“Galileo got it wrong. The Earth does not revolve around the Sun. It revolves around you and has been doing so for decades. At least, this is the model you are using.” –Srikumar Rao
It’s the end of the week, so that means its time to take on another one of your questions from the question/suggestion box, and continue our ongoing Ask Ethan series! Even though there’s a backlog of hundreds of questions, you should keep sending the new ones in, as all questions are fair game for any segment. This week’s question comes from reader Brian Mucha, who asks us:
Where did the sun and planets get their angular momentum resulting in their rotation. I am not asking about the orbits but the actual rotation. I understand the ice skater analogy where bringing in the extended arms increase the skaters rotation due to the conservation of angular momentum. But the skater starts with spin. IF the skater is standing still they can extend and retract their arms all day and they wont spin.
So when the planets and the sun started to form how was their initial angular momentum achieved?
Ahh, the old question of rotation, and why everything does it.
It’s easy to make something spin faster once it’s already going: you just change its moment of inertia.
What does that term mean, moment of inertia?
You know Newton’s second law: the one that tells you force is equal to mass times acceleration (F = ma). Technically, it’s a little more accurate to say that force is how another quantity — momentum — changes over time. It means if you apply any external force to a mass, its momentum — or how it’s currently moving — will change, and it tells you exactly by what amount it will change. And if you don’t apply an external force to something, its momentum cannot change.
And if everything in the entire Universe only consisted of point masses along the same line, we’d never need anything else. But in the real Universe, masses-in-motion are distributed in more than one dimension.
And whenever you have that, your system has not just momentum, but also angular momentum. And while momentum changes are dependent on mass, angular momentum changes are dependent on a combination of the mass and how that mass is distributed. That combination of factors — mass and how it’s distributed — is what makes up moment of inertia. So yes, Newton’s second law relates how objects change their momentum (i.e., how masses experience changes in their velocities), and there’s an equivalent law that relates how objects change their angular momentum, or how moments of inertia experience changes in their rate of rotation.
How the figure skater who pulls her arms and legs in spins faster is one example of this: as her mass becomes distributed closer to the axis-of-rotation (and her moment of inertia gets smaller), her rotation rate increases to compensate. If your mass-and-how-it’s-distributed changes (goes up or down), your rate of rotation will also change (go down or up) to compensate. But just like Newton’s second law tells you that you can change a system’s momentum by applying an outside force, you can change a system’s angular momentum by applying an outside torque.
And a torque is just a force applied in such a way that it causes an object’s rotation to change.
Now here’s where it gets interesting: every star system in the Universe once began as a cloud of gas-and-dust. These clouds may have been thousands or millions (or in some rare cases, maybe even larger) of times the mass of our Sun, but they were once incredibly diffuse, and spread out across many hundreds or thousands of light years. If these gas clouds had (or the ones we see today have) any sort of global rotation to them, it’s far too small to be detectable, as it would take billions of years for such a gas cloud to make even one complete rotation.
But gas clouds — like all objects in the Universe — don’t exist in isolation. They exist in the presence of all the other matter-and-energy in the Universe, all of which is subject to the laws of gravitation. And whenever any two masses in the Universe are in relative motion to one another, so long as they’re not moving exactly and directly towards-or-away-from one another, the gravitational force they exert on each other causes a torque.
This phenomenon is known as a tidal torque, and was first theoretically understood by Jim Peebles — my Ph.D. advisor’s Ph.D. advisor (or my grand-advisor) — back in 1976. (So, you asked the right person!) It’s why pretty much every mass that exists in this Universe, whether it was born with non-zero angular momentum or not, has one now, 13.8 billion years onward. That includes every gas cloud, including the one that gave rise to our Solar System. We can break these large gas clouds up further, into the regions that give rise to the individual stars and star systems that came into existence.
Each one of these regions that eventually result in a star/star system, with whatever angular momentum they have inside, are typically distributed in shapes known as triaxial ellipsoids. A triaxial ellipsoid is a fancy way to say that they’re like spheres, except inevitably if you draw three perpendicular axes on them (X, Y, and Z, for example), one of the axes will inevitably be the shortest of the three. When a region gravitationally collapses, it’s going to collapse along the shortest axis the fastest, and because normal matter — the stuff all stars and planets is made out of — interacts (i.e., collides) with itself, that means it’s going to go “splat,” like a pancake. (In fact, the scientific word for this process is known as pancaking.)
But along the other two axes, you’ll have a disk-like distribution, which is going to have an overall, net rotation in the direction of whatever its angular momentum is! It’s the reason why — in our Solar System — all the planets revolve around the Sun in the same direction (counterclockwise, looking downwards from north of the Sun’s north pole), the Sun rotates in that same direction, almost all the moons revolve around their planet in that same direction (with notable exceptions explained here), and finally, why practically all the planets rotate about their axes in that same direction, too.
There are only two major exceptions to the rule: Venus, which hardly rotates at all (but does so in the opposite direction), and Uranus, which rotates practically on its side. Both of these worlds are thought to have had their angular momentum significantly changed by the intervention of an outside body, most likely a significant collision a long time ago. That is to say, their rotation was changed by the influence of an external torque!
So that’s the story of why planets, moons, stars and star systems revolve and rotate the way they do! Thanks for a good question, Brian, and to anyone else who has a question or suggestion for me, drop me a line!