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It Can Be Tricky Calculating the Location of Lagrange Points
I didn’t plan on writing this. My goal was to make a series of videos exploring all the cool aspects of Lagrange points (video playlist here). However, stuff gets complicated and I made some mistakes. So, here I am — trying to fix those mistakes. Oh, one more thing. My goal wasn’t to find the locations of Lagrange points, it was to build my own model (mostly from scratch) to calculate these things.
Introduction to Lagrange Points
Wait. What the heck is a Lagrange point? In short, there are 5 locations (labeled L1 — L5) near the orbit of two bodies. The net gravitational field at these locations is such that a low mass object could orbit there with the same angular velocity as the two large bodies. This means that the object will stay stationary relative to those objects.
Maybe a diagram will help. Imagine a binary star system (with two unequal mass stars) with circular orbits around a common center of mass (here’s how to calculate stable orbits for a binary star system). Here is the L1 Lagrange point.
Yes, there’s a lot of stuff going on in this diagram — but here is the most important stuff (I’ll…
