The aim of this section is to show that the method used so far allows us to treat some other cases; in particular, we focus our attention on the differential inequality (18), that is,

The aim of this paper is to study the qualitative behaviour of non-negative entire solutions of certain differential inequalities involving gradient …

We investigated the possibility that the cosmological expansion may impact the orbital motion of a localized two-body system at first order in the Hubble parameter H.

A two-body system hypothetically affected by an additional radial acceleration H v_r, where v_r is the radial velocity of the binary's proper orbital…

If and when other teams of astronomers will independently estimate their own corrections Δ˙ϖ with different ephemerides, it will be possible to fruitfully repeat all the tests presented here. In doing them we always used the formal errors in Δ˙ϖ re-…

Many long-range modifications of the Newtonian/Einsteinian standard laws of gravity have been proposed in the recent past to explain various celestia…

In this paper we present the study of the topology of the equipotential hypersurfaces of configuration space of the mean-field phi^4 model. Our purpo…

We, first, analytically work out the long-term, i.e. averaged over one orbital revolution, perturbations on the orbit of a test particle moving in a …

The present-day best measurement of the geodetic precession has been obtained by continuously monitoring the motion of the Earth-Moon system in the field of the Sun with the Lunar Laser ranging technique; its relative accuracy is 9×10−4. In this pap…

The inclination $I$ of an Earth's satellite in polar orbit undergoes a secular De Sitter precession of $-7.6$ milliarcseconds per year for a suitable…

I calculate the classical effects induced by an isotropic mass loss of a body on the orbital motion of a test particle around it; the present analysi…

In this paper, we used the latest results from Solar System planetary ephemerides to study the impact of f(T) gravity. In particular, we focused on spherically symmetric solutions obtained for Lagrangians in the form f(T)=T+αTn. Since the case f(T)=…

In the framework of $f(T)$ theories of gravity, we solve the field equations for $f(T)=T+\alpha T^{n}$, in the weak-field approximation and for spher…

We have demonstrated that also the post-Newtonian gravitoelectric component of the static gravitational field of a non-rotating body can discriminate between opposite directions of motion for a pair of counter-revolving test particles moving along i…

It is known that, in the weak-field and slow-motion approximation of general relativity, the stationary component of the gravitational field of a rot…

The expansion in multipoles of the gravitational potential of a rotating body affects the orbital motion of a test particle orbiting it with long-ter…

An empirical formula recently appeared in the literature to explain the observed anomalies of about $\Delta\dot\rho\approx 1-10$ mm s$^{-1}$ in the g…

We analytically work out the cumulative, i.e. averaged over one orbital revolution, time variations of the radial velocity v_r of a typical S star or…

We numerically work out the impact of the general relativistic Lense-Thirring effect on the Earth-Mercury range caused by the gravitomagnetic field o…

We analytically worked out the general relativistic gravitomagnetic long-term rates of change of the relevant Keplerian orbital elements of a test particle orbiting a primary M at distance r from it which, in turn, moves in the external spacetime de…

We study a general relativistic gravitomagnetic 3rd-body effect induced by the spin angular momentum ${\boldsymbol{S}}_\textrm{X}$ of a rotating mass…

We discuss how, in a Universe restricted to the causal region connected to the observer, General Relativity implies the quantum nature of physical ph…

We analytically worked out the post-Keplerian corrections to some orbital periods which are degenerate in the purely Keplerian two-body scenario. We considered the Newtonian acceleration due to the oblateness J2 of the primary, and the post-Newtonia…

The orbital motion of a binary system is characterized by various characteristic temporal intervals which, by definition, are different from each oth…

Here, the general expressions for the post-Newtonian gravitoelctric direct orbital shifts arising from eq. (4.1) are displayed for an arbitrary orientation of the primary’s spin axis. In this case, the inclination I does not necessarily refer to the…

The orbital dynamics of a test particle moving in the non-spherically symmetric field of a rotating oblate primary is impacted also by certain indire…

Recently, Will calculated an additional contribution to the Mercury's precession of the longitude of perihelion $\varpi$ of the order of $\dot\varpi_…

We study the generalization of the dispersionless Kadomtsev - Petviashvili (dKP) equation in n+1 dimensions and with nonlinearity of degree m+1, a mo…

We consider a binary system composed of a pulsar and a massive, fast rotating, highly distorted main sequence star as a potential scenario to dynamic…

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