Mostly, I’m interested in L4 and L5, but the more I try to explain it to myself the more I realize I have no idea how any of them work except maybe L1- just an equilibrium of the two forces?
In: 5
Alright. Let me take a shot (and if I’m saying something wrong, somebody correct me). I’m gonna focus on L4 and L5.
You know how gravity works, right? When you’re sitting high up there in space, you’ve got plenty of gravitational potential energy. But then you start to drift towards a high-mass object, like the Sun. You *start to gain speed* towards that high-mass object.
A Lagrange orbit works ’cause the same thing happens at the L4 and L5 Lagrange points. Specifically, it works because of the way gravity interacts between objects when they’re moving.
So say that there’s an object at L4 or L5 of the Sun-Earth orbit. Why isn’t it crashing towards the Sun or towards the Earth? Well, it’s not crashing towards Earth because like the Earth, it’s got some speed to it. It has to have speed in order to be orbiting the Sun at all. Also, at the L4 and L5 point, it’s equally far apart from the Sun or the Earth. Point is, all the forces balance out there and it can stay where it is, orbiting the Sun, just, in the same orbit as the Earth. It’s like any other orbit in that way.
Now. Why are L4 and L5 *stable?*
Okay, let’s say that suddenly, for whatever reason, our object at L4 or L5 starts to drift sunward.
Well, when it drifts sunward, it starts to *gain speed*, right? Because it’s getting closer to the sun, and that’s how gravity works.
Here’s the problem: it already had a lot of speed to start with. When it starts to drift sunward from the L4 or L5 point, it’s on the inside of the Earth’s orbit. That speed that it just gained, causes it to go *too* fast, deflecting outward, breaking out of the circle of the Earth’s orbit for a different reason, but with a similar result, to a gravitational slingshot.
By ending up on the outside of Earth’s orbit, now it’s *even farther* from the Sun than it started as… and in order to “climb” that gravitational gradient, it had to expend gravitational energy, just like a ball slowing down when it’s thrown upwards. So it slows down.
But the Earth? The *Earth didn’t slow down* in *its* orbit. The Earth starts to catch up. And as the Earth catches up, it starts to pull the object back toward itself.
But here’s the key: because of the angles of the circle, the Earth pulls the object *back over the line, to the inside of the circle*. As the Earth catches up, it pulls the object back not just towards the Earth, but *also towards the Sun too*. And as that object starts to go back over the line, it gains gravitational energy again, speeding up again; and the angle that it’s speeding up at *causes it to leave the circle again*.
And then the cycle repeats. In other words, the object starts orbiting around the Lagrange point.
Now, the whole orbit around the Lagrange point thing has to meet a lot of conditions in order to work. It works *because* the object has enough speed to be orbiting the Sun. The two objects, such as the Sun and the Earth, can’t be too equal in their masses; if the Earth’s gravitational pull were too strong relative to the Sun’s, it’d just attract the object instead of creating a Lagrange point orbit. The object has to be near a Lagrange point; it can’t be too far advanced along Earth’s orbit, or Earth wouldn’t be able to affect it enough, and it can’t be so close to the Earth, that Earth pulls the object all the way down into an orbit around itself. It has to hit that sweet spot.
But as long as all of those conditions are met, the forces all balance and the object stays in a stable orbit around the L4 or L5 Lagrange point: speeding up when it moves in, moving out because of the speed almost like a gravitational slingshot, slowing down as it moves out, and then getting pulled back in as the Earth creeps up behind it.
That’s my understanding anyway.
Latest Answers