What Is L5?


L5 is one of the "Lagrangian" points in the Earth-Moon system. Lagrangian points are locations in space around a two body system in which the gravitational attraction and centrifugal forces of the bodies cancel each other out (the pull is equal in all directions). Their existence was postulated by a French-Italian mathematician (named Joseph-Louis Lagrange, of all things!), and proven by empirical observation and (recently) computer modeling. Lagrangian points also can be determined for systems more complicated than two bodies, but the math rapidly gets REAL complicated.

In the Earth-Moon system (actually, any two-body system), there are five Lagrange points where the gravitational attraction (from the Earth and the Moon) and the centrifugal force (generated from an object's motion around the center of mass of the system) balance each other out. In other words, if you put something at one of these points, it will neither fall toward the Earth or the Moon, nor fly out of orbit into interplanetary space.

drawing showing the relative locations of
	the Lagrangian points in the Earth/Moon (Terra-Luna) system Of the five Lagrangian points in the Earth-Moon system, the first 3 are located along the line through the centers of Earth and Moon: One lies between the Earth and the Moon ("L1"); one is beyond the Moon as seen from the Earth ("L2"); one is on the opposite side of the Earth from the Moon ("L3"); and two are in the Moon's orbit, one each sixty degrees ahead of ("L4") and behind ("L5") the Moon, as it travels around the Earth.

The first three Lagrangian points, L1, L2, and L3, (the points in line with the Earth and Moon) are "gravitationally unstable:" If you put something there, it will remain where you put it as long as the balance is maintained, i.e., until it is disturbed. Once the solar wind blows on it, for example, or a meteor runs into it, the object is going to fall one way or the other - much like having something balanced at the top of a hill.

The other two Lagrangian points are "gravitationally stable:" Something placed at L4 or L5, when disturbed (within limits), will fall back toward its original position - as though it was at the bottom of a valley.

In actual fact, objects don't tend to stay at L4 or L5. Instead, they follow small dumbbell-shaped orbits around the Lagrangian point. This feature will make it possible to put more construction than would be possible if the balance were only achieved at a true (mathematical) point: Since objects tend to orbit L4 or L5, each thing we want "there" just has to be in a different, non-intersecting orbit from everything else there, yet it can still take advantage of the unique gravitational properties of the space.

L4 and L5 are "gravity wells" just as the Earth and Moon are: Leaving requires climbing out of the well (a "hole in space") we find ourselves in. However, to travel to the asteroids, Mercury, Venus, Mars, or even to any of the outer planets (Neptune, Uranus or Pluto) or out into interstellar space, departure from L5 (or L4) is far less work, since they are "shallow" gravity wells - things aren't held down nearly as well there. This is good for space business, for example, because shipping costs will be lower, due to the reduced fuel requirements. Working from L5, asteroid mining and tapping the resources of the gas giants could be economically feasible: It would almost be possible using the rockets we have available now. By the same token, using L5 as a starting point for space exploration and development makes a lot more sense than trying to start directly from the Earth, again because of the reduced energy costs when undertaking a new journey. All of these factors combine to make L5 a very attractive location for private enterprise to work from.

There are also Lagrange points in the Earth's orbit around the Sun, in mathematically similar locations, in the orbits of Saturn's moons - in fact in any system of heavy bodies in space. The L-points in Jupiter's orbit (also known as "Trojan points") around the Sun have enough stuff in them (asteroids and such) that they can be located with a telescope from Earth. ESA amd NASA have a satellite at the L1 point in the Earth-Sun system, about a million miles toward the Sun from the Earth, and a second on the way there. The satellites are used for studying the Solar wind beyond the influence of the Earth's magnetic field, and spend most of their fuel maintaining their position against the flow of the wind: They are "at the top of the hill" and the Solar wind is constantly trying to blow them down...

L5 is popularly chosen over L4 as a location for building space colonies. The only reason I've ever heard for this is people have said "All you have to do is slow down a little (when launching from the Moon) and you just land there." That is true, but in fact, it takes the same amount of energy to slow down to land at L5 as it would to speed up and land at L4.

Rather than confuse the issue, we've chosen to follow the lead taken by our predecessors in developing the space colony concept, and to aim toward L5. Since the choice, one way or the other, is actually moot, it's better for our motives to capitalize on as much work as has been done before us as possible. Rather than reinventing the wheel to change directions and land at L4, it makes the most sense to go to L5.

 

See also the Lagrange Points page on the Microwave Anisotropy Probe page for a similar discourse.

 

 


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L5 Development Group - What Is L5? / Webmaster / Last modified December 30, 2003 @ 1:10 am
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