Lagrange Points Simplified

They’re always talking about Lagrange points in SF stories. What the heck is a Lagrange point? And why would you want one? Well, we’ll let Wikipedia provide the full explanation if you’re that curious. For the rest of us, let’s review the graphic below:

LaGrange Points, in a diagram featuring Jupiter

Lagrange points are named after the Italian-French mathematician, Joseph Louis Lagrange, who in 1772 set out to discover an easy way to calculate the gravitational interactions between an arbitrary number of bodies in a system. In point of fact, the L1, L2 and L3 points were discovered a few years earlier by Leonhard Euler. However, Lagrange discovered the L4 and L5 points, which, quite frankly, are considerably more useful than the other points.

In the graphic, Jupiter rotates around the Sun. The Lagrange points represent locations where an object of negligible mass (by comparison with Jupiter or the Sun), can occupy a stable position orbiting in conjunction with the two larger masses. Basically, if you put something smack-dab on a Lagrange point, it will stay there.

Now, the L1, L2 and L3 points are considered unstable. An object that ventures away from one of those points will gradually experience additional forces to pull it away. Venture too far away from L1, and you’ll be drawn to either Jupiter or the Sun, depending on which direction you moved.

By comparison, L4 and L5 are stable. An object at those points tends to remain at those points, which makes those locations ideal for space stations or observatories. Even better, in a rotating system, the L4 and L5 points actually take on a more expansive, kidney-shaped geometry, so they can “hold more stuff” than the other Lagrange points.

A good analogy is to think of the L1, L2 and L3 points as cones with a ball balanced on top. Any movement, and the ball falls off the cone. By contrast, the L4 and L5 points are like bowls, with a ball at the bottom of the bowl. Perturb the ball and it may rotate around the center of the bowl, but it will eventually be drawn back to the bottom.

Because L4 and L5 are stable orbital positions, Jupiter has collected numerous asteroids at the L4 and L5 points in its orbit. Asteroids at the L4 position, which leads Jupiter in its orbit, are known as the Greeks. Asteroids at the L5 position, trailing Jupiter in its orbit, are known as the Trojans. Their names are based on The Iliad, which also features the story of Troy. Both places would be ideal locations for a nation or mini-nation, or at least a center for industrial production.

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