I'm looking to not tidally lock my planet, but place it between two suns that rotate around each other. The goal is to have constant sunlight on all sides of the planet and for the suns to rotate at a constant speed relative to the planet. I want to clarify, I don't want the planet to relocate within the system at all.
It should rotate with the same side of the planet always facing the same side of the sun, with equal sizes binary stars. This would remove the "year", as there's no orbit to speak of, due to the lack of movement around either star.
Is this method to make a stationary planet possible?
Bonus: Could it have a livable atmosphere?
Let me know if my intent is unclear, and I'll update accordingly.