# What if Jupiter's rotational period was equal to that of the Earth?

I was amazed when I learned that Jupiter rotates on its axis once in only 9.8 Earth hours. (Yes, you can call me uneducated!) What if the rotation period was 24 Earth hours? What would change in the composition and climate of the planet?

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## 1 answer

I have one major point to make: A good portion of Jupiter does *not* complete one rotation in 9.8 hours.

Jupiter isn't like a giant ball of rock. It's called as "gas giant" for a reason, which is that it has a large, massive, turbulent atmosphere that's constantly moving and changing. This means that its atmosphere undergoes differential rotation, a phenomenon in which gases at different heights move at different speeds. So "9.8 hours" refers to the lower gaseous layers and inner structure.

The major change that would happen if Jupiter had a longer day would be that its equatorial bulge would shrink. This is best explained by the classic ice skater analogy: A rotating object with a greater radius will have a smaller angular velocity, and vice versa. So if Jupiter rotates faster, the bulge will shrink.

I'm not up for doing much math, but we can use some modified equations to give a rough approximation (I won't plug any numbers in; you can do that, if you want). Anyway, we can relate the equatorial radius to the polar radius using the equation $$\frac{a_{e_0}-a_p}{a}=\frac{5 \omega^2 a^3}{4GM} \to a_{e_0} = \frac{5 \omega^2 a^4}{4GM}+a_p\to(\Delta a)_0\equiv a_{e_0}-a_p=\frac{5\omega^2a^4}{4GM}$$ where the variables are given on the Wikipedia page. Having a rotational period of 9.8 hours (35280 seconds) gives us an angular velocity $\omega$ of $0.000178 \text{ radians/second}$. A period of 24 hours gives us an angular velocity of $0.000073 \text{ radians/second}$ - a mere 40.83% of the previous period. That means that the equation is now more like $$a_e = \left( \frac{2}{5} \right)^2 \frac{5 \omega^2_0 a^4}{4GM}+a_p\to(\Delta a)=\frac{4}{25}\frac{5 \omega^2_0 a^4}{4GM}=0.16(\Delta a)_0$$ which is only one sixth of the original distance. The change in rotational period has made the difference between the two radii a lot smaller. Note, though, that this isn't going to be wholly accurate, as I didn't take differential rotation into account.

What would change in the composition and climate of the planet?

The composition wouldn't change. The climate most likely wouldn't, either, but given that there's a lot we don't know about Jupiter's atmosphere, it's tough to tell for sure.

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