Hey, flat Earthers! You chose the wrong planet!

Recently, planetary astrophotographer extraordinaire Damian Peach got access to the 1-meter ChileScope (in, um, Chile), and has been on a tear posting simply fantastic images of Saturn and Jupiter that he’s been taking with it.

He took this one on February 26, 2017, at 06:46 UTC, and it’s wonderful:

It’s not the Jupiter you usually see, because the famous Great Red Spot (and the somewhat less famous Oval BA) are not visible. They’re on the other side of the planet, making Jupiter look oddly naked. No moons or moon shadows are visible, either. This isn’t an unusual view of the planet —the spot is on the far side half the time, after all!— but it’s just not the shot you usually see posted.

I have to admit, when I saw it, my first thought was, “Oh, that’s nice, but where’s all the fun stuff?!” My brain can be a jerk, sometimes. After all, this is a magnificent photo of Jupiter, and better than professional telescopes could do when I was a kid and first fell in love with astronomy!

But then my brain made up for its jackassery by coming up with a fun thought indeed. Look, it said, you can really see how oblate Jupiter is!

Ah, yes, brain. Well done. You can see it. Oblateness is the term science-types use to describe how flattened a sphere is. In fact, we don’t call such an object a sphere  any more; it becomes a spheroid, the three-dimensional version of an ellipse rotated around one of its two axes. If you spin an ellipse around its long axis you get a prolate spheroid, similar to a football or rugby ball. Spin it around the short axis, and you get an oblate spheroid: a flattened sphere. Sit on a beach ball, and you’ll get the idea.

Jupiter is highly oblate, second only to Saturn in its deviation from sphericity*. To make it easier to see, I took Peach’s image and overlaid a circle on it centered on Jupiter as best I could:

The circle has a diameter equal to Jupiter’s polar diameter (the distance between its north and south poles), and you can see it falls short along the equator. In the image I fiddled with, Jupiter’s polar diameter is 900 pixels, and its equatorial diameter 960 pixels. It’s about 7% wider than it is high! That’s a flattening ratio of about 1:15, which is pretty close to what I see listed for Jupiter online. Not bad considering I did all this freehand.

So, why is Jupiter oblate? Spin! Jupiter’s “day,” the time it takes to spin once, is just under 10 hours, less than half an Earth day. That creates a terrific centrifugal force**. This is the same force that you feel on a merry-go-round or one of those barf-inducing spinning platforms on playgrounds, the force that throws you to the outside. The centrifugal force is directed outwards, and depends on how fast you’re spinning and how far you are from the rotation axis.

For a rotating planet like Jupiter, the centrifugal force is 0 at the poles, because you’re on the spin axis there. It gets stronger with lower latitudes, until you reach a maximum at the equator, because there, you’ve maximized your distance from the spin axis. Because it’s a force outwards, it counteracts the inward pull of gravity.

Well, counteracts it a little. The inward force of Jupiter’s gravity at the cloud tops (the “surface” we see) is about 2.5 times Earth’s; if you weigh 150 pounds on Earth you’d weigh 375 pounds on Jupiter!

But on the equator, that’s mitigated by the centrifugal force, which amounts to about 1/5^th of Earth’s gravity. So, if you could stand on the clouds at Jupiter’s poles, you’d weigh 375 pounds, but at the equator, you’d only weigh 345 pounds! Phew***.

And that’s why Jupiter is oblate, with a pronounced equatorial bulge. If it were just sitting there, it would be a near-perfect sphere. But it spins, fast, so at the equator the centrifugal force flings the material outward a bit, causing it to be wider there.

Incidentally, as I said, Saturn is more oblate than Jupiter, even though it’s smaller and spins a touch more slowly. Why? Because its gravity is lower than Jupiter’s! At the cloud tops, its gravity is only just a bit higher than Earth’s, or half of Jupiter’s. But at Saturn’s equator, the centrifugal force is about 1/6^th Earth’s gravity. That’s less than Jupiter’s outward force, but you wouldn’t be fighting Jupiter’s huge gravity, there. So, the ratio of centrifugal force to gravity is higher on Saturn than Jupiter, making the gorgeously ringed planet more oblate.

Like Jupiter's, you can see Saturn’s oblateness through a telescope, but even though it’s flatter it can be harder to see because the rings throw our perspective off. Once you see it, though, it’s pretty obvious. I’ll note that a planet’s gravity is related to its size and density. Saturn is huge, but it’s very low density; on average lower than water!**** That’s why it’s gravity is so surprisingly lower than Jupiter’s.

I think that’s pretty cool. You can tell a lot about a planet just by measuring a few basic things about it, like how big it is, how fast it spins, and what shape it is.

So, I guess I have to forgive my brain after its initial outburst. The follow through was pretty good.

P.S. Damian Peach is pretty good with NASA’s Jupiter data, too.

* Which is easy to write, but rather difficult to say out loud.

** Which is not a fictional force, but is quite real in a rotating frame, and should not be confused with centripetal acceleration, which is essentially the same thing but in a non-rotating frame.

*** If you could spin up the Earth, you’d weigh less at the equator, too. But as a weight loss plan, I wouldn’t recommend it. Just to start, spinning the Earth faster would mean much stronger hurricanes. Also, the energy it would take to get our planet spinning faster would melt the surface down to the crust. So, there are some issues with it. Also, correction: I did the math wrong initially. At the equator it's 2.5g inward - 0.2g outward, so the force on you would be 2.3 times your mass, or 345 pounds.

**** The standard joke is that if you put Saturn in a bathtub it would float ... but it would leave a ring.