With recent and archival Rossi X-Ray Timing Explorer ( RXTE ) X-ray measurements of the heavily obscured X-ray pulsar EXO 1722-363 ( IGR J17252-3616 ) , we carried out a pulse timing analysis to determine the orbital solution for the first time . Using a single pulse period derivative , we connected datasets separated by over 2.4 years without pulse number ambiguity ( > 180 , 000 pulses ) , implying continuous spin-up of the pulsar from 2003 August ( and possibly earlier ) until 2006 February ( and possibly later ) . The orbital solution also shows that a torque reversal occurred sometime between 1998 November and 2003 August . The binary system is characterized by a _ { x } \sin { i } = 101 \pm 3 lt-s and P _ { orb } = 9.7403 \pm 0.0004 days ( 90 % confidence ) , with the precision of the orbital period being obtained by connecting datasets separated by more than 7 years ( 272 orbital cycles ) . The orbit is consistent with circular , and e < 0.19 at the 90 % confidence level . The mass function is 11.7 \pm 1.2 M _ { \sun } and confirms that this source is a High Mass X-ray Binary ( HMXB ) system . The orbital period , along with the previously known \sim 414 s pulse period , places this system in the part of the Corbet diagram populated by supergiant wind accretors . Using previous eclipse time measurements by Corbet et al . and our orbital solution , combined with the assumption that the primary underfills its Roche lobe , we find i > 61 \arcdeg at the 99 % confidence level , the radius of the primary is between 21 R _ { \sun } and 37 R _ { \sun } , and its mass is less than about 22 M _ { \sun } . The acceptable range of radius and mass shows that the primary is probably a supergiant of spectral type B0I–B5I . Photometric measurements of its likely counterpart are consistent with the spectral type and luminosity if the distance to the system is between 5.3 kpc and 8.7 kpc . Spectral analysis of the pulsar as a function of orbital phase reveals an evolution of the hydrogen column density suggestive of dense filaments of gas in the downstream wake of the pulsar , with higher levels of absorption seen at orbital phases 0.5–1.0 , as well as a variable Fe K \alpha line .