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To date, well over a thousand planets have been discovered orbiting otherstars, hundreds of them in multi-planet systems. Most of these exoplanets havebeen detected by either the transit method or the radial velocity method,rather than by other methods such as astrometry or direct imaging. Both theradial velocity and astrometric methods rely upon the reflex motion of theparent star induced by the gravitational attraction of its planets. However,this reflex motion is subject to misinterpretation when a star has two or moreplanets with the same orbital period. Such co-orbital planets may effectively"hide" from detection by current algorithms.  In principle, any number of planets can share the same orbit; the case wherethey all have the same mass has been studied most. Salo and Yoder (A & A 205,309--327, 1988) have shown that more than 8 planets of equal mass sharing acircular orbit must be equally spaced for dynamical stability, while fewer than7 equal-mass planets are stable only in a configuration where all of theplanets remain on the same side of their parent star. For 7 or 8 equal-massplanets, both configurations are stable.  By symmetry, it is clear that the equally-spaced systems produce no reflexmotion or radial velocity signal at all in their parent stars. This could leadto their being overlooked entirely, unless they happen to be detected by thetransit method. It is equally clear that the lopsided systems produce a greaterradial velocity signal than a single such planet would, but a smaller signalthan if all of the planets were combined into one. This could seriously misleadestimates of exoplanet masses and densities. Transit data and ellipsoidal(tidal) brightness variations in such systems also are subject tomisinterpretation. This behavior is also representative of more naturalsystems, with co-orbital planets of different masses.

Radial Velocities of Stars with Multiple Co-orbital Planets