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Many long-range modifications of the Newtonian/Einsteinian standard laws ofgravity have been proposed in the recent past to explain various celestialphenomena occurring at different scales ranging from solar system to the entireuniverse. The most famous ones are the so-called Pioneer anomaly, {i.e.} astill unexplained acceleration detected in the telemetry of the Pioneer 10/11spacecraft after they passed the 20 AU threshold in the solar system, thenon-Keplerian profiles of the velocity rotation curves of several galaxies andthe cosmic acceleration. We use the latest observational determinations of theplanetary motions in the solar system and in the double pulsar system to putconstraints on such models independently of the phenomena for which they wereoriginally proposed. We also deal with the recently detected anomalousperihelion precession of Saturn and discuss the possibility that it can beexplained by some of the aforementioned models of modified gravity.

Long-Range Models of Modified Gravity and Their Agreement with Solar System and Double Pulsar Data