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A smaller celestial body like a moon or an asteroid can be in a horseshoe orbit around a planet.

Since it might go inside the tidal lock radius (but does not stay inside it all the time), during the approach, the possibility it may be tidally locked exists, but the orbit would soon take it outside that radius.

Would this horseshoe orbiting body be tidally locked to the planet?

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Geometry says no. Since the orbital (DISREGARD - direction reverses) (INSERT - period changes) in a horseshoe orbit, the rotation of the body around its axis would have to change as well, and this is not going to happen over the course of a single orbit. Tidal locking takes a long time.

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  • $\begingroup$ Do the absolute orbital direction in relation to the third body (the sun) changes, or just the relative direction related to the main planet? I thought it changed just the speed (a slow phase when it is approached by the planet and accelerated, and a faster phase when it goes around and approaches the planet from behind). $\endgroup$ – Mindwin Jun 1 '16 at 14:51
  • $\begingroup$ Doesn't matter, although your objection is correct and I've edited. (I got carried away in the original.) Any change in orbital velocity changes orbital period, and this will break tidal lock unless the rotational period of the orbiting body also changes - and that's hard to do with tidal forces. $\endgroup$ – WhatRoughBeast Jun 1 '16 at 15:33
  • $\begingroup$ Great. Full disclosure, this question stems from another in worldbuiding. I had a doubt if horsehoe-orbit bodies could be tidally locked to the other. Janus and Epimetheus have a horseshoe orbit to one another, but are tidally locked to Saturn (they don't have a horseshoe orbit relative to Saturn). $\endgroup$ – Mindwin Jun 1 '16 at 16:09

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