  The Rossiter-McLaughlin (RM) effect is the distortion of stellar spectral
lines that occurs during eclipses or transits, due to stellar rotation. We
assess the future prospects for using the RM effect to measure the alignment of
planetary orbits with the spin axes of their parent stars, and to confirm
exoplanetary transits. We compute the achievable accuracy for the parameters of
interest, in general and for the 5 known cases of transiting exoplanets with
bright host stars. We determine the requirements for detecting the effects of
differential rotation. For transiting planets with small masses or long periods
(as will be detected by forthcoming satellite missions), the velocity anomaly
produced by the RM effect can be much larger than the orbital velocity of the
star. For a terrestrial planet in the habitable zone of a Sun-like star found
by the Kepler mission, it will be difficult to use the RM effect to confirm
transits with current instruments, but it still may be easier than measuring
the spectroscopic orbit.
