The Pioneer and the Sun
This article explains the Pioneer anomaly, by means of gravity from the Sun.
The two space stations, Pioneer 10 and 11, were moving in radial directions out of our planetary system in two opposite directions. When leaving our planetary system at about 20 AU (astronomical unit equal to the radius of our planet’s orbit) the rockets were turned off. However, communication with Earth was working to about 70 AU. Speed was measured by Doppler effect, and distance was indicated by propagation time. A very small decrease in space station speed was observed by both methods of measurement.
Einstein is said to have indicated that potential of gravity, divided by squared light speed, could give a slowing of light speed. This relation gives dc/c=-0.5*10^-9 at 20 AU. We get an effect on frequency due to 2-way Doppler effect as df/f=-10^-9. With carrier frequency equal f=2.3*10^9 Hz we get df=-2.3 Hz at 20 AU. Between 20 and 70 AU we therefore get an increase in frequency of 2.3(1-20/70)=1.6 Hz. This effect can cause an illusion of a decrease of speed in the space station, in agreement to observations.
An alternative view
It is possible that dc/c=0 and instead dc2/c2=-0.5*10^-9. Here c2 is 2-way speed of light and dc2/c2=-v^2/c^2. We can find this relation by supposing that light speed is c+v and c-v. By substituting potential of gravity by ether wind squared we get the same result as Einstein. This version, based on ether wind, was described by this author in 2013 on my personal CNPS page and called The Pioneer Anomaly and the Ether Wind. ( The version available at GSJournal contains an error since the calculations start at 10 AU instead of at 20).
Explaining gravity by the ether wind is one step in the understanding of gravity. However, we have more steps to take, since we do not know much about the ether. The effect from the ether wind is caused by a vector, and not by a scalar and therefore only radial component (to Earth) in light is affected.
To explain the bending of light near our sun we must first realize that coherent light, generated in cavities or detected in telescopes, should be described by a ray model and not by a vector sum. The ray model means that transverse ether wind is irrelevant and light is described as c(1+vl/c), where vl is component in the ether wind parallel to c. The bending of light near our sun can now be described by the gradient in vl. This mechanism is described in earlier articles by this author.