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Space is nothing, or space is something?
The dominant model in astronomy is that space is nothing, and therefore, it does not bend light. Dominant models spread by genetic imperatives such as food, sex and territorial dominance, where intellect is one imperative but it is not the dominant one. Science was a method of selection of ideas where it should select only by intellect, but, in reality this is not what ideas select by, so a group claiming to be operating by scientific method for selecting belief, is in fact operating by the human condition, and this is why you get "scientism" and the craziness of people who fanatically claim to "be science", a delusion really. In this "scientism" (i.e., people believing they can actually be "rational" just by wanting to really badly, even though their instincts do not care about that), anything that could not be easily explained has typically been replaced by "nothing". God was replaced by nothing. From "God created the universe" to "nothing created the universe". Etc. "Nothing", which cannot actually exist, does exist in "scientism". The idea that space was something, and that this provides a medium for waves (waves being by definition perturburations in a medium, i.e., something) was replaced by "nothing" by "scientism". Believers in scientism who decided space is nothing (which is, well, a ridiculous belief) had to believe that what they saw in the sky was light that had not been affected in any way, such as bent or such (they made the occassional exception where they really really had to, such as the effect near stars... i.e., they introduce contradictions in their model and underlying premises as there were some things they could not manage to ignore). Thus, parallax, was simple straight line geometry, and from that the stars had to be really far away. If, instead, you consider the model where space is something, and not nothing, it bends light. A solar system, behaves like a spherical gradient-index (GRIN) lens is made of concentric shells with gradually varying refractive index. The index is lowest at the center and increases toward the outer edge, following a logarithmic profile. Objects seen through the lens appear compressed toward the center and smaller than they really are. This applies whether the observer is outside looking in, or inside looking out. If the sun had a binary companion star, any planet within that binary system would be compressed towards the center, and any parallax between the binary star and background stars would be reduced even more than what parallax normally is by our solar system: our companion star would appear further away, even compared to other stars, than it is. If our binary star had a barycenter around one of its larger planets, a gas giant, this barycenter would not be compressed, since it is the system as a whole moving. The gas giant would appear close to the star. It would orbit the star with the period of the barycenter. We would be able to see our own orbit around the binary star in ways similar to our orbit around our sun, but slower. Each "month" in the binary orbit, the sun would rise in a new constellation at a certain time of the year, just as it rises in a new constellation every month of the year. The spectrum from our binary star, would be that of a nearby star, i.e., it would have strong enough signal that it could be contrasted to the background radiation of the interstellar space medium, and would lack hydrogen wavelengths.