For Flit: Lagrange Points

>> Wednesday, July 29, 2009

Flit asked: Lagrange points? should I know what those are? Suppose I could google but it's past my bedtime and I'm still not done the first (of 8) folders I wanted to get through...

Here’s the most simple explanation I can make: Lagrange points are the points in a two body system (like a celestial body and a large satellite) where the gravitational forces and centripetal forces effectively cancel out so that an object (which has a negligible mass relative to the other two bodies) moves such that it remains in place relative to the two bodies. That last part is important, because the object doesn’t “stop” – it’s moving with the two bodies but stays in the same location relative to their location (see second picture).

It’s often compared to geostationary and it’s a good analogy. Geostationary could sound like a “stationary satellite” – but it’s not. It’s moving quite briskly, orbiting the planet once a day so that it remains over the same area of the earth as it turns. Relative to the surface of the earth, it’s stationary. Note that geostationary satellites are only located over the equator. If you put them at a different inclination (even if the period is the same) it will veer above and below the equator during the course of the day.

In this case, the object is stationary relative to the center of gravity of both bodies, not the surfaces of the bodies, so it wouldn’t necessarily look to be in the same spot from the surface of either body. However, it would always be in the same spot, orbit-wise. Why is this exciting?

Couple of reasons. First, all the forces canceling out means that this location has a very low gravity gradient, true zero gravity. The orbit would be readily maintained with minimal effort unlike things in low earth orbit today.

The points are not all made equal. L1, which lies on the line between the two bodies, is the optimal place to enter orbit of either body with minimal energy. In theory, there perfect place to provide, say, a moon servicing station between the earth and the moon. The earth-sun L1 is the perfect place to get sun observations (without worrying about being blocked).

Conversely, the sun-earth L2 is the perfect place to get space observations without being blinded by the sun’s light (as long as you have a non-solar array dependent power system). It always has its view of the sun in eclipse by the earth. That’s where we intend to put the James Webb telescope (the successor to HST) and we have a couple there now with more to come.

The L3 point for the sun-earth interaction is actually on the far side of the Sun, as if in counterweight to our own planet in the same orbit. In this case, the earth would always be eclipsed by the sun. However, given that there are many other bodies in the solar system besides the earth and moon, the sun-earth L3 point is actually quite unstable. Ah, that imperfect universe. There’s also an earth-moon L3 where one would be facing the other side of the moon (which would eclipse the earth) all the time. I presume it’s more stable.

Actually, all three of the collinear Lagrange points are somewhat unstable. They’re stable in two directions, but nudged them toward one body or the other and they’ll go readily.

The last two Lagrange points, that are oddly triangular, are the most stable (assuming one of the massive objects is much larger than the other). This is the spot often discussed as an excellent place for a human space colony as the orbit is self-correcting and generally very stable.


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