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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?

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George Robinson
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    the depicted spacetug would not be able to apply that force vector, though. the thrusters would need to be much more beefy, and farther out than the most extreme points of contact on the pushplate. – bukwyrm Jul 17 '19 at 18:39
  • In this scenario friction causes the asteroid to roll and rotate. – John Alexiou Jul 17 '19 at 21:00
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    The diagram is incorrect, as the force needed to make the center of mass curve has to be directed towards the center of curvature. In this scenario the spacecraft needes to switch from the outside of the path to the inside to make it change directions. – John Alexiou Jul 17 '19 at 21:03
  • @ja72: Do you claim, that e.g. the force F2 pointing at the CoM has a force component at point P2, which is tangential to the surface of the asteroid and causes it to rotate about its CoM, through the tangential friction between the pushplate and the asteroid? – George Robinson Jul 26 '19 at 16:11
  • @ja72: Regarding your second objection: Please comment about it regarding this question: https://physics.stackexchange.com/questions/491409/u-turn-in-deep-space – George Robinson Jul 26 '19 at 16:13
  • @GeorgeRobinson - for an object to follow a curved path, it needs some transverse acceleration. It doesn't matter if that comes from thrust or friction, as long as there is a component of force perpendicular to the direction of motion. – John Alexiou Jul 26 '19 at 16:34
  • @ja72: Let's discuss the conditions needed to achieve a curved path in that other question. This question is concerned primarily whether asteroid's rotation about its CoM can occur when the force vector, acting on it, lies on a line passing through the CoM. Your 1st objection (about tangential friction) is related to that issue - the 2nd objection is not. – George Robinson Jul 26 '19 at 23:45
  • @ja73: If the assumption, that the acceleration of the asteroid along the gray dashed path is zero, was true as in that other question - I would agree with you that the illustration needs to be corrected to show components of the force pointing towards the center of that path's curvature. ...but since there is no such assumption, I will leave the illustration in this question, as it is. – George Robinson Jul 27 '19 at 06:46

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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).

Whit3rd
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  • The spirit of the question is how not to cause a spin by pushing it around. I wrote that the asteroid has uniform density so there should be no tidal forces. Also, in deep space, solar wind should not be an issue. – George Robinson Jul 13 '19 at 21:12