Steve, I'm not very erudite on astrophysics, so I consulted Wikipedia, first in the voice: binary star
https://en.wikipedia.org/wiki/Binary_star#Configuration_of_the_systemThe orbits of the components of a binary system vary according to the mass ratios of the components themselves and this is illustrated pretty clearly in the wiki page:
for stars of similar mass

for stars of different mass

There are other cases, but the essential mechanism is that t
he two stars rotate around a common baricenter. The rotation period may vary amply, from a few hours to hundred of thousand years.
Now, in SY's model, the sun is rotating around the baricenter of a dual system , in a 24000 years period. The sun may be also rotating around its dual, but this only if the dual is much higher in mass.
The whole galaxy is also rotating and the baricenter of the dual system (with both binary stars) rotates around the galactic center with a 230 million earth years period:
https://en.wikipedia.org/wiki/Galactic_yearThe first rotation is what interests us. the galactic rotation is irrelevant to SY's model, whereas it may be relevant to other models described in the Hindu scriptures (for example, the year of Bhrama).
Now, while rotating around the dual system baricenter, the sun goes periodically closer and further to the galactic center, which I think is SY's grand center. Closer causes a satya yuga, further causes a kaly yuga.
The grand center may be another celestial object which emanates spiritual radiations, but I doubt that it is the sun's dual, otherwise SY would have explicitly mentioned it.
The above is exactly the same as your conclusion in the preceding post:
That Sun (that our Sun rotates around) and our Sun rotate around Sagittarius A* which is the center of our galaxy. So, if our views are the same, I'm wondering now why your inception was a negative.