In typical drag-free satellite designs, the largest internal force that perturbs the proof mass from a drag-free trajectory is the mass attraction of the satellite. Spinning the satellite with the spin vector normal to the orbital velocity vector eliminates most of the errors due to a constant body fixed gravitational force from the vehicle. If, however, there is a spatial gradient in the vehicle gravity field at the proof mass, spin does not necessarily eliminate this disturbance. An integral controller is discussed here which substantially attenuates the disturbances not eliminated by the spin. The mechanism by which mass attraction errors are reduced with integral control and the factors influencing its stability are examined. Mechanization errors of the integral controller show that drag-free performance with a disturbing acceleration level of 10 ~1 3 g (or position error of 1 km after one year) is quite feasible. In a nonspinning, nonintegral control drag-free satellite with mass attraction properties the same as that assumed here, drag-free performance of 10 ~1 0 g would result.-cos(tu/,0 C AC C r fbx,fby f ex, fey feh,fev f ex, fey = |/i | = fix,fty -F e = F G = h = I h j v = IhcJvc = k c = k p = m b = r = r d = •6 = Nomenclature (df ex /dx + df ey /dy)/2 (8f ex /dx -df ey /dy)/2 (8f ex /dy + df ey /8x)/2body fixed disturbing specific forces on satellite control specific force on satellite horizontal and vertical components of force on proof mass due to mass attraction magnitude of inertially fixed force on proof mass body fixed components of mass attraction on proof mass magnitude off ix j iy inertially fixed disturbing specific forces on satellite disturbing forces on proof mass force of gravity on proof mass in-track trajectory error integral of f eh and f ev integral of x bi and y bi integral control gain position gain mass of proof mass proof mass position with respect to an inertial reference deadspace radius sm(co h t) w = Xb,yb = position coordinates of proof mass in satellite fixed reference frame Xbt,ybi = proof mass position in an inertial reference frame x e ,y e = mass center location in satellite fixed reference frame x u ,yu = integral control bias coordinates y = velocity/position gain 77 = complex expression for x b +jy b