  A few observational and/or experimental results have dramatically pushed
forward the research program on gravity as those from the radio-metric Doppler
tracking received from the Pioneer 10 and 11 spacecrafts when the space
vehicles 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 $ \sim
6 \times 10^{-9}$ Hz s$^{-1}$. Those signals, if interpreted as a gravitational
pull 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 appears
to be a violation of Newton's inverse-square law of gravitation, and is
referred to as the Pioneer anomaly, the nature of which remains still elusive
to unveil.
  Within the theoretical framework of nonlinear electrodynamics (NLED) in what
follows we will address this astrodynamics puzzle, which over the last fifteen
years has challenged in a fundamental basis our understanding of gravitational
physics. To this goal we will first, and briefly, review the history of the
Pioneers 10 and 11 missions. Then a synopsis of currently available Lagrangian
formulations of NLED is given. And finally, we present our solution of this
enigma by invoking a special class of NLED theories featuring a proper
description of electromagnetic phenomena taking place in environments where the
strength of the (electro)magnetic fields in the background is decidedly low.
