How We Know So Much About Planets That Are Super Far Away

NASA's Kepler Space Telescope has discovered the densest exoplanet yet, but how can we determine the mass of a planet that is so far away?

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Astronomers discover rare planet: Kepler-432b is a dense, massive celestial body with extreme seasons
http://www.sciencedaily.com/releases/2015/02/150212114243.htm
"Two research groups of astronomers have independently of each other discovered a rare planet. The celestial body, called Kepler-432b, is one of the most dense and massive planets known so far. The teams report that the planet has six times the mass of Jupiter, but about the same size. The shape and the size of its orbit are also unusual for a planet like Kepler-432b that is revolving around a giant star. In less than 200 million years, this "red giant" will most likely swallow up the planet."
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