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The Bat Cave EAR

Evie is an aeorspace engineer and will blog about current events in various fields including but not limited to: Space, Astronomy, Genetics, Biology, Green Energy, Neuroscience, Physics, Quantum Physics, Evolution, Environmental issues, Engineering.. Pretty much anything and everything that catches her eye. Stay tuned! Thoughts, comments, requests – always welcomed!

My posts are presented as opinion and commentary and do not represent the views of LabSpaces Productions, LLC, my employer, or my educational institution.

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Awesome Stuff
Monday, November 8, 2010

Physics is cool.

It turns out that in the big bad dark vastness of the ever expanding, contracting, and moving universe, you can find certain spots that are always at rest.

Well I mean that’s all relative. They’re at rest relative to more massive bodies orbiting in their vicinity.

Say you’ve got your Sun and you’ve got your Earth, and you’re a much much smaller object, like a satellite, or space telescope. Well as it turns out, there are 5 points in space, not too far from both those bodies, which if placed at, you would appear to be holding your position steady with respect to both those large bodies.

This means, that even though you’re in motion, the Sun is in motion, the Earth is in motion, and the rest of the galaxy is hurling toward the unknown, you will still be in very good company. Your Earth and your Sun will literally always be there. In the same exact (relative) spots.

I think that is pretty damn cool.

What you're seeing here is an animated sketch of the relative motion of the bodies in question. The big yellow ball in the middle is the Sun, the blue small one is the Earth, and the labeled green points are the 'parking spots'. This pic is from Wikipedia, see original here.

If you want to see the actual mathematic derivation of this, you can click here for a great .pdf with good follow along explanations. But it is heavy on the math.

The guy who discovered these 5 points was Joseph Louis Lagrange, hence why they’re called the Lagrange points. He made the discovery in the late 1700’s along with his mathematician buddy Leonhard Euler. Or at least, that’s how the story goes. I wasn’t there, can’t say for sure.

Anyway, apparently as long as the mass of the 2 bodies in question is much much larger than you, and the orbit one makes around the other is circular, then the gravitational forces and orbital motion balance exactly, creating 5 spots with relative stagnation.

This picture is of the Sun-Earth system, and the Lagrange points are labeled L1 through L5.

The awesomeness of Lagrange doesn’t end with these points. He also came up with this totally cool plot that shows the distribution of gravitational potential energy.

Gravitational potential energy just means the energy an object has simply due to its position in a gravitational field. So on Earth that’s like the idea that you have more potential energy when you climb up on a chair (that energy can be released when you jump down) as oppose to you being on the floor, and having no gravitational potential energy at all (‘cause gravity has already pulled you down as far as you can go.) I might not be explaining that well. Click here for a better version.


So the plot, it’s of contours representing gravitational potential energy.

Every contour in the picture shows equipotential areas for an Earth-Moon like system. The points where the counters meet, are L1, L2 and L3, while L4 and L5 seem to have their own separate contours going.

L1, L2 and L3 are points of unstable equilibrium. That’s kind of like having a ball sit on top of a dome. It’s fine so long as nothing disturbs it. But, the smallest force from any direction will send it rolling down the side. This means that if any satellite were to be placed at one of these spots, it would need to have propulsion capabilities to adjust itself, if it were to fall out of that stable point.

Still, being in a ‘permanent parking spot’ in space is very desirable, and we humans have sent up quite a few space instruments to park in these spots. For a list of all the known stuff we’ve sent to the various Lagrange points click here. We’ve sent a lot, to all kinds of planets and moons in the solar system.

L4 and L5 are points of stable equilibrium, that’s like setting a ball at the bottom of a bowl. It’s not going anywhere. L4 and L5 are larger than the other 3 points, and if an object were to be thrown out of the center point, it would simply orbit around L4, L5 but would not drift off. That means that if an object accidently enters that zone, it’s not leaving, and it turns out there is quite a bit of the space equivalent of drift wood floating around those points.

Each of the Lagrange points has its advantages and disadvantages.

In the Sun-Earth system for instance, L1 lies always between the Sun and Earth, and hence is a great location to study the sun and solar wind.

L2 lies always behind Earth, and therefore is always in Earth’s shadow. Not only can it see the universe around us without being blinded by the sun, but also it can have sensitive instruments that don’t have to worry about heat and radiation from the Sun and the Earth.

L3 is actually one of my favorites. You see, it always lies directly behind the sun relative to us. So from where we’re at right now, we can NEVER see what’s over there. It is the ultimate hiding spot, don’t you think?

L4 and L5 are like the most perfect built in nooks for space colonies, refueling stations, you name it! It’s perfect for a relatively stationary hotel, maybe throw in a casino, some space hot tubs, fine dining, I mean come on, the ultimate vaca spot, no doubt.

I find these stationary areas to be brilliant. I’m really hoping that sooner rather than later, we can make use of L4 and L5 on the Earth-Moon system, and have an actual spaceship refueling outpost there, along with a ‘space junk’ holding area.

As I said in a previous post, space junk is a very real and growing problem that we have to deal with. And since we’ve already spent so much time, money, and effort launching what now is considered junk, into space, why not gather it all up, haul it over to L4 or L5 and gently land it on the Moon for some reuse and recycling. That junk is a valuable resource, and we really should treat it as such.


For more check out the ESA website, they have cool flash animations showing each of the points and how the bodies in question move (or don’t move) relative to each other.

Here is the NASA version

Great site with great info Lagrange Points of the Earth-Moon System


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I don't get L3. Wouldn't you just have both the earth and moon pulling you toward them?

Dr Becca, Ph.D.
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Everything I know about the Universe I learned from Monty Python.

Dr Becca, Ph.D.
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Oh...a little NSFW!!

Kelly Oakes
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I've always wondered, don't the other planets affect the Lagrange points? I guess the pull from them must just be sufficiently smaller than Earth's... hmmm.


"It is the ultimate hiding spot, don’t you think?"

I can see a science fiction novel coming out of this...

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@Namnezia – Well the same can be said for L2, and more so because of the proximity. It is a bit counter intuitive, but it turns out a lot of stuff is. When you get into compressible fluid dynamics in supersonic flow, or even the idea of time being relative, you find things you wouldn’t expect. I can’t explain why it is like that, it just seems to be the way nature behaves.

@Becca – Hahah.. that is a great source of info, I love it!

@kelly – Yea, the other planets do affect it but like you said, it is insignificant. It seems that the gravitational forces decrease with the square of the distance, so the magnitude of the effects die off over space pretty quickly.

About the sci fi thing.. well I am writing one for NaNoWriMo.. hmm.. see how that develops!


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Evie said:

When you get into compressible fluid dynamics in supersonic flow, or even the idea of time being relative, you find things you wouldn’t expect. I can’t explain why it is like that, it just seems to be the way nature behaves.

Weren't these discovered in the 1700's way before the theory of relativity?




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Yea, I was just using those as examples of things that to me are counter intuitive.

Lagrange used Newtonian mechanics, to develop his own Lagrangian Mechanics, and used that to approximate how a system of 2 bodies with significant mass and one of negligible mass would interact gravitationally. That’s when he found the theoretical presence of those 5 points. This was in 1772. Much later in 1906, right around the time special relativity was published, and a decade before general relativity,  large groups of asteroids were found orbiting the L4 and L5 zones in the Sun-Jupiter system. That was the first evidence that the points existed.

Mike VH

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Just wanted to say "Great article!" even though nobody's been here for quite awhile. Got here by googling lagrange points upon reading of the deactivation of the Herschel space telescope. Interesting that the final action was to kick it out of L2 to make room for other satellites.

You suggested that Lagrange points gather "cosmic driftwood" and I was wondering how thick it was. Dense enough so that things at that point are likely to bump into each other?

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