We present the results of a Doppler tomographic reconstruction of the UV spectra of the double-lined , O-binary TU Muscae ( catalog HD 100213 ) based on observations made with the International Ultraviolet Explorer ( IUE ) . We used cross-correlation methods to obtain radial velocities , confirm the orbital elements , estimate the UV flux ratio , and determine projected rotational velocities . The individual component spectra are classified as O7 V + O8 V using UV criteria defined by Penny , Gies , & Bagnuolo . We present a model fit of the eclipsing light curve from observations from the HIPPARCOS satellite and published observations of Andersen & Gronbech . We derive an orbital inclination , i = 77 \fdg 7 \pm 1 \fdg 0 . This analysis indicates that both stars are currently experiencing Roche lobe overflow ( RLOF ) , which confirms earlier results that this is one of only a few massive contact binaries . Our derived masses , M _ { p } / M _ { \odot } = 16.8 \pm 0.4 and M _ { s } / M _ { \odot } = 10.5 \pm 0.3 , are significantly lower than those computed from the Doppler shifts of lines in the optical spectrum . We suggest that the difference occurs because mutual irradiation decreases the upper atmospheric temperature gradient in the inwards facing hemispheres of both stars , which makes lower excitation lines appear weaker ther and shifts their center-of-light away from the center-of-mass . We compare the current state of HD 100213 with predicted outcomes of massive close binary evolutionary models , and suggest that the system is currently in a very slow Case AA mass transfer stage .