I read this article, Questioning Einstein: Is Relativity Necessary? (Bethell (2010), Proc. Natural Philosophy Alliance, v.6, no. 2), regarding the 2 stars of Mizar A and wondering if it is true that we do not see back and forth aberration effects when observing binary star systems? If true, is there a known explanation?
In 1889 Edward Pickering had discovered spectroscopic binary stars, orbiting a common center of mass so closely that they appear as a single star even in the most powerful telescopes. The two stars of Mizar A, in the handle of the Big Dipper, are only 18 million miles apart. Their separate character is apparent only from the alternating Doppler shifts in their spectral lines. They orbit one another at a velocity of 50 kilometers per second, or 1.7 times the Earth’s orbital velocity.
It follows that even if we still don’t know the true velocity of the binary systems with respect to the sun, we do know that there is a difference, sometimes large, between the separate stars of the binary system relative to us. In the case of Mizar A, at a given moment in its 104-day cycle, one star is approaching us at the high velocity of 50 kilometers per second (relative to the center of mass of the system) while the other star is moving away from us at the same velocity. Irrespective of the movement of the system as a whole, then, the twin elements of the orbiting pair are moving at velocities that exceed the Earth’s orbital velocity by quite a large margin.
By Einstein’s formula, alternating back and forth aberrations should therefore be observed, corresponding to the period of their orbits. The aberration angle of each star should increase and then decrease as they circle each other. This would be easily observable by modern instruments. The differential aberration would be so large that the stars would become visibly separate in the sky before closing again. In the case of Mizar A, the angular separation of the binary components would be more than a minute of arc. But they always remain as an unresolvable point in the sky. And because binary systems are so common, we should be seeing this back and forth apparent motion of binary components all over the heavens. But we never do