In this paper, the equations of motion for modeling a spacecraft near an earth-threatening asteroid are proposed and studied for deflecting the asteroid using a gravity tractor that effectively tows the asteroid with mutual gravity attraction. The motion of the spacecraft is expressed by separation distance between the two objects, two Eulerian angles expressing the attitude of the spacecraft–asteroid system, and their derivatives; it is assumed that the spacecraft and asteroid are connected with a variable-length gravity tether. The motion of the spacecraft in an artificial halo orbit (AHO) is investigated using the proposed equations. These equations are suitable for the investigation because the spacecraft in the AHO moves in a circular orbit at a constant angular velocity and distance from the asteroid. The results indicate that the AHO is unstable, and a linear quadratic regulator will be required to control the spacecraft. Numerical simulation results suggest that the AHO–AHO transfer can be realized by employing a control law that linearizes the proposed equations. The achievable deflection distance yielded by 1000 days of a towing mission is calculated for fictional Earth impactors; the results indicate that the proposed system is feasible for conducting long-term simulations.