Where Do Rings Come From? (The Roche Limit)

thanks to brilliant for helping support this episode hey crazies everybody loves Saturn am I right just look at this thing it's Majestic but it's not actually the only planet with rings Jupiter Uranus and Neptune have them too they're just harder to see where do these planetary rings come from how long will they last and why doesn't Earth have rings because frankly that would be Wicked awesome [Music] as with most stories it seems natural to start this at the beginning no no we talked about this

it's way too far back I mean the beginning of planetary Rings OMG I suppose this is what I get for not being specific enough let's go back to when planetary Rings were first discovered to the timeline the first observations of rings came in 1610 when Galileo pointed his telescope at Saturn as you can see from his sketch he didn't know they were Rings Galileo thought they were giant moons but like a good scientist he kept observing by 1612 his giant moons had completely disappeared from view thi

s wasn't too suspicious though those moons could have easily moved behind Saturn in reality he was looking at the Ring's Edge on but he didn't know that thankfully he got a better look a few years later in 1616 he drew another sketch that makes Saturn look like it has handles or ears we wouldn't actually figure out they were Rings until Christian Hawkins looked at Saturn in 1655. the faint rings of the other three gas giants are much more recent discoveries 1977-79 and 84 respectively Jupiter's

rings are so faint we didn't discover them until the Voyager space probe flew by does that mean only gas giants have rings oh no we've actually found dwarf planets with rings really yep there's no reason a rocky planet like Earth couldn't have rings huh in fact in the next 30 to 50 million years we expect Mars's Moon Phobos to become ranks so rings come from moons yes and comets and asteroids sometimes there's a whole list of ways rings can form ring stability depends more on where they form bac

k to the timeline we've been trying to figure out planetary Rings since we first discovered them but progress wouldn't be made until 1848 when eduar Roche published what we now call the Roche limit it's a critical distance from a planet inside which other objects break apart and form Rings Earth's Moon became a Moon instead of rings because it Formed outside that limit billions of years ago a mars-sized object collided with Earth launching Earth material out into space this material was still gr

avitationally bound to Earth but more so to itself which allowed it to coalesce into the moon if that material hadn't been launched as far it would have formed Rings instead and we can predict where that limit is sure approximately let's consider a real life example I mentioned earlier Mars's Moon Phobos was going to turn into rings soonish if this is Phobos then Mars should be right about here Phobos is Tiny by comparison so I'm going to exaggerate sizes for clarity which is something I've neve

r ever done before anyway with the size of Phobos exaggerated we can see the source of its inevitable demise according to Newton's Laws gravity depends on distance we see here that some of phobos's mass is closer to Mars and some of it is farther away that means gravity is not uniformly distributed across Phobos it's stronger in some places and weaker in others the total amount of force doesn't actually matter though only the tidal forces matter that's how different each arrow is from the arrow

at the center we're using the center gravity as a reference for all the others so while all the gravities point toward Mars not all the tidal forces do it makes sense now why Phobos is going to break apart so then why don't all moons break apart because tidal forces aren't the only forces involved it can be a bit overwhelming to look at all these forces at the same time so consider a single tiny Rock sitting on the surface of Phobos let's say on the side facing Mars This Rock has a tidal force o

n it pulling up toward Mars but that's not the only force acting on the Rock if this was the only Force The Rock would lift off the surface and drift toward Mars we know that's not happening so there must be some other force overpowering it like maybe the Gravity from Phobos itself that moon has mass so it has self-gravity that's the gravity between its parts it's what Phobos and any other large object uses to hold itself together for our single rock that looks like this it has a tidal Force up

a gravity down and a push up from the ground to keep things balanced at the moment that downward gravity is bigger than the tidal Force so the rock stays put but that won't always be the case the orbit of Phobos is gradually decaying as it gets closer to Mars the tidal force will increase while its self-gravity stays the same eventually it's gonna it close enough that the tidal Force overpowers gravity that rock is going to lift off the surface and since that rock is just a placeholder for all t

he rocks that make up Phobos the entire moon will come apart the distance at which that occurs is called the Roche limit and it looks something like this it only depends on the mass of the planet the mass of the Moon and the size of the moon technically though this version is called the rigid Roche limit because it assumes the Moon is perfectly rigid unfortunately assuming the Moon is perfectly rigid is a bit of a stretch pun intended so Roche himself went a little further he assumed a moon dest

ined to become Rings would stretch out a bit before actually breaking this only changes the coefficient out front giving us the fluid Roche limit if deformation is allowed the roast limit is actually larger wait wait the moon breaks up sooner if it isn't rigid yeah it blew my mind too when I first learned it as it turns out the deformation increases the tidal forces thereby causing more deformation which increases the tidal forces even more it's a positive feedback loop of course both the rigid

and fluid models make one giant assumption that a moon is just a clump of tiny rocks held together by gravity which might seem kind of silly when you first think about it but it's actually a decent approximation most of the time particularly with some of the more massive moons and asteroids you really only need to account for molecular forces in a couple situations artificial satellites in the ISS are well within their own Roche limits yet they survive because they're too small for Gravity to be

what holds them together also some materials like ice are kind of sticky that's why Comet Lovejoy was able to survive back in 2011 even though the comet was inside its own Roche limit with the Sun but most of the time this equation works pretty well a realistic object will break apart somewhere between these two limits for Earth's Moon that's between about one and a half and three Earth radii Which is less than five percent the total distance to the Moon that means the Moon is quite safe and if

it hadn't been launched that far it would have formed Rings instead of a moon but those Rings would have been long gone by now why well planetary rings are temporary the orbits are unstable so those tiny bits of rock and Ice gradually fall into the planet data from the Cassini Mission show Saturn's rings are only about 10 to 100 million years old and our current estimates predict they'll only be around for another 100 million years or so plus Saturn has a couple larger moons inside the ring sys

tem keeping the Rings in line so they're especially long lasting Earth's Rings would have collapsed into Earth long before life even evolved here no human would have ever seen views like this for Earth to have rings now we would need a more recent cataclysmic event but you really want a Majora's Mask situation on your hands I certainly don't creepy AF anyway planetary rings are the result of a larger object getting too close to a planet outside the Roche limit we get moons inside the Roche limit

we get ranks because tidal forces can be and until next time remember it's okay to be a little crazy if you want to learn more about tidal forces brilliant.org can help their gravitational Physics course starts by introducing Newton's law of gravity and then later applying that law to real world situations like ocean tides for example you're not just memorizing formulas and equations though brilliant is designed to build your intuition the idea is that when you see a problem you'll have the too

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lick the link in the description below the first 200 of you will get 20 off Brilliance annual premium subscription it'll also let brilliant know you heard about them from me which helps out the channel there were a lot of people appreciating our talk on Quantum field Theory and wanting more no worries there will be more I'm finally learning qft myself so you'll get a video every time I know enough to make one there's a lot to learn though anyway thanks for watching