One objection to RCM theory has been that if light leaves its source in a continuum of velocities, and the observer only sees that component that reaches him at a relative velocity of c in his reference frame, then we would observe anomalies in certain astronomical observations. This argument was used against Ritz theory that light always leaves at a velocity of c with respect to a source. For example, in certain eclipsing binary stars, one could possibly see one of the stars in two places at once, as both its speed and direction of movement change. This could be tested even with the eclipsing of Jupiter's moons by the planet at various points in its orbit. However, this objection does not hold for RCM.
In the video, we see a stylized image of the Earth, Jupiter and one of its moons from two vantage points. On the right panel, we see the sun centered view, with Earth and Jupiter orbiting the sun, and the moon orbiting Jupiter. It is on this view that the argument is raised, and it goes like this: We on earth are seeing only that component of light that left its source at a velocity of c with respect to Earth. Since the Earth is constantly changing its velocity with respect to Jupiter and its moon, then, depending on the relative position and velocity of Jupiter and the Earth, the moon will appear to eclipse (or be eclipsed by) Jupiter at erratic times. When we are moving away with respect to Jupiter, we require a component at some value c+v, and while we are moving toward Jupiter, we require a component of c-v. This difference, over the time required to reach Earth from Jupiter, should be measurable and obvious.
The problem with the above analysis is that it imagines what is being seen on Earth from a sun centered perspective. The same problem arises in special relativity when one doesn't properly perform the transformation from what is observed in one reference frame to that which is observed in a different reference frame. To see the distinction, we consider the panel on the left.
In the left hand panel, we see the view of things from an Earth-centered perspective, where the rotation of the Earth on its axis is ignored for simplicity without affecting the validity of the discussion. In the Earth centered view, i.e. the reference frame of an observer on the Earth, all light is reaching the Earth at a velocity of c. The only motions of interest are those of the planet Jupiter and its moon with respect to the Earth. In each case, according to RCM theory, the light component of interest is that component that has a velocity of c with respect to the Earth. Thus, for example, when Jupiter is moving away at some velocity v, the component is c+v with respect to Jupiter (the source), but c with respect to Earth (the observer). In the reference frame of the observer on Earth, this light covers the distance (d) from its point of origin in a time given by t=d/c. If Jupiter is moving toward the Earth, the component of interest with respect to the source is c-v, but, again, with respect to the Earth bound observer it is c, and the time is again t=d/c. Note that the timing and phasing of all eclipses is the same in both panels, as it should be.
From the above we see that the proposed discrepancies in the observed patterns and timing of Jupiter-moon eclipses do not occur. The analysis is valid for any astronomical observations to be proposed.