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The Sun's rotation period varies from about 25 days at the equator to about 38 days at the poles. As I understand it, this is because the Sun is not solid, and because of the way centripetal force works, the equator must move faster than the poles.

Question: if this works, why do Jupiter/Saturn/Uranus/Neptune have well-defined days? Why don't the equators of these planets rotate faster than the poles as well? For example, Wikipedia's article on Jupiter gives the length of a Jovian day as 9h 55m 30s, which is so precise that it implies Jupiter does not have a rotational period which varies with latitude.

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It's a matter of how "day" is defined.

Wikipedia's article on Jupiter cites this IAU/IAG paper for the length of a Jupiter day. In it, footnote (e) of table I has the following:

The equations for W for Jupiter, Saturn, Uranus and Neptune refer to the rotation of their magnetic fields (System III)

The radio emissions of the gas giants have well-defined periodic variations. These variations are caused by the rotation of the magnetic fields of those planets, and are evidence that they have a reasonably coherent core of some sort that's rotating at a uniform speed. The periodic variations then represent the rotation speed of that object, which is taken as the rotation speed of the planet.

We're reasonably certain the Sun doesn't have a coherent core. Measuring the variation of the magnetic field doesn't show a well-defined period, and doesn't provide a useful definition of the Sun's rotation speed.

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    $\begingroup$ I just add that for Jupiter there is definitively no a fix day based on std rotation. At least no for the outer layer. It does even rotate in stripes and a simulation as in Celestia package is a kind of spectacle. $\endgroup$
    – Alchimista
    Mar 22, 2019 at 8:08
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    $\begingroup$ “The assumption is that whatever's generating the magnetic field forms a reasonably coherent mass that's rotating at a uniform speed.” — I’d strengthen this by pointing out that it’s not just an assumption, it’s based closely on empirical facts: the magnetic field has a measurable uniform periodic behaviour, and based our understanding of planetary magnetic fields, we’re confident this corresponds to rotation of a somewhat coherent core. With the sun, as I understand it, we don’t see any uniformly periodic behaviour that we would expect to correspond to some kind of rotating mass. $\endgroup$ Mar 22, 2019 at 13:37
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    $\begingroup$ The Sun's magnetic field don't have a period as @PeterLeFanuLumsdaine stated. $\endgroup$
    – Mindwin
    Mar 22, 2019 at 14:06

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