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Assuming Carl is away from the Internet access, I just simulated his
situation with I.P. The two stars have identical mass of 2e30 kg; the
distance between them is 1.5*10^15 m. The stars orbited exactly the
same circle many times, as expected. Then the simulation was stopped
and a much less massive satellite (m=2*10^25 kg) was added at r=
3.595e^15 m. The three particles were initially on the horizontal line,
at locations -1.5e15, +1.5e15 and 3.595e15 meters. The speeds of large
stars were 149.1 m/s (clockwise) while the speed of the satellite was
357.36 m/s (also clockwise).
Under such initial conditions, the three particles were initially
collinear. But not for too long. After about one T (period for each
star) the satellite started approaching the nearest star. Then it
started orbiting around it. But this also did not last too long. It
less than 2*T it hit the small circle representing the star which was
initially far away from it.