Given a double planet system where the two bodies are of similar mass;
Can a moon orbit one or both planets in a stable orbit? How about an artificial satellite?
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Yes, it is possible. Pluto and Charon are a double "planet" system, and have moons like Kerberos, Nix and Hydra that orbit the heavier masses.
The problem of orbital stability has mostly been studied for planets orbiting two double stars, either in "P-type" orbits around both or "S-type" orbits around one of them. (There are also "L-type" orbits near Lagrange points.) Since gravity doesn't care about scale what matters is the distance the moon orbits from the planets (measured in units of their separation), and the ratio of their masses.
Simulations show that there are stable orbits if they are far away, more than 2.5 times the planet separation (Musielak, Cuntz, Marshall & Stuit 2004):
In practice there will be bands of resonance or chaotic motion here if the period of the moon matches the planet period in a rational ratio, and that could fling it away. The stability is also better when the moon orbits in the opposite sense from the planets.