Orbital mechanics is a fun subject, as it involves a lot of seemingly empty space that’s nevertheless full of very real forces, all of which must be taken into account lest one’s spacecraft ends up performing a sudden lithobraking maneuver into a planet or other significant collection of matter in said mostly empty space. The primary concern here is that of gravitational pull, and the way it affects one’s trajectory and velocity. With a single planet providing said gravitational pull this is quite straightforward to determine, but add in another body (like the Moon) and things get trickier. Add another big planetary body (or a star like our Sun), and you suddenly got yourself the restricted three-body problem, which has vexed mathematicians and others for centuries.
The three-body problem concerns the initial positions and velocities of three point masses. As they orbit each other and one tries to calculate their trajectories using Newton’s laws of motion and law of universal gravitation (or their later equivalents), the finding is that of a chaotic system, without a closed-form solution. In the context of orbital mechanics involving the Earth, Moon and Sun this is rather annoying, but in 1772 Joseph-Louis Lagrange found a family of solutions in which the three masses form an equilateral triangle at each instant. Together with earlier work by Leonhard Euler led to the discovery of what today are known as Lagrangian (or Lagrange) points.
Having a few spots in an N-body configuration where you can be reasonably certain that your spacecraft won’t suddenly bugger off into weird directions that necessitate position corrections using wasteful thruster activations is definitely a plus. This is why especially space-based observatories such as the James Webb Space Telescope love to hang around in these spots.
Continue reading “Lagrange Points And Why You Want To Get Stuck At Them”
