In thee last explanation and model you appear to be describing it just as I did. In thee first one you said and I will quote;
Thanks Steve for all the data on galaxy rotation, if I remember well according to Sri Yukteswar the sun, rotating around its dual, alternatively travels closer and farther from the grand center, which is a source of spiritual energy. That's the basis of the Yugas theory. Satya Yuga closer to Sagittarius A*, kaly yuga further form Sagittarius A*. Unfortunately, there is still no clue about the Sun's dual. Even the Binary Institute could not find any duals after substantial research.
I don't know how such a dual is escaping the refined astrophysical calculations. Otherwise, Sri Yukteswar might have been deceived in his interpretations by some other thoughts in the causal realm.
He remains a totally inspiring master anyway.
Do you see above where you stated ; “ Satya Yuga closer to Sagittarius A* , Kali Yuga further from Sagittarius A* “
In fact Sagittarius A* has nothing to do with Sri. Yukteswar’s model. In his Holy Science he is only referring to your model of two stars below as you provided (thanks).
for stars of different mass

The model you have provided above is the correct one. The small star is etching out an ecliptic … sometimes closer at other times further away. Similar to the path of Pluto around our Sun.Both those stars (the Sun and it’s dual) are also moving within a whole arm of the Milky Way Galaxy. Around Sagittarius A* which takes approx. 24 million years.