Effects of Trojan exoplanets on the reflex motions of their parent stars

This paper collects and corrects certain results on the radial velocity variations of stars in Trojan systems, where two exoplanets separated by 60° of longitude share the same orbit. Radial velocity measurements can seriously misjudge the masses and densities of planets in such systems. derive a simple new method for combining tidal perturbations from two or more sources, such as the tides raised on Earth by the Sun and Moon. This method then shows that the observable effects of tides raised on stars by Trojan planets are also misleading. However, the combination of both tidal and radial velocity measurements can determine the mass of each planet. I conclude with a discussion of possible scenarios for the formation of co-orbital exoplanets.