Using long-term transit timing to detect terrestrial planets

ABSTRACT We propose that the presence of additional planets in extrasolar planetary systemscan be detected by long-term transit timing studies. If a transiting planet is on aneccentric orbit then the presence of another planet causes a secular advance of thetransiting planet’s pericenter over and above the effect of general relativity. Althoughthis secular effect is impractical to detect over a small number of orbits, it causes long-term differences in when future transits occur, much like the long-term decay observedin pulsars. Measuring this transit-timing delay would thus allow the detection of eitherone or more additional planets in the system or the first measurements of non-zerooblateness (J 2 ) of the central stars.Keywords: planetarysystems–celestial mechanics–gravitation–extrasolarplanets– stellar oblateness 1 INTRODUCTIONThe study of long-term orbital precession was one of thetriumphs of celestial mechanics, when the planetary theo-ries of Laplace and Lagrange showed that essentially all theknown long-term precessions of the planetary orbits couldbe explained by their mutual gravitational interaction. Theperturbation caused by the small planetary masses ‘breaks’the perfect central force character of the Sun’s gravitationalfield, causing the planetary orbital nodes to regress and theirperihelia to slowly advance, with typical periods of 10