We present a phase-resolved spectroscopic study of the secondary star in the cataclysmic variable U Gem. We use our data to measure the radial velocity semi-amplitude, systemic velocity and rotational velocity of the secondary star. Combining this with literature data allows us to determine masses and radii for both the secondary star and white dwarf which are independent of any assumptions about their structure. We use these to compare their properties with those of field stars and find that both components follow field mass-radius relationships. The secondary star has the mass, radius, luminosity and photometric temperature of an M2 star, but a spectroscopic temperature of M4. The latter may well be due to a high metallicity. There is a troubling inconsistency between the radius of the white dwarf inferred from its gravitational redshift and inclination and that inferred from its temperature, flux, and astrometric distance. We find that there are two fundamental limits to the accuracy of the parameters we can derive. First the radial velocity curve of the secondary star deviates from a sinusoid, in part because of its asphericity (which can be modelled) and in part because the line flux is not evenly distributed over its surface. Second we cannot be certain which spectral type is the best match for the lines of the secondary star, and the derived rotational velocity is a function of the spectral type of the template star used.
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