SUMMARY: You often hear about the "Lagrange Points", but do you know what they are? These are 5 points in the Earth-Sun system where a third, low mass object (such as a spacecraft) can maintain its position with very little fuel. L1 is a point directly in between the Earth and the Sun, ideal for observing our star - that's where NASA/ESA's SOHO is right now. Another useful point is L2, which lies on the opposite side of the Earth, away from the Sun. L2 is a great place to observe the Universe without having to directly orbit the Earth. Many upcoming space-based observatories will be headed to L2 in the next few years. There are three additional Lagrange Points in the system as well, L3, L4 and L5.

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Exellent review of these important concepts.

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I first heard of these when reading about Gerard O'Neal's notions of cities in space. Those large wheel or cylindar pairs would first be parked in these Lagrange points for a variety of convient reasons described or inferred in this article.

What I never really heard was the effective size of these regions. They obviously aren't tiny, discrete points in space or, again as the article infers, only a single object could be located there. I expect that they are zones in which those positive effects would be noticed (and near-zones where there would be similar benefit, though not quite as effective), but what would be the effect size and shapes of these gravitational-mechanical counter-balanced L-points?

It does sound a little strange, but essentially, just how much usable space is at these places in space?

How many cubic meters is a Lagrange point? Does this question even make any sense?

Do the other planets, like Mercury, Saturn, or Jupiter also have Lagrange points? Would those points be more beneficial to our exploration?

Beyond Satellite importance, Lagrange points represent minimum energy locations for transit between bodies, for example the Earth-Moon system. If one has enough energy to get to the Lagrange point between the Earth and Moon and pass through that point, that is the minimum energy for lunar travel (the figure eight of Apollo trajectories). If one can get to the Lagrange point on the far side of the moon, or the Earth, one can escape the Earth-Moon system with minimal energy. Other points require more energy to escape the Earth-Moon system.

Its been a few years, but as I recall one can reduce the dynamic equations to a single 5th order equation that relate the position and change in position with time of the 0 mass body with the two massive bodies. One constant (the sixth) is trivial as it corresponds to the common plane of the two massive bodies upon which the Lagrange points lie. The roots of that equation correspond to the constants defining the Lagrange points for the 0 mass object.

L4 and L5 for the Jupiter Sun system are where the Trojan asteroids are located, and this was the initial conformation of the theory I believe.

Andy

All the planets have them, but I don't think the L4 or L5 points for Pluto would be too meaningful since the influence of Neptune would often be a much larger influence then Pluto would be.

Concerning volume of the space... you can think of these as maxima and minima in the gravitational potential, and they are big sprawling humps and bowls. Take a look at the top chart here, showing the locations of the asteroids. Pay close attention to the two groups of them ahead and behind Jupiter in its orbit. These are the ones stuck in the Jovian L4 and L5 locations. They are spread out over a space larger than Earth's orbit around the Sun.
Asteroids

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Also curious how big in area the points are. And... do they have to be on the same orbital plane as the Earth in relation to the sun, or could they be 'up or down' in the 3 dimensional sense?

They have to be nearly in the same plane, but can be a little bit up or down, comparable to how far they can be left or right. The JWST will be launched to the L2 point, where like other spacecraft in that general location, it will be in a "Halo Orbit", which keeps it going up and down through the plane of the Earth's orbit, and never directly in the Earth's shadow.

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Great article, with one minor complaint: While the causes for L1, L2, and L3 were satisfactorly explained, I felt that the writer glossed over L4 and L5 which seemed to me to be the most interesting Lagrange points. It was sort of like reading a really good book only to be disappointed by the ending.

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The funny thing about Newton is that he wasn't proven wrong; he was proven inaccurate.

It was his danged inability to throw apples at relativistic speeds toward the ground.

I tend to agree with Dave F's comment. A little more detail on L4 and L5 would be nice. For example, how much "stuff" could be there. Would it be enough for a permenant station to "mine"? For example, could water ice be captured for station use? Or would the station be in continious danger of collision?
Where exactly is this L4 and L5 in reference to earth orbit? Geosync? I have placed the out of service ACTS S/C into what our orbit analysists call a graveyard location where it will not need fuel to keep station. This sound like the L4 or L5 location.

A 3d View of the universe could be obtained by placing observation devices at the Lagrange Points around the sun and triangulating the data. The wo points adjacent to the earth would act as relays for data from the device on the opposite side of the sun. Although the triangle would involve having a base that is only light seconds in length against cosmic distances tens of magnitudes greater I still believe with todays precision electronics the data gleaned would resolve most of the cosmic mysteries. Although less colourful this endeavour should take presidence over mars rovers,comet interceptors or shuttle launches.

I agree with Gerald. Even if we continue with the Mars/Moon landings & other exploration, I think using the large baseline provided by smaller telescopes in L4 and L5 would provide concise enough data to probably lay to rest the red-shift = distance arguments one way or the other.

Of course, with science being what it is, there would be other "mysteries" brought to light--certainly enough to keep the conspricists going.

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