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
  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. 
Herman J. Mosquera Cuesta
physics.gen-ph