Rindler modified Schwarzschild geodesics

The mysterious attractive constant radial force acted in the past on Pioneer spacecrafts-the so-called Pioneer anomaly-is considered within the context of Rindler acceleration. As an idea this is tempting since it is reminiscent of the cosmological constant. Fortunately the anomalous force acts radially toward the sun so that it differs from the mission of a cosmological constant. Without resorting to the physical source responsible for such a term we investigate the modified Schwarzschild geodesics. The Rindler acceleration naturally affects all massive / massless particle orbits. Stable orbits may turn unstable and vice versa with a finely-tuned acceleration parameter. The overall role of the extra term, given its attractive feature is to provide confinement in the radial geodesics.