How do astronomers determine that they've discovered "single" large extrasolar planets and not "multiple" lesser planets?
If planets have different distances to their host stars, as all of the planets in our Solar system and the many known exoplanet systems, the planets will orbit with different periods. This means they go around their host stars at different speeds and will separate themselves spatially and frequency-wise. In all the methods to find exoplanets (microlensing, pulsar timing, radial velocity, transits and direct imaging) these planets are separable. For example, with direct imaging, you can see two different points of light. With radial velocity measurements, you can separate out the frequencies. As a planet revolves around a star, the star too revolves a bit around their common center of mass. A large planet will cause a sinusoidal shift at a single frequency (the time of that planet's year) in the star's apparent motion towards or away from us. Two planets will have two different length years, and cause wobbles in the star's motion of two different frequencies. That's how we know when we're looking only at a single planet.
If there is a binary planet system, where two planets orbit each other's common center of mass which goes around the host star this can be harder to detect with some methods. With direct imaging, the two planets might appear so close as to look like one. With radial velocity measurements, the effect on the star will mostly look the same because the the two planets will basically appear to the host star as one gravitational tug. For the transit method, distinguishing binary planets from single planets is easier though because the transit start times will vary depending on which part of the binary orbit lines up with the star. As of 2015, though, no binary planets have been found around other stars.
Updated on July 18, 2015 by Everett Schlawin.