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
First we need [our trusty Lagrange point map](https://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Lagrange_points2.svg/1202px-Lagrange_points2.svg.png)
Lagrange points are about having the same angular speed as the body of interest(We’ll stick with Earth here) so that items at that point complete an orbit in the same amount of time and don’t move relative to Earth
An object trying to complete an orbit of the Sun in 365 days inside the orbit of Earth would be moving too slowly and would fall into a lower orbit picking up speed on the way. Trying to complete an orbit in 365 days outside the orbit of Earth results in too much speed which pushes the object into a higher(longer) orbit so it takes more than 365 days
Okay, since we’ve got those two states covered, how do you get an object to orbit closer to the sun in the same time as the Earth? You need to reduce the inward force! Since you can’t shrink the Sun its about finding the point where Earth’s gravity provides the right balance to give the outward tug and keep things stable. This is L1
L2 is further out than the Earth so you need more force so Earth’s gravity gets combined with the Sun’s gravity to make a spot where the extra speed is perfectly compensated by the extra Gravity
L3 is pretty similar to L2 in principle. Its on the exact opposite side of the Sun from Earth so the gravities combine, but since Earth is sooo far away its only a *tiny* bit out past Earth’s orbit
L4 and L5 are the odd balls. They’re actually orbits around the center of gravity(barycenter) of the Earth-Sun system not around the Sun. They’re an equal distance to the Sun and Earth and are actually stable. If something in L4 (behind Earth) shifts closer to Earth then it’ll pick up speed, shift out from the sun a bit, losing speed, then shift further away from Earth so it loses its gravity tug and falls inwards, picking up speed, and then shifting closer to Earth again. L4 and L5 pick up little asteroids called Trojans, Jupiter has a ton of them
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