We investigated possible strategies to reduce the experimental uncertainty on the angle α of the Cabibbo-Kobayashi-Maskawa (CKM) matrix in B meson systems .
Phenomenology of general relativistic gravitoelectromagnetism
In the weak-field and slow-motion approximation, the field equations of the Einstein's General Theory of Relativity get linearized, thus closely resembling the Maxwellian linear equations of electromagnetism. As a result, many interesting effects on the motion of test bodies [1, 2, 3, 4, 5] and electromagnetic waves [6, 7] occur. We analyzed tests of some general relativistic gravitoelectromagnetic orbital effects in the gravitational field of the Earth with artificial satellites [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], in the Solar System (Moon , Sun-planets [22, 23, 24, 25, 26, 27, 28, 29, 30, 31], Sun-spacecraft ,
Mars [33, 34, 35], Saturn , Jupiter [37, 38, 39, 40]), in some extrasolar planetary systems [41, 42, 43, 44], and in the Galactic centre . According to some researchers, Earth's artificial satellites may be used to test some exotic models of modified gravity as well; this proposal was investigated in . Also the impact of General Relativity on unbound, hyperbolic orbits [47, 48] was analyzed in the framework of the so-called flyby anomaly. Gravitomagnetism has connections with gravitational waves as well; they were elucidated in .
Some methodological issues about testing General Relativity
Several tests of General Relativity are often performed in an “opportunistic” way by exploiting spacecraft-based missions originally designed for different purposes. This may pose certain subtle issues analyzed in [1, 2, 3].
Gravitational and non-gravitational satellite orbital perturbations in space-based tests of general relativity
We investigated in detail many classical orbital perturbations of gravitational [1, 2, 3, 4] and non-gravitational  origin because they are of crucial importance in realistically assessing the error budget
[6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]
in many ongoing or proposed satellite-based tests of general relativity like, e.g., LARES [22, 23, 24, 25, 26, 27, 28, 29, 30].
Tests of the equivalence principle in space-based scenarios
We studied the possibility of testing the weak equivalence principle with some existing or proposed Earth's artificial satellites without any mechanism of compensation of the non-gravitational orbital perturbations [1, 2]. The equivalence principle was used also to constrain some orbital parameters of the planetary system hosted by the pulsar PSR B1257+12 . Complete orbital effects due to a violation of the strong equivalence principle in an external field were investigated  as well.
Earth-based tests of general relativistic gravitoelectromagnetism
We studied the possibility of performing some laboratory-scale terrestrial experiments to test some predictions of the linearized approximation of General Relativity [1, 2].
Derivation of new gravitomagnetic effects
We derived, in the weak-field and slow-motion approximation, some new gravitomagnetic spin-orbit effects affecting the path of bodies moving in the field of rotating masses and investigated the possibility of detecting them in space-based scenarios [1, 2, 3, 4, 5, 6, 7, 8]. Gravitomagnetic effects arising from possible Lorentz violations around static bodied were investigated  as well.
Study of some approximated solutions of the Einstein's field equations
We analytically worked out the geodesic equations of an approximated solution of the Einstein's field equations in which the rotational effects are larger than the mass ones in order to investigate its physical plausibility .
Multidimensional braneworld models of gravity
We analytically derived some weak-field effects of certain multidimensional braneworld models of gravity recently proposed [1, 2, 3], and investigated the possibility of putting them to the test with Earth's artificial satellites , Solar System's planetary motions [5, 6], and binary pulsar's dynamics .
Phenomenology of Dark Matter and the cosmological constant in the Solar System
The latest determinations of the extra-precessions of the perihelia ϖ of some Solar System's planets allowed us to tackle the problem of the influence of the Dark Matter distribution [1, 2] and of the cosmological constant [3, 4] in the Solar System. The effect that a potential accumulation of non-annihilating Dark Matter on the Sun may have had on the Solar Systems; evolution was investigated as well . Inhomogeneous cosmological models, like the Lemaître-Tolman-Bondi solution, have recently received attention in view of their potential ability to explain the Universe's acceleration without resorting to Dark Energy. Their local effects on the dynamics of some Solar System's objects were investigated to phenomenologically put constraints on some key parameters of the LTB models .
Solar System phenomenology of local effects of cosmological origin
Using the most recent upper bounds on the anomalous perihelion precessions of some planets of the Solar System, phenomenological constraints on local, Coriolis-type rotational effects of cosmological origin were posed
. Possible local orbital effects of the order of H caused by the expansion of the Universe have been examined as well [2, 3].
Constraints on Varying Speed of Light (VSL) theories and on spatial variations of fundamental coupling constants
We used the latest observational determinations of the extra-precessions of the perihelia ϖ of some planets of the Solar System to put constraints on the time variation of the speed of light in the context of some recently proposed VSL theories . The orbital effects of putative spatial variations of the fine structure constant for the major bodies of the Solar System were investigated  as well. Solar System's orbital dynamics was used to rule out a possible temporal variation of the Newtonian constant of gravitation G  which could account for the observed discrepancy among its measurements performed over the years in Earth-based laboratories with various techniques.
Phenomenology of other long-range modified models of gravity
We used the latest observational determinations of the extra-precessions of the perihelia ϖ of some planets of the Solar System to put constraints on several long-range modified models of gravity [1, 2, 3, 4, 5, 6, 7,
9, 10, 11, 12, 13, 14,
16, 17, 18] recently put forth to address the Dark Energy and Dark Matter puzzles. Also the Hořava-Lifshitz gravity, which involves a breaking of the Lorentz spacetime symmetry at a certain level, was investigated from a phenomenological point of view by constraining it from Solar System's [17,19] and extrasolar planetary motions .
Galactic dynamics in modified models of gravity and Dark Matter
The motion of the Sun throughout the Milky Way in the past 4.5 Gyr was studied according to different models of Dark Matter, MOdified Newtonian Dynamics (MOND) and MOdified Gravity (MOG) .
Also the motions of the Magellanic Clouds in the Milky Way's field were studied within such three models .
The motion of the Sun in the Galactic field backward in time was investigated as well to tentatively put preliminary anthropic constraints on the Cosmological Constant Λ .
Test particle motion around a mass-varying primary
The orbital effects of the time variation of the gravitational parameter µ=GM of a central mass on the motion of a test particle around it were investigated  and applied to the future evolution of the Solar System . The case in which a non-isotropic mass variation occurs for the orbiting particle was studied as well .
Unexplained perihelion precession of Saturn and other possible astrometric anomalies in the Solar System
In 2008, it seemed that an anomalous secular precession of the perihelion of Saturn had been determined by analyzing some years of radio-technical data from the Cassini spacecraft with some versions of the EPM and INPOP ephemerides in use at that time. Its possible origin in terms of standard or exotic gravitational physics was investigated in [1, 2] obtaining negative answers. Another astrometric anomaly detected in the last decade by analyzing long LLR data records covering about 39 years consists of an anomalous increase of the eccentricity of the orbit of the Moon. Possible explanations in terms of standard and non-standard laws of gravitation were examined [3, 4, 5]. Some possible explanations for the so-called flyby anomaly, consisting in an unexplained change in the radial velocity experienced by certain spacecraft at some of their Earth flybys, were studied in [6, 7]. An overview of the possible anomalies of gravitational origin in the Solar System was offered in .
The Kuiper Belt, the Oort cloud and putative distant planet(s)
By using the estimated extra-precessions of the perihelia ϖ of the inner planets of the Solar System and simple ring models we constrained the mass of the Kuiper Belt Objects and compared our result with other estimates obtained with different, non-dynamical techniques [1, 2]. We also investigated the impact of neglecting the Kuiper Belt Objects in some spacecraft-based high-precision tests of post-Newtonian gravity recently proposed . The perihelia of the inner planets were also used to put dynamical constraints on a hypothetical distant body of planetary/stellar size [4, 5] which allowed to rule out some scenarios proposed in the literature .
The ranging data of the spacecraft Cassini, which orbited Saturn since 2004 to 2017, were used to study the effect of some hypothetical planetary scenarios (Planet Nine or Telisto and Pianet Eleven or Taraktor) on the Earth-Saturn range [7, 8].
The ongoing New Horizons mission to the Pluto system could also be used to put tighter constraints on such a putative object . The orbital dynamics of objects in the Oort cloud was studied in the framework of MOND by taking into account the impact of the External FIeld Effect (EFE) . The possibility that an astronomical object of planetary-stellar mass may come close the Earth in a time span of a few years moving along an unbound, hyperbolic orbit was studied as well .
The Pioneer anomaly
If the Pioneer anomaly-an almost constant and uniform acceleration directed towards the Sun of about 1 nm/s² detected in the data of both the Pioneer 10 and 11 spacecraft approximately in the range 20-70 AU-was of gravitational origin, it should fulfil the equivalence principle. Thus, the same acceleration should act also on the major natural bodies of the Solar System orbiting in the spatial regions in which the Pioneer anomaly manifested itself in its presently known form. We focussed our investigations on such an aspect [1, 2, 3, 4, 5, 6,
Some foundational aspects of Special and General Relativity
We investigated the twin paradox by analytically working out the time delay Δτ in both the Special and General Theories of Relativity [1, 2]. While the non-accelerated observer was described with the former one, the latter one was used to describe the point of view of linearly and rotationally accelerated observers. An historical overview of General Theory of Relativity in its centennial year was offered in .
Study of bulk properties of some astronomical and compact astrophysical objects, and black holes
We looked for deviations from the third Kepler's law to investigate some bulk properties, like the quadrupole mass moment Q, of compact astrophysical objects in binary systems getting also information on some of their orbital parameters [1, 2, 3]. The same approach was used also to determine the dynamical tidal deformation parameter k in the eclipsing
binary system V621 Cen , and for studying the orbital effects induced by the huge centrifugal distortion of the star Regulus on the motion of its companion . The long-term time variations of the transit duration of the extrasolar transiting planet WASP-33b were investigated in order to detect some relevant physical parameters of its hosting star
; its orbital precessions were investigated in . The post-Keplerian corrections to the otherwise degenerate orbital periods of a test particle orbiting a spinning oblate primary were analytically calculated in  along with the perspectives of measuring them with exoplanets. A general investigation of the effects caused by the centrifugal oblateness of the host star on some typical observables of transitting exoplanets was conducted  as well. The impact of several dynamical effects, connected with the physical properties of the supermassive black hole hosted in the Galactic centre, on the radial velocity of the star S2 was investigated both analytically and numerically in [10, 11, 12, 13, 14].
Post-Newtonian effects in binary pulsar systems
We investigated the possibility of using the 1/c² post-Newtonian gravitoelectric correction to the secular precession of the mean anomaly as further post-Keplerian parameter in binary systems hosting at least one neutron star acting as a pulsar . It was also studied the state-of-the-art of the possibility of detecting the 1/c² post-Newtonian spin-orbit periastron secular precession (analogous to the Lense-Thirring gravitomagnetic precession of the pericentre of a test body) in the recently discovered double pulsar binary system; this would allow to measure the pulsar's moment of inertia gaining important information about its bulk properties [2, 3].
The double pulsar system was used also to put constraints on some modified models of gravity by inspecting possible deviations from the third Kepler's law . Some features of the orbital configuration of the planetary system hosted by the pulsar PSR B1257+12 were studied . It was also used to put phenomenological constraints on possible accretion of non-annihilating Dark Matter onto the pulsar itself . The post-Newtonian perturbations on the orbital part of the pulsar timing delay were studied in .
Constraints on PPN paramters from Solar System's orbital motions
Recent advances in Solar System's planetary orbit determination allowed to preliminary infer tighter bounds on some PPN parameters such as α1, α2 , α3 , and ξ .
The orbital effects induced on a gravitationally bound two-body system by a traveling gravitational wave with frequency much smaller than the orbital one were calculated in . The connection between gravitomagnetism and gravitational waves was reviewed in .
Pseudonyms in physics
The case of the pseudonyms used by I. Ciufolini on arXiv to anonymously criticize some competitors was treated in .
The Faint Young Sun Paradox and modified models of gravity
The Faint Young Sun Paradox (FYSP) consists of the fact that, according to
consolidated models of the Sun's evolution history, the energy output of our star during the Archean, from 3.8 to 2.5 Gyr ago, would have been too low to keep liquid water on the Earth's surface. Instead,
there are compelling and independent pieces of evidence that, actually, our planet was mostly covered by liquid water oceans, hosting also forms of life, during that eon. A modified model of gravity with non-minimal coupling may have, in principle, the potential capability of solving the FYSP. Such a possibility was investigated in .