV/c 2). The Koide formula and the new formula yield different values for the mass of the tau lepton with high precision in both results. Both mass values are significantly more accurate than the current experimental value. The discrepancy between the results of the two formulas requires explanation.

It is shown that Newton's law of gravity is not the only law of gravitational interaction in the Universe. Newton's law of universal gravitation (FN=GmM/r^2) is only one of three laws of gravitational interaction. In addition to Newton's law of gravitation, two new laws of gravitation are given: Fк=mR^3/(T*r)^2; Fcos=(mc^2)√Ʌ. These two laws of gravitational interaction remained undiscovered for more than 300 years. The three laws of gravitation (FN=GmM/r^2, Fк=mR^3/(T*r)^2, Fcos=(mc^2)√Ʌ) revive classical gravity and develop Newtonian dynamics towards a complete model of gravity. Newton's law of gravitation together with the two new laws of gravitation provide a complete and consistent description of gravitational interaction in the Universe.

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.

The law of cosmological gravitational force is proposed in addition to Newton's law of gravitation. The law operates beyond the limit of applicability of Newton's law of gravitation and is applicable to the gravitational interaction of the universe. The new law of gravitational force shows that any body of mass m is subject to the cosmological force proportional to the mass of the body and the cosmological constant Ʌ. The formula for the law of cosmological force is: F = (mc^2)√Ʌ. Instead of the gravitational constant G, the cosmological constant Ʌ is included in the cosmological force law. The new law gives the value of the force very close to the value of the Pioneer anomaly.