Constraining Orbital Parameters Through Planetary Transit Monitoring
  The orbital parameters of extra-solar planets have a significant impact on the probability that the planet will transit the host star. This was recently demonstrated by the transit detection of HD 17156b whose favourable eccentricity and argument of periastron dramatically increased its transit likelihood. We present a study which provides a quantitative analysis of how these two orbital parameters affect the geometric transit probability as a function of period. Further, we apply these results to known radial velocity planets and show that there are unexpectedly high transit probabilities for planets at relatively long periods. For a photometric monitoring campaign which aims to determine if the planet indeed transits, we calculate the expected transiting planet yield and the significance of a potential null result, as well as the subsequent constraints that may be applied to orbital parameters. 
Stephen R. Kane, Kaspar von Braun