– 16 – 4. Mass Measurements and Lensing: White Dwarf or Terrestrial Planet? The primary goal of the Kepler mission is to search for terrestrial planets orbiting sun- like stars, especially in the zone of habitability. We do not yet know how common such planets are. The results described in § 3 establish, however, that orbiting white dwarfs are well represented in the Kepler data. White dwarfs have radii similar to planetary radii and, as Figure 3 shows, many are likely to orbit in their host star’s zone of habitability. It is therefore important to be able to distinguish between planets and white dwarfs. The discoveries of KO-74b and KOI-81b illustrate that it is possible to identify transiting objects that are candidate white dwarfs. Yet, even though both systems are likely to be products of mass transfer, the natures of the hot compact objects and their evolutionary histories are not yet definitely established. Furthermore, not all white dwarfs will be hot and luminous enough to produce distinctive eclipses. While dwarfs cool with age, and “ultracool” white dwarfs with temperatures below 5000 K have been discovered (Vidrih et al. 2007; Harris et al. 2008). The key property that is different for planets and white dwarfs, irrespective of age, is the mass. Mass measurements are therefore of central importance, ideally through radial velocity measurements. Interestingly enough, this may be difficult to do for some white- dwarf blue straggler systems, because high rates of stellar rotation can result from mass transfer and complicate the measurements. On the other hand, high rotational velocities may be a signature that supports the mass transfer scenario. As mentioned in § 2, there are preliminary indications that the rotation rates of KOI-74a and KOI-81a are high (Latham 2010). Even if high rates of rotation are rare, the large numbers of interesting systems discov- ered by Kepler may make it challenging to obtain radial velocity measurements for all of them. It is therefore useful that, because of its sensitive photometry, Kepler is well-suited to make optimal use of light curve deviations to measure mass. Both tidal effects and, for the first time, Doppler boosting have been used to provide mass estimates of KOI-74b and KOI-81b. If a modest number of systems can be studied through both light-curve and radial- velocity techniques, we may be able to rely more heavily on the former. In addition, when the transiting object is a stellar remnant, its high density may allow us to detect its action as a gravitational lens that deflects light from the star it orbits. Measuring the lensing effects can provide an independent estimate of the gravitational mass of the white dwarf. The Einstein radius is R$_{E}$ = 2 . 97 × 10 $^{9}$cm [ M$_{WD}$ M ⊙ a AU ]$^{1}$ 2 (7)