The capabilities of Eddington for the detection and analysis of extrasolar planets are outlined. The primary goal of the PF (Planet finding) part of the mission is the detection of planets that are Earth like - which limits their size to less then 3 Earth radii - and which are potentially habitable - which limits their temperature or their orbital distance and period. Secondary goals will be the detection of larger planets and their analysis. For evaluations, stellar light-curves from Eddington were simulated, and artificial transits were included in a subset. These curves then served as the base for detectability tests, giving us an outline of the stellar-size versus planet-size versus planet-temperature parameter space in which Eddington may perform reliable detections. For stars smaller than about G5V, and brighter than mV = 16, Eddington will detect any transiting planets with minimum sizes of 1 - 2.5 Earth radii. As Eddington will survey several hundredthousands of stars, for transits, a significant number of Earth-like planets would be detected, provided that the fraction of stars with such planets is not a small number. Also, there will be detections of large numbers of giant planets through transits, as well as a complete survey of Hot Giant planets, as these can be detected by reflected light - even if they are not causing transits.