We can look at the pioneer 10 spacecraft as it moves beyond the solar system in the same manner in which we looked at Jupiter's moons. RCM operates the same way, meaning the analysis from Earth's frame is the same as it is in the prior example. However, in actuality, the data reduction for received signals involves a complicated (though straightforward) process of converting all signals received on Earth to the hypothetical signals that would have been received by an observer situated at solar barycenter (effectively the center of mass of the Sun or solar system).
In this system, the Pioneer is moving directly away from the sun at a nearly constant velocity, and the Earth is orbiting the sun at a nearly constant speed. Special relativity relies on a Doppler shift formula that corrects what is received on Earth to what would be received at the sun, based on length contraction and time dilation between relatively moving bodies. Given the constant offset in calculated acceleration of the spacecraft from what is expected, it seems likely that there is either a flaw in these calculations, or a flaw in the underlying theory on which they are based, and not an anomaly in the nature of gravity itself, as some have proposed.
crenshaw@teleinc.com 