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An experienced space time traveler teleports from place to place and planet to planet with a vehicle or using psychic powers. Now suppose that this traveler teleports to a habitable planet.

Suppose that he sees twin suns in the day sky, close together. By twin suns, I mean they seem to have identical apparent diameters and identical colors, to the best of the traveler's vision. They also appear very close together, so it is easy to compare them and think of them as twin suns.

If the spacetime traveler stays on the planet for a while, how could he/she determine if the planet orbits both suns or orbits one of them with the other sun farther away? How long would that method take?

Assume that the traveler doesn't have an astronomical radar device to directly measure the distance to each sun.

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    $\begingroup$ I have a feeling that geometry and how scaling, gravity, and orbits work will result in "The planet must orbit both of them", and the "you're gonna get one sun very soon." $\endgroup$ – Aify Mar 10 '17 at 19:25
  • $\begingroup$ Terminology note. It's weird but "habitable" in a sense used in scientific articles means "with a high potential for native life" and not "colonizable". In particular a very heavy star system's stability is not counted in millions of years, so it can only have uninhabitable planets, but the planets can be suitable for your traveler to live. (Just not enough stability for a native evolution). $\endgroup$ – kubanczyk Mar 11 '17 at 12:41
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Quite simply, if the planet orbits both stars then they will always appear close together in the sky. If it only orbits one of them, then they will move further apart throughout the year until they are on opposite sides of the planet, before moving back again:

diagram of a planet moving around two stars

diagram of a planet moving around one star

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    $\begingroup$ Fig. 1 is a P-Type (or circumbinary) orbit. A planet orbiting only 1 of the two stars would be an S-Type orbit. S-Type orbits can only occur when the two stars are far apart (so far that the companion star may appear to be just another star in the sky). A P-Type orbit occurs if the two stars are very close together. If the stars are close, but not too close, any planets that formed (which is unlikely) would have been chucked into deep space. $\endgroup$ – Tim Mar 10 '17 at 20:58
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    $\begingroup$ @Tim In that case, it would seem the premise of the question is flawed, and that seeing two "suns" in the sky would always mean a P-type orbit? $\endgroup$ – ApproachingDarknessFish Mar 10 '17 at 21:16
  • $\begingroup$ Probably. The B star might appear as an unusually bright star however. $\endgroup$ – Tim Mar 10 '17 at 22:19
  • $\begingroup$ +1. Also, it's probably the case that only a circumbinary planet can be in a habitable zone around the stellar pair (probably at distances ~3AU or so for two G type stars). A planet orbiting only one star in the pair would have to be very very lucky to stay in the habitable zone for long. $\endgroup$ – Youstay Igo Mar 11 '17 at 17:59
  • $\begingroup$ @Tim could the B star be far away but very large, like a blue giant, so that it looks as bright as the A star? Or would such a big star mess too much with the orbits? $\endgroup$ – Zan Lynx Mar 12 '17 at 4:49
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Yes, if both stars are visible and close together... then either one is a distant red giant (is it red?) or both are the roughly same class, a f,g,or k. Or they are both o or b and the planet is much further away. (There's an excellent book, Dole's Habitable Planets for Man - bigger stars like o,b burn out too soon probably don't have time for life to evolve ) Also, to ensure a stable planetary orbit around the outside of the two, the stars would need to be very close. Presumably their mutual orbit would be less than a month, so the change in relative position should be visible over a few days.

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Without advanced devices or ability to observe the stars from two points simultaneously to determine parallax, measuring distance to these stars would be difficult. Your traveler may have to stay on a planet for a measurable part of the year to tell whether it orbits one or two stars.

However, it is possible to make direct observation of stars' spectral class and luminosity. This should give general idea about their mass and distance. If, as in your case, two stars are nearly identical, and have nearly identical apparent magnitude, a good bet is that the planet is on a P-type orbit around both of the stars.

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