Would it theoretically be possible for a planet to stay at the same place in an "orbit" of its parent body?

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See title. This is a shower thought that popped into me while slowly waking up. I’m thinking, what if due to e.g. gravitational shenanigans, the pull on a planet is such that a planet stands relatively motionless in a fixed position towards its star?

Is that possible or am I forgetting some astronomy basics?

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It could be stationary at the barycenter of a binary star system, but any perturbation would tend to destabilize it.

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