[cripplecreek]

It all depends on the distance. If Jupiter were as close as mars the effects on earth would probably be enough to make earth a very different place.

The orbital mechanics would be pretty much the same if Jupiter were a small sun. When it comes to binary star systems we’re talking about even greater distances.

When we talk about orbiting the sun we really aren’t accurate. Earth, the sun and other planets actually orbit a common gravitational center.

[who_would_fardels_bear]

But there is no significant heating from Jupiter. I am assuming that a dual star system means that both stars would contribute some heating effect to the planet, which would differ widely as the suns and planets orbited around a "common center".

Also, the way our system is set up it is really a bunch of quasi-independent two-body problems. The effects of the other planets on our orbit with the sun are negligible. If you have two large suns, then with respect to any planet in the system you have a three-body problem which is a whole different ball of wax.