Not long ago, I had a question about Lagrange Points and I asked one of the top mathematics professors in the area of planetary science a question. Leave it to me, a non-scientist type thinker to ask the wrong question, thus, get less than the answer I’d hoped for you see. My question was one which I could not find anywhere online, and perhaps it is because, well, no one really knows for sure exactly what the answer is. “Am I the first person to ask this question,” I thought, “certainly not, I couldn’t be” I reasoned.
So, here is the question; “Dear Planetary Mathematics Professor, Can you tell me or describe to me the shape of a Lagrange Point? In my question, I will assume that the two planetary objects creating this point are relatively spherical.” The brilliant mathematician then states to me; “A Lagrange point is a ‘point’. It doesn’t have a “shape”, unless you call a point a shape.”
How silly did I feel after that, okay yes, I asked the wrong question didn’t I, as I should have asked what is the shape of the region caused by the Lagrange equilibrium phenomena? You see, logically speaking, it would be a shape – and philosophically speaking a point is a shape really, as there really is no such thing as absolute zero (nothing exists nowhere philosophy theory).
Okay so, back to why I think it is a shape. Gravity from two objects pulling on each other would cause the point to warp and thus, you have a shape, and that shape would matter – and thus, I pose this question. The shape is important and it’s the point of equilibrium might be a point in your mathematical equations, but the equilibrium that exists there is an area, thus has fuzzy boundaries – shape. What is that shape, what is the shape of each type of Lagrange equilibrium area?
It’s been suggested by another that it would be a “saddle-like” shape in 4D, and that is one theory, but a mathematical equation could be used to figure this out, so, are you sure that the lagrange points are not shapes, I mean even gravity is not evenly distributed on planet earth, and our sphere is not even perfect on this pale blue dot. I guess I disagree that the Lagrange point is not a shape or evenly distributed, but can you prove me wrong mathematically?
The answer I presume is NO, and if the math comes back, and if the right formulas are used, the lagrange equilibrium phenomena cannot be an actual point, but there is a center of the that region, which I believe to be moving around constantly, probably creating vortex flows and small space debris to move around and flow, just like our weather on Earth, which some day will also be proved by our dear old astronomy and planetary mathematics professor. Hope you enjoyed today’s discussion.