A planet with changing gravity?

On earth gravity stays constant (besides negligible fluctuations), but it may be possible to change that. What kind of geology, natural satellite, or other anomaly could cause periodic changes in gravity? (And what magnitude of difference would they have). The ideal goal is to map the change to a kind of sine wave, so that the bounds of the changes stay constant. The periodicity of the planet's gravity can range from days to years.

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A planet with changing gravity?

A planet with changing gravity

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