Artist’s concept of an exoplanet and its moon transiting a sun-like star. Such a system could be used to directly weigh the star. Credit: David A. Aguilar (CfA)
Many exoplanets (planets that orbit stars other than our sun) have been found by using the transit method. Briefly, the planet is directly observed passing in front of its star. If that planet also has a moon, astronomers have the three data points they need to figure out the mass of the star. They can directly measure the orbital periods (time it takes to complete an orbit) of the moon and planet, the size of those orbits relative to the star, and the size of the moon and planet themselves relative to the star. Taken together, these data can be used to determine the size of the star. You need all three objects (star, planet and moon) for this method to work though.
You may be wondering, as I was, how many transiting exoplanets also have moons. The answer is none. So far, not a single ‘exomoon’ has been found. That does make Kipping’s method a bit less useful, but he isn’t discouraged:
"When they're found, we'll be ready to weigh them.”