What does "Roche limit" (or "Roche radius") mean?

Question posed by Jennie.

First things first: we need to know a bit about gravity, and then a bit about tidal forces before we start talking about Roche limits:

Gravity is a force. You probably already know that it's the force that stops you flying off into space and keeps your phone on the table. To be a bit more scientific about it, gravity is a force that pulls two particles towards each other: the Earth is pulling you towards it, which is why you don't float off into space, and why you come back when you jump up, but what a lot of people don't realise is that you are also pulling on the Earth.

Gravity is quite a weak force, and it takes a lot of particles all working together to produce a force that's noticeable. That's why you and the Earth being pulled together feels very much like a one way thing: the Earth is so much bigger than you, and is made up of so many more particles, it exerts a much larger gravitational pull than you do.

O.k, that's the first thing about gravity: the more mass you have, the more of a gravitational attraction you get.

The second thing about gravity is that it's stronger the closer you are to whatever it is that's attracting you. For example, if you go and sit on a beach in Cornwall, you're experiencing a stronger gravitational pull from the Earth than your friend who's just climbed up Mount Everest. Your mate who's an aeroplane pilot and currently on their way to Bali is experiencing even less of an attraction, and your great aunt Sally who's visiting uncle Bob on the International Space Station is feeling the pull of Earth still less*.

Tidal forces
Tidal forces are not, strictly speaking, forces. They are effects of gravity. You're probably most familiar with the word 'tidal' from talking about the tides- the raising and lowering of the seas. Tides, you'll be glad to hear, are indeed caused by tidal forces (or effects), but that's not the whole story.

More specifically, tidal forces are to do with the second point made about gravity under the previous heading. Here it is again so you don't have to look back:
The second thing about gravity is that it's stronger the closer you are to whatever it is that's attracting you.
From this, of course, it follows that things that are further away experience a weaker gravitational attraction. We've already spoken about how you and your mountaineer, pilot and astronaut friends all experience different gravitational attractions from the Earth due to being different distances away from it, but we can shrink the problem down to just look at you:

Stand upright. Your ears are now further away from the Earth than your toes are, right? If we think logically about the statement above, then your toes are experiencing a greater pull from the Earth than your ears are (or your ears are experiencing less of an attraction than your toes, if you'd rather think of it that way round). You don't actually feel this because, as I said before, gravity is really weak, and you're quite small compared to Earth. Try to imagine what it would feel like if we could make gravity strong enough: it would feel, to you, a lot like someone was trying to stretch you like a rubber band**.

The Roche limit
Now think about the moon, and imagine you're standing on the side facing the Earth, looking back at us. Also imagine that I'm standing on the exact opposite side of the moon to you, facing away from Earth. Even though we're standing on the moon, the Earth's gravity still reaches out this far (or the moon would have wandered off a long time ago), and so we're both being tugged at by the Earth's gravity. But you're being tugged a little stronger than I am, because I'm further away from the Earth than you are. Again, we don't really notice this for a couple of reasons: we're closer to the moon so its gravitational forces feel stronger; and we're quite far away from the Earth.

But move the moon closer to the Earth, and what would happen? The Earth's gravity is attracting not the moon as a solid object, but every particle that the moon is made of: gravity is trying to stretch the moon in the same way that it tries to stretch you when you're standing on the Earth- the moon is like a giant rubber band. As the moon gets closer to the Earth, the gravitational forces that the moon feels get stronger but, and this is the really important bit, the difference between the forces felt by you and I on opposite sides of the moon get larger.

Eventually, when we move the moon close enough to the Earth, the differences in the forces on each side of the moon gets too large, and it can't take any more. The rubber band snaps. The moon can't stay together as a ball any more, and breaks up.

The distance from a planet at which this would happen to a satellite can be calculated, and depends on the density and radius of the planet and the density of the satellite (moon). This distance is called the Roche limit (or Roche radius).

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Have a question about this topic? Comment below! Got an astronomy related question of your own? Ask it here.

*Contrary to popular belief, this is not the reason why Bob and Sally are 'weightless' in space. They are not, in fact, weightless at all. But that's another post.

** If you have a problem with this concept, try to imagine this: You and yet another mate are holding opposite ends of a rubber band. Your friend starts to run away from you in a straight line, and you start to chase them, but they are running faster. You're both travelling in the same direction, but what happens to the rubber band?


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