Posted by: T. Boyd | March 11, 2010

Finding Rest at a Lagrangian Point

Come unto me, all ye that labor and are heavy laden, and I will give you rest. (Matthew 11:28)

If you have studied the problems of keeping a satellite in orbit around the earth, you know that there have to be periodic adjustments made to its speed and direction. Otherwise the orbit will degrade so that a satellite can no longer perform its function. The adjustments are usually made by commanding small jets to eject a precise amount of compressed gas that is stored on the satellite. The ground controllers call these adjustments “burns.”

And this problem is prevalent no matter where you would try to place a space object in the solar system except at some very special points in space called Lagrangian Points. They are labeled L1, L2, … L5. There are 5 L points for each pair of orbiting bodies, like the Sun-Earth system and the Sun-Mars system as well as for the Earth-Moon pair of bodies, as seen in the diagram that is in the Wikipedia: Lagrangian Point article.

Lagrange points for Earth-Moon

The two points, L4 and L5, are the best choices for a stable location because if the satellite drifts away from the point in any direction, the effects of gravity plus momentum will keep it close to the Lagrangian point. The blue arrows show the limits of the “safe region”.

On the other hand, L1, L2, and L3 only have temporary stability and a satellite at those positions has to have periodic adjustments to keep it there. Drifting any amount toward or away from the earth or moon will produce instability. Thus, though it takes less “fuel” to keep a satellite at those points, the “burns” are still required.

I just chatted on-line with my friend Chandra in India – he worked on a version of this problem in college. It was called the 3-body problem discussed by Newton in 1687 and by Euler in 1767, and then by Lagrange in 1772.( ref: Wikipedia article: Three-body_problem)

For only 2 bodies in space, the prediction of their orbits around each other is easily calculated. But add a 3rd body and their orbits become unpredictable except in restricted circumstances. Outside those restrictions, the motion is chaotic – in fact, the academic field of Chaos was established to deal with this kind of motion.

I find it amazing that our Lord Jesus, who was the one through whom the universe was created (Hebrews 1:2), is also the one that made the laws by which it behaves. He knows all about the chaos that it is all heading for, and provides for us a safe, stable resting place in Him.

Take my yoke upon you and learn of me; for I am meek and lowly in heart: and ye shall find rest unto your souls.
For my yoke is easy, and my burden is light.

(Matthew 6:29-30)


  1. […] Chaos and the 3 body problem – see Finding Rest at a Lagrangian Point […]

  2. Sharon, I like your comment “other days when we seem almost worthwhile…” Our creator loves it when the ability He gave us to think and work produces something new and valuable. I also believe that our creativity-type nature will continue into eternity – can you imagine the libraries and shops that will be available? And singing groups? Leslie wants to ring bells (change ringing) and I want to build and play pipe organs!

    • I’m looking forward to those Heavenly days when I can hear you playing the pipe organ you built, accompanied by Leslie’s bells. I can do the artwork to promote the events!

  3. From Rosemary, a friend:

    Thank you for that analogy. May we always stay within our lagrangian points.


  4. From my friend, Sharon:

    Amazing, Boyd! I always look forward to your articles. And it amazes me even more that people have figured all this stuff out — as early as the 1600’s! There are days when I’m sure God knows he made a big mistake creating humankind, and then there are those other days when we seem almost worthwhile……(!)


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