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A few observational and/or experimental results have dramatically pushedforward the research program on gravity as those from the radio-metric Dopplertracking received from the Pioneer 10 and 11 spacecrafts when the spacevehicles were at heliocentric distances between 20 and 70 Astronomical Units(AU). These data have conclusively demonstrated the presence of an anomalous,tiny and blue-shifted frequency drift that changes smoothly at a rate of $ \sim6 \times 10^{-9}$ Hz s$^{-1}$. Those signals, if interpreted as a gravitationalpull of the Sun on each Pioneer vehicle, translates into a deceleration of $a_P= (8.74\pm 1.33) \times 10^{-10}$ m s$^{-2}$. This Sunward acceleration appearsto be a violation of Newton's inverse-square law of gravitation, and isreferred to as the Pioneer anomaly, the nature of which remains still elusiveto unveil.  Within the theoretical framework of nonlinear electrodynamics (NLED) in whatfollows we will address this astrodynamics puzzle, which over the last fifteenyears has challenged in a fundamental basis our understanding of gravitationalphysics. To this goal we will first, and briefly, review the history of thePioneers 10 and 11 missions. Then a synopsis of currently available Lagrangianformulations of NLED is given. And finally, we present our solution of thisenigma by invoking a special class of NLED theories featuring a properdescription of electromagnetic phenomena taking place in environments where thestrength of the (electro)magnetic fields in the background is decidedly low.

Nonlinear Electrodynamics: Alternative Field Theory for Featuring Photon  Propagation Over Weak Background Electromagnetic Fields and what Earth  Receivers Read off Radio Signals from Interplanetary Spacecraft Transponders