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In the absence of detectable pulsations in the eclipsing High Mass X-raybinary 4U 1700-37, the orbital period decay is necessarily determined from theeclipse timing measurements. We have used the earlier reported mid-eclipse timemeasurements of 4U 1700-37 together with the new measurements from long termlight curves obtained with the all sky monitors RXTE-ASM, Swift-BAT andMAXI-GSC, as well as observations with RXTE-PCA, to measure the long termorbital evolution of the binary. The orbital period decay rate of the system isestimated to be ${\dot{P}}/P = -(4.7 \pm 1.9) \times 10^{-7}$ yr$^{-1}$,smaller compared to its previous estimates. We have also used the mid-eclipsetimes and the eclipse duration measurements obtained from 10 years long X-raylight-curve with Swift-BAT to separately put constraints on the eccentricity ofthe binary system and attempted to measure any apsidal motion. For an apsidalmotion rate greater than 5 degrees per year, the eccentricity is found to beless than 0.008, which limits our ability to determine the apsidal motion ratefrom the current data. We discuss the discrepancy of the current limit ofeccentricity with the earlier reported values from radial velocity measurementsof the companion star.

Orbital evolution and search for eccentricity and apsidal motion in the eclipsing HMXB 4U 1700-37