How would that work exactly, a figure 8 orbit?
As the mass of the third object the Jupiter size planet is negligible, the easiest way to understand the problem is to treat it as a two body problem, where you have the entire mass of the two suns centred at the barycenter, and the planet orbiting around both of them.
How do I know this? Both suns are on the same side, and very close to one another. In a figure 8, which is a restricted but possible solution, you’d see sunsets and sunrises on opposite sides of the sky, as the planet would pass between the stars.
http://faculty.ifmo.ru/butikov/ManyBody.pdf
Read this to get a better idea of the different ‘classes’ of possible orbits.
That's what I wonder.