In this short voyage to the Pioneer 10 and 11 missions our main guide will be the comprehensive and richly documented recent review on the Pioneer Anomaly by [Turyshev, S. G. & Toth, V. T. (2010). Living Rev. Rel. 13 (2010) 4. arXiv:1001 from which we retake some ideas and references. (The attentive readers are kinldy addressed to this invaluable article). The Pioneer 10 and 11 spacecrafts were the first two man-made space vehicles designed to explore the outer solar system. The trajectories of the spaceships were projected to passage nearby Jupiter during 1972-1973 having as objectives to conduct exploratory investigation of the interplanetary medium beyond the orbit of Mars, the nature of the asteroid belt, the environmental and atmospheric characteristics of Jupiter and Saturn (for Pioneer 11), and to investigate the solar system beyond the orbit of the Jovian planet. 1 The Pioneer missions were the first space probes to adventure over the asteroid belt, heading for close-up observations of the gaseous giant planets, and for performing in situ studies of the physical properties of the interplanetary medium in the outer solar system. The design of their missions was guided by the simplicity, having a powerful rocket-launching system to push the spacecrafts on an hyperbolic trajectory aimed directly at Jupiter, which the spacecrafts were expected to fly-by approximately 21 months after launch (see Fig. 1). By the late 1960's, the aerospace engineering technology available to the designers of the Pioneer missions made it no longer practical to use solar panels for operating a spacecraft at large distances, as for instance that of Jupiter. A cause of this, a built-in nuclear power system, in the form of radioisotope thermoelectric generators (RTGs) powered by 238 Pu, was chosen as the means to provide electrical power to the spaceship. As even this was relatively new technology at the time the missions were designed, the power subsystem was suitably over-engineered, being the unique design requirement to have a completely functional space probe capable of performing all planned scientific tasks by running only three (out of four) RTGs. The entire design of these spacecrafts and their science missions was characterized by such conservative engineering, and for sure it was responsible for both the exceptional longevity of the two spacecrafts and their ability to deliver science results which by far exceeded the expectations of their designers. The original plan envisioned a primary mission of two to three years in duration. Nevertheless, following its encounter with Jupiter, Pioneer 10 remained functional for over 30 years. Meanwhile, Pioneer 11, though not as long lived as its engineering-copy craft, successfully navigated a path across the solar system for another encounter with Saturn, offering the first close-up observations of the ringed planet. After the encounters with Jupiter and Saturn (for Pioneer 11, see Fig. 1), the space ships followed, near the plane of the ecliptic, hyperbolic orbits of escape head...