A recent study has compared the deviations of circular orbits in nonrelativistic and relativistic contexts, obtaining general solutions for the deviation equations. The research focused on identifying the conditions under which trajectories close to circular orbits remain closed curves. For the nonrelativistic case, the potentials allowing this characteristic were determined, while in general relativity, the corresponding metric components were specified. This analysis provides a deeper understanding of orbital stability and precession in different theoretical frameworks.

The work also derived explicit expressions for the pericenter shift of nearly circular orbits in a static, spherically symmetric spacetime. This shift is a key phenomenon in general relativity, observed, for example, in Mercury's orbit. Furthermore, estimates have been made regarding the influence of the cosmological constant on this pericenter shift, a factor that could have implications for orbital dynamics on cosmological scales. The cosmological constant, representing the vacuum energy density, introduces a repulsive force that could subtly alter the trajectories of celestial objects.

Finally, the researchers identified a specific spherically symmetric metric in which the Shirokov effect is absent. The Shirokov effect is a geodesic precession induced by the rotation of a massive body, similar to the Lense-Thirring effect. The ability to nullify this effect in a particular theoretical configuration opens avenues for a better understanding of the couplings between rotation, gravity, and spacetime geometry, and could be relevant for the design of precision experiments or for the interpretation of future astrophysical observations.