Can a Binary Star system be possible where in one star is stationary and the other star revolves around it? (Just like a planet revolving a star. i.e planets in the system and the star revolving around their own center of masses to balance the system).
Answer
As others explained: When two masses interact gravitationally, it's not like the smaller mass is orbiting the larger mass. Both bodies orbit the common barycenter. When one of the two masses is extremely large compared to the other, the barycenter of the system is almost in the center of the larger mass, so the effect on the larger mass is negligible (like a satellite orbiting the earth). But it still won't be completely stationary. The effect would just be too small to measure.
But I would like to get back to your original question, "Can a Binary Star system be possible where the mass difference is so large that the effect on the larger star is negligible": There isn't that much difference in the masses of stars. Stars need to be massive enough to generate enough pressure to maintain nuclear fusion, but not so massive that they collapse into black holes. Also, the larger the star, the faster does it undergo fusion and the shorter its lifespan. For that reason the heaviest known stars have just about 100 times the mass of our sun, while the lightest know stars have just one tenth of a solar mass. A mass difference of factor 1000 isn't small enough that the effect on the larger mass wouldn't be notable.
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