Reproducing the Pioneer 10 Anomaly with a Cosmic Lens
Anderson et al. say: ?We have reported an anomalous, constant acceleration of Pioneer 10 and 11, a = (8.74 ?1.33)E-8 cm/s2, directed towards the Sun, at distances ~20 - 70 AU.? This anomaly can be reproduced by a multi-layer, onion-like, spherical cosmic lens centered on the Sun with an inner radius of 20 AU. If the effect stops at around 70 AU then the lens has eight layers, and the outer radius of the lens is 68.58 AU, and the effective refraction index through the eight layers is 1.000587235. If the effect extends beyond 70 AU, then there are more than eight layers. The innermost layer has a thickness of 3.33 AU and a refraction index of 1.000067963, and the eighth layer has a thickness of 9.79 AU and a refraction index of 1.000155628. The ratios between the volumes of adjacent lens layers is a constant, and that constant is within 0.2% of 41/3. In order to make the volume ratios exactly equal to 41/3, the anomaly error bars need to change from ?1.3300 to ?1.3357. The anomalous acceleration towards the Sun is just the calculated ?observed? acceleration minus the Newtonian acceleration. The Newtonian acceleration is simply a = GM/R2, where GM is the heliocentric gravitation constant, and R is the radial distance from the Sun to the spacecraft. The calculated ?observed? acceleration is just the Newtonian acceleration times the effective index of refraction at the spacecraft's location. The effective index of refraction is the product of the individual layer refraction indexes that are interior to the spacecraft's location.