How do Lagrange Points Work?

Surprisingly simple yet heavily procrastinated by myself, the Lagrange points of planets are some of the busiest places in our solar system! What are they, and why are they so packed with satellites?

In a system like the Sun and Earth, we have both gravitational forces of each body and then also the centrifugal force. In most points in space, these forces would be unbalanced, so if you wanted to keep a spacecraft in orbit you’d need to do some work to maintain that orbit.

However, there exist points in space where the gravitational forces are balanced with the centrifugal force, so you can reduce (but not eliminate entirely) the work needed to maintain position. These are the Lagrange points, and there are 5 points labelled L1 to L5.

Let’s Have a Quick Look into Each Point

Let’s use the example of the Sun and Jupiter, ’cause why not?

L1 is between the Sun and Jupiter, where their gravities both balance perfectly! Interestingly, L1 has a smaller orbit path than Jupiter’s, but and object in L1 has the same orbital period as Jupiter. This is different to, let’s say Venus, where it is zooming around the Sun in comparison, but what’s happening is that L1 is affected by Jupiter’s gravity whereas Venus isn’t too much.

L2 is outside the orbit of Jupiter, where the combined gravity is balanced with the centrifugal force experienced at L2. Jupiter’s gravity will shorten the orbital period, so we have a similar situation to L1 in that the orbital period of L2 is the same as Jupiter’s.

Now we go crazier! L3 is on the opposite side of the Sun to Jupiter! It isn’t normally exactly on the orbital path, because L3 would experience not only the Sun’s gravity but also Jupiter’s. This increase in gravity makes L3 be slightly outside Jupiter’s orbit in order to keep the orbital period the same. Nobody uses L3.

L4 and L5 each form equilateral triangles shared by the celestial bodies and the point.

L1, L2, and L3 aren’t actually all that stable. If you disturbed something orbiting at these points, they will drift away and lose orbit. L4 and L5 are a bit better, and objects tend to stay in some kind of orbit, but this depends on the mass of both celestial bodies.

Lagrange Points are great for Satellites, Artificial or Natural!

Because the work needed to maintain orbit is reduced, the Lagrange points are great points to place satellites. Agencies will often put satellites and spacecraft in L1 and L2 with L3 being unfavourable given it’s distance.

One of the most notable spacecraft in Earth’s L1 point is the LISA Pathfinder, which is used for detecting gravity waves. L2 is occupied by a lot of cool spacecrafts such as WMAP & Planck Space Observatory, and in the future it will be occupied by James Webb and WFIRST (which is definitely short for What the F*** Is This Ridiculous Space Telescope?)

There are also objects in the Earth-Moon Lagrange points (ARTEMIS being one), and many other Sun-Planet or Planet-Moon points too! Most objects occupying these points are natural satellites, which almost exclusively orbit L4 and L5 thanks to their superior stability.

My favourite example are Jupiter’s Trojans! The trojans in the Greek Camp occupy L4, and those in the Trojan Camp are at L5.

And yes, this naming convention was based on the Trojan War. And also yes, all the asteroids are named after participants in the Trojan war, accordingly with which side they’re on.

The only exception to this naming convention is Hektor, the Trojan hero in the Greek camp. He was named before the convention started, but I suppose they could have made Hektor’s camp the Trojan camp. Mistakes were made!

You won’t believe this, but Hektor also has a moon! Orbiting this reddish asteroid is a 12km wide satellites called Skamandrios!

Here’s a cool webpage from JPL showing lots of data about Hektor, including an orbit diagram if you click on “show orbit diagram”. You can clearly see Hektor makes an equilateral triangle with the Sun and Jupiter!

That’s all for today. If you want to learn more about Trojans (the asteroids, of course!), NASA will be launching Lucy later this year, a spacecraft that will be the first to visit the Trojans (and Greeks)!

1. I never thought about the orbital periods for L1 and L2. That’s really weird (in the Kepler’s laws sense of weird).

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• My Hubble Abode says:

It’s really trippy, probably because we tend to think objects orbiting the sun are only controlled by the Sun’s gravity, but here we’ve got a planet to deal with in addition. Even outside the points, you still have to consider nearby planets and moons. Space just gets crazy when you start to incorporate more things!

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2. […] Webb will also be orbiting fairly far away from Earth, within the L2 Sun-Earth Lagrange point (learn more about that here, the Sun-Jupiter one is above). This position blocks the Sun’s heat and light, which keeps […]

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3. Thanks for this helpful article. I have a big interest in Planet 9/X . I imagine the LaGrange points for such a distant world would be located at incredible distances! Would that even be a thing?

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• My Hubble Abode says:

I’m glad you liked this article! Planet 9 or Planet X’s LaGrange points would be extremely distant, but since L4 and L5 lie on the planet’s orbital path they would probably be ideal places to find satellites. However, we would need to think about more than just planet 9 and the Sun’s gravity, for example all the TNOs near the planet. That requires 3+ body mechanics, which is a whole problem in itself!

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