This paper analyses the problem of the autonomous absolute orbit control of a space- craft in low Earth orbit using different on-board feedback control systems. Three types of control are compared. The first implements an analytical control algorithm. The second and third controllers considered are the linear and the quadratic optimum regulator from the classical control theory. For the implementation of the linear regulators the problem has been formulated as a two spacecraft formation keeping in which one of the spacecraft is virtual and not affected by non-gravitational orbit perturbations. The relative Earth-fixed elements have been introduced as a set of parameters which can express the relative mo- tion of two spacecraft in an Earth-fixed reference frame. These relative elements allow the general formalization of the requirements of an absolute orbit control system design and its formulation as a particular case of spacecraft formation flying control problem. A direct mapping between the relative Earth-fixed and orbital elements enables the direct transla- tion of absolute to formation control requirements and the straightforward use of classical control theory techniques for the orbit control of distributed spacecraft systems. The val- idation, performance estimation and comparison of the control algorithms are realized by means of numerical simulations with a high level of realism.