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Consider the case of a tidally locked planet: its axis of rotation must be perpendicular to the plane of its revolution around the parent star. Therefore, no precession.

It is possible for a planets to have a precession period that is the exact same time period as the planet's solar year, such that the planet rotates however its seasons never change? One pole would be in perpetual sunlight (starlight) and the other in perpetual darkness.

I am aware of the physical mechanism which causes stable tidally-locked planets, however could there be a physical mechanism which would cause a stable precession-year ratio of 1:1?

I am interested in the subject for the dual purpose of better understanding precession, and additionally as a plot ploy in a short story that I am authoring. Therefore answers which tend towards either or both of those goals are most appreciated.

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A tidally locked planet does not require the axis of rotation to be perpendicular to the plane of revolution. It only requires the length of a day to be equal to the length of a year. The most notable example proving this point is the Moon. Its axis of rotation is not perpendicular to the plane of its orbit, which gives latitudinal lunar librations –  Jim Apr 8 at 13:39
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See youtube.com/… (33 minutes +). You might find the rest of the video interesting too. –  Kvothe Apr 8 at 13:39
    
@Kvothe are you implying that the moon is not tidally locked? –  Jim Apr 8 at 13:41
    
I'm not implying anything about the moon. That video is about a tidally locked planet, not a moon. –  Kvothe Apr 8 at 13:51
    
@Kvothe: Thank you, that is a wonderful video. I haven't seen the whole thing yet, but I will. However, interesting as it is, the video does not address the question of a stable 1:1 precession:year ratio. –  dotancohen Apr 8 at 18:35
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