newtonian mechanics - How to prevent an asteroid from spinning while pushing it?

Consider a perfectly spherical asteroid in deep space (away from other celestial bodies). The asteroid has uniform density so its Center of Mass (CoM) coincides with its geometric center. The asteroid is rigid and does not deform when touched or pushed. Initially the asteroid does NOT spin about its CoM in the inertial reference system. The pale green rectangles appearing on the asteroid's surface in the Diagram below visualize the lack of asteroid's spin.

A maneuverable spacetug (space-pusher for European readers) continuously applies a variable force to the surface of the asteroid, e.g. at a points P1, .. P7 (small yellow dots), via a rigid and flat pushplate, which is mounted in front of the spacetug (thick blue line), in order to push the asteroid along an arbitrary path (gray dashed curve). The spacetug continuosly applies the variable force vector (red arrows) along the lines connecting the points P1, .. P7 and the CoM. The acceleration of the asteroid along the gray path is NOT assumed to be zero. The pushplate does not slide on the surface of the asteroid - instead, the pushplate "rolls" on the asteroid's surface from its point of view.

QUESTION: Is keeping the force vector pointed at the CoM, sufficient to prevent the asteroid from spinning about its CoM as it is pushed along an arbitrary path?

Answer

If the hypothetical asteroid is not spinning to begin with, yes, force on the center of mass (for instance, gravity coupling of the 'tug' craft with the asteroid) does not exert any torque, so will not cause any rotation.

If a mechanism can be coupled to the asteroid that can extend a small mass on a string, the asteroid-mass pair can have a large-ish rotational moment, so would become a nearly rotationless object when the string length is long (a kilometer, perhaps?). Then, you can simply release the mass (cut the string) and engage the tug with a nonspinning asteroid.

A realistic force analysis would have to include light pressure, outgassing, ablation, electrical forces (solar wind can carry charges) and a tiny tidal force (depending on some elasticity or nonspherical mass distribution).