As you know, precessing ellipses appear as solutions to the equations of the general theory of relativity. At the same time, it is generally accepted that in classical mechanics there are only the following equations of orbits: circles, ellipses, parabolas and hyperbolas. However, precessing ellipses also appear in classical mechanics. As you know, orbital precession is observed not only when the planets move in the Solar System. The precession of the periastron of the orbit is also observed in close binary systems, the components of which have evolved into pulsars. In such systems, the masses of the components – neutron stars – are of the same order of magnitude. Consequently, they will move in similar orbits around the center of mass. The orbits will be uniformly precessing ellipses. We write down the equation of such an orbit and derive from it an expression for the force of attraction acting between bodies. As a result, it turns out that, in addition to the Newtonian force, which is inversely proportional to the square of the distance between the bodies, a term appears in the expression for the force that is inversely proportional to the cube of the distance.