Balancing a Marble Imagine you had a marble and you wanted to put it at the point between the Earth and the Moon where the force of gravity was equal from both. The two forces would cancel out, and the marble would remain in that location forever. If the sun and the earth were not…
Recap In the last two posts on what is the 3-body problem and the dynamics of the three body problem I’ve shown you the following GIF with a spacecrafts trajectory in the earth moon system. The trajectory is bouncing around what I’ve labeled a ‘forbidden region’. In this post we’ll go over the number behind…
Chaos I’ve recreated one of my favorite mathematical demonstrations below. Three double pendulums, all starting with near identical initial conditions, all rapidly diverging. I love this demonstration because it’s such a great example of chaotic dynamics. What is Chaos? Chaotic dynamics, in a nutshell, means that a system is extremely sensitive to initial conditions. That…
Recap In the last post we introduced the 3-body problem along with some constraints that turned it into the circular restricted 3-Body Problem (CR3BP). In the beginning of that post, I had a GIF that traced out a trajectory in the Earth-Moon system. In this post, we will derive the equations of motion for the Circular…
A Whole New Ballgame In the past, this blog has covered the 2-Body problem which is solvable (Kinda) and the general n-body problem which isn’t. We have a lot of insight into how the 2-body dynamics work, but unfortunately, they break down as soon as we get away from any major body. If you want…
The Klaxon Starts Ringing Imagine it’s the year 2300. Earth and Mars are at war. You’re an Earth warship, blue, based on an asteroid in the asteroid belt. A martian drone, red, lands on the opposite side of the asteroid. It’s out of line of sight so how do you aim your rail-gun to destroy…
Review of the n-body Problem The n-body problem is when some number of bodies are interacting with each other gravitationally, and you want to figure out what their movement will be at some arbitrary point in the future. I wrote a full post on the problem and it’s difficulties here. I highly recommend that post…
Introduction of the 2-Body Problem In the last orbital dynamics post I introduced the n-body problem and how there is no general analytic solution. There is a general analytic solution for a simplified version of this problem called the 2 body problem, and that’s what this post, and the next several, will be about. In this…
Introduction to n-Body problem Lots of post on this site begin with an appeal to Newtons second law. It’s an extremely useful tool for analyzing dynamic systems. This post wont begin this way. It’ll begin with Newtons third law. “For every action there is an equal and opposite reaction” This means that anytime a force…
Part 2 of a series on the math behind suicide burns.
