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§ 3.2.3 The L1, L2, L3, L4 and L5 "Libration" points

There are two points called L1 and L2 on the chart on energy requirements. Their relevance is as follows:

Both L1 and L2 orbit the Earth in the same amount of time that the Moon orbits the Earth. L1 and L2 serve as lunar-stationary or lunar-synchronous points in space, just like communications satellites in geostationary orbit stay above one point on Earth. This is because the Moon keeps one face pointed towards the Earth all the time (i.e., its rotation period equals its orbit period exactly).

In other words, if you're on the surface of the Moon and you look up at an object stationed at the L1 or L2 points, it won't move over time. Objects everywhere else in orbital space will move.

The Mass Driver, discussed in the lunar launch section, would shoot payloads to a Mass Catcher located at one of these two points. Lunar material can be shot off the lunar surface and into circular orbit around Earth without being placed in lunar orbit first, and rockets could head there, too.

Likewise, a solar power station or giant mirror system at these two points could service the lunar surface during most of the long lunar night by beaming down energy, light and warmth at night, in a longer term scenario.

In reality, stationkeeping would be required to keep an object at L1 or L2 due to the effects of the Sun's gravity. The fuel propellant required for stationkeeping would be small.

The rest of this article covers the physics, not the relevancy, of the L1 and L2 phenomenon, as well as the L3, L4 and L5 points, for those who are curious to know. Notably, L4 and L5 are two candidate regions for emplacing industrial facilties in high Earth orbit. Indeed, a famous space advocacy organization promoting asteroidal and lunar materials utilization called itself the L-5 Society.

These points are also called the LaGrange points (after their mathematical discoverer) or the "libration points".

The physics of L1, L2, L3, L4 and L5

L1 and L2 are two unique points caused by the interaction of the Earth's and Moon's gravities. They are also shown in the following chart, along with L3, L4 and L5.

The L1 point is where:

the Earth's pull = the Moon's pull + the orbital centrifugal "force"

When an object placed between them is balanced by two pulls in the two directions, it's as if the object is balanced at the peak of a hill. A nudge one way or the other would cause the object to fall inward towards Earth or outward towards the Moon. (It's actually a little more involved than this in that nothing falls straight down in a three-body rotating system, but you get the idea.)

The L2 point is another place where you can place an object and it will always stay there if balanced perfectly. The cause of the L2 point is:

the Earth's gravity + the Moon's gravity = the orbital centrifugal force

The L3 point is simply the place in Earth orbit opposite the Moon which orbits the Earth in the same period of the Moon. It has no relevant economic potential (unless you never want to see the Moon for some reason).

The L4 and L5 "points" actually denote the centers of two regions -- objects will tend to drift around these two points in erratic orbits (appearing to orbit the empty points in a noncircular and nonelliptical shape) , without leaving the L4 or L5 region, and without requiring much stationkeeping propellant to stay in the region. The L4 and L5 points are located in Earth orbit 60 degrees in front of and 60 degrees behind the path of the Moon around the Earth. What happens is that when the Moon accelerates/decelerates objects in L4/L5 region, it changes their centrifugal force relative to Earth and hence their orbit around Earth, causing them to climb away from or fall towards Earth, in which case their orbital speed decreases or increases as they climb away or fall towards Earth, and as a result they fall behind or pass up the L4/L5 point and the cycle repeats. (Another way of looking at this is that an object placed at L4 or L5 orbits the center of mass of the Earth-Moon system in one month.)

Like everywhere else, the Sun's gravity perturbs objects in the L4 and L5 points so that it's not a perfect picture, but it's fairly close.

In the 1970s, many people saw the L4 and L5 regions as favorable for placing industry to process asteroidal and lunar material, and space colonies as well, because they all stayed in proximity to each other, unlike objects in different orbits outside this zone (unless the latter are all in the same orbit and just strung out in a circular curve), and stayed "close" to the Moon in terms of energy.

Whether or not space industry is located at L-4 or L-5 is a minor issue. Space industry could be located in most any Earth orbit. But the L-4 and L-5 points are referenced by many studies as candidate sites, hence their discussion here.

Different studies put the manufacturing facilities in different places, e.g., in a high orbit or an L point. Few put them in a low Earth orbit, due to the energy required to bring asteroidal materials down. Only some finished products come down. Wherever the industry is located, the initial large colonies will be located nearby.

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