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For example, if astronomers photograph a "planet", which is in close proximity to a given star, then this "planet", could actually just be another "star" in the background, many light years away.

It might just be in the photograph by chance.

How can astronomers determine if this is in fact a planet orbiting that star, or just another star many light years away?

For example, a common method to find planets orbiting stars is to via transit. ie, we can observe how the star appears to slowly change it's brightness, and it get's it back to normal again. This basically tells astronomers that this must be a planet.

But how do astronomers know that this isn't just the "first star" transitting a star "in the background"?

I think there are two parts to this question: How do we know that the transiting object is a planet, and how do we know that it's gravitationally bound to the parent star, rather than an interloper?

If the object is indeed orbiting a star, we should see periodic transits. If a candidate transit is observed, follow-up observations should also be able to observe it. A lack of further confirmation would be a strike against the idea that the object is indeed bound. An additional tool that's useful here is spectroscopy. If the body is orbiting, it should cause a Doppler shift in the light from the star. This shift can be measured throughout the body's orbit. If a periodic shift is observed - with the same period as the transits - then we have another bit of evidence for an exoplanet.

Now, the light curves of transiting exoplanets can look similar to those of eclipsing binaries - binary stars where the orbital plane of the components is aligned with the line of sight of the observer. A couple key elements can help astronomers differentiate between the two:

• An eclipsing binary should display a secondary eclipse when the less luminous component passes behind the first. This is not likely to be prominent in the case of a transiting exoplanet.


• The mass of the orbiting object can be determined by measuring the radial velocity of the star, as determined by looking at the Doppler shift. This is an easy way to distinguish an exoplanet from a star.

In short, an occultation of a background star by an interloper would not be periodic and would not be associated with Doppler shifts in the other star's spectrum. The mass of the orbiting body - as well as the presence or absence of a significant secondary eclipse - can help us determine its nature.

They can measure radiation from the celestial body and determine if it is a star or not.