When a planet is only observed to transit once , direct measurement of its period is impossible .
It is possible , however , to constrain the periods of single transiters , and this is desirable as they are likely to represent the cold and far extremes of the planet population observed by any particular survey .
Improving the accuracy with which the period of single transiters can be constrained is therefore critical to enhance the long-period planet yield of surveys .
Here , we combine Gaia parallaxes with stellar models and broad-band photometry to estimate the stellar densities of K2 planet host stars , then use that stellar density information to model individual planet transits and infer the posterior period distribution .
We show that the densities we infer are reliable by comparing with densities derived through asteroseismology , and apply our method to 27 validation planets of known ( directly measured ) period , treating each transit as if it were the only one , as well as to 12 true single transiters .
When we treat eccentricity as a free parameter , we achieve a fractional period uncertainty over the true single transits of 94 ^ { +87 } _ { -58 } \% , and when we fix e = 0 , we achieve fractional period uncertainty 15 ^ { +30 } _ { -6 } \% , a roughly threefold improvement over typical period uncertainties of previous studies .