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Half of the planets in the solar system have an axial tilt of $25.5\pm 3^\circ$: earth (23.5°), mars (25.3°), saturn (26.7°) and neptune (28.3°). If random collisions in the early solar system caused the axial tilt of the planets, it seems like there should be a lot more variation in the planetary tilts. Is there some mechanism that favors tilts around 25°, or is this just a statistical fluke?

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Mars (the planet with an axial tilt closest to that of the Earth) has an axial tilt that varies greatly over time. For instance, 4 million years ago, the mean obliquity was $∼35 ± 10°$. From the same article:

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Earth on the other hand has had its rotational features stabilized due to the effect of our large Moon.

So it is only by chance if the axial tilt of Mars is currently similar to that of Earth.

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