# 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?

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.