Random Rambling: Astronomy
We have... let's say an eclectic mix of interests, and we feel our patrons do too. With that thought in mind, we present a feature we call "Random Rambling." It isn't quite random, but it's close: we made a little spinner with some of our favorite subjects. Every Friday, we give the thing a spin, and then you, lucky people that you are, get to learn a fact related to the subject the spinner landed on.
This week's topic is:
Astronomy!
So let's talk about tidal mechanics.
"...But, astronomy," you say, and don't worry, that's what we're focused on. Specifically, how the tidal forces experienced by a planetary body are impacted by multi-satellite systems. But that can sound scary, especially when we whip out the equation that governs that interaction:
Looks scary, yeah? In English, that translates to: Tidal forces vary directly with the size of the two planetary bodies. As each of them grows more massive, so do the tides. If one gets twice as big and the other twice as small, the changes would cancel out. In addition, they very inversely to the square of the distance between the two bodies. If they're moved so that they're twice as far apart as normal, the tidal force gets four times weaker. That gets modified slightly if the body experiencing the tidal force isn't perfectly round, which is why we have a cube in the bottom and an extra 'r' on the side; for a perfect sphere, they'd cancel out and just leave an r² on the bottom.
If you want to calculate the effect multiple satellites would have on the same world's tides, you would run that calculation above for each satellite. You could call the tidal force from each satellite Fx, where the x is the number of the satellite you're looking at. Then, you simply note that forces have a direction. That means that the total tidal force experienced on the planet is going to be a trigonometric function of the satellites involved and their location relative to the planet. When they're all oriented in the same direction, they'll all "pull" the same way, and their tidal forces will combine. When they're on opposite sides, they'll act against each other. In that case, the largest tidal force will become weaker by the exact amount of the smaller tidal force.
You don't have to be a master of math, astronomical or otherwise, to understand what this means on a general level. Generally speaking, the following is true when you're dealing with a planet that has multiple satellites:
- The closest satellite is almost always the one with the strongest tidal effect on the planet.
- Generally speaking, if a satellite is twice as far away, it will have to be four times bigger to cause the same effect.
- Figuring out the exact tidal effect of multiple satellites at once involves vectors and/or trigonometry, but generally, when all the satellites are on the same side of the planet, they more or less pull together; on opposite sides, they pull against each other.
On a planet being pulled by multiple satellites, tidal effects can most easily be seen in the form of tides. Let's say, for a random example, that we've got a world about ten times as massive as Earth. It has three satellites, which combined add up to the same mass as the moon. The closest and most significant satellite is about 2.5 times closer than the moon is to the Earth. Now, we could find the exact numbers involved and calculate the total tidal effect that way, but we can also use these references in the equation above to get rid of most of the math:
That says "The tidal force Earth experiences is a function of its mass, the moon's mass, and the moon's distance."
That says "The maximum tidal force our planet experiences looks like the same equation, but with 10 times Earth's mass and 2.5 times less distance." Or, in other words,
"Our hypothetical planet's strongest tides are 1.6 times stronger than Earth's."
For the record, this is the secret to doing math in astronomy in general. The numbers involved get stupidly large extremely fast, so we tend to plug in values we can understand and solve the equations that way instead. For example, when we discuss the mass necessary to create a black hole, we don't say "16,000,000,000,000,000,000,000,000,000,000 kg." We say "8 solar masses."
Anyway: Tidal forces work both ways. With satellites, however, we don't typically worry about tides (with the fascinating exception of Europa). Instead, we worry about something called the Roche Limit. You see, massive objects like planets and moons are held together by gravity, which is the weakest of the fundamental forces. The only reason why planets don't fly apart is that there's so darn much of it when planets are involved that the overall force of gravity counteracts the other forces.
...Usually.
Tidal forces, however, can add up fast as well; after all, they're a gravitational effect themselves. The fastest way to do that is to bring the planetary bodies closer together. After a certain point, the tidal force being exerted by the big planet is stronger than the gravity of the smaller moon. Among other things, that means that if you were standing on the moon when it got that close to the planet, you'd start floating ever so slowly toward the planet, slowly picking up speed as you got closer, until you reached terminal velocity. So would that part of the moon that was closest to the planet, and the planet would start breaking apart into smaller chunks.
Since moons (and you, if you were standing on the moon when this happened) are normally in orbit around the planet when this happens, the "downward motion" would be counteracted by the outward motion of orbiting. "Falling" all the way to the planet could take years, centuries, or even longer. Until then, the parts that got pulled off the moon would form a ring around the planet.
The distance at which a moon gets turned into a ring is called the Roche Limit. More massive planets have larger Roche Limits, and as far as we can tell, once they have a large enough Roche Limit a planet is pretty much guaranteed to have at least a small ring.
That's one of the fun things about astronomy. From the perspective of one world, the other one floating in the sky could either decide how good the surfing is... or it could decide whether you're standing on a planet or floating in a ring. It all depends on how close you are and how big your pile of stuff is, compared to theirs.