This Thursday, April 11th, a washing machine sized-spacecraft will attempt to land on the Moon. If it succeeds, it will be the first privately funded spacecraft on the Moon, and make Israel the fourth country to land on the Moon after Russia/USSR, the USA, and China. This post will go over the basics of what…
Introduction to the Library As I’m doing research I end up writing a lot of code. Most of the time it’s one-off scripts and functions for a specific task, but sometimes I do something enough that I add it to my permanent in-house library. I’ve decided to collect several of these functions related to astrodynamics,…
Everything Orbits About Something In our solar system, Moons orbit around planets, which themselves orbit around the sun. Well, actual they orbit about the system barycenter, the combined center of mass between the two bodies. But can we get an object to orbit around a region without a barycenter? Yes! (Kinda) There are actually a…
Recap of Lagrange Points In the circular restricted three body problem, there are a set of 5 points that if we place our spacecraft there, it’ll never move relative to the two bodies. These are called the Lagrange points and are the only equilibrium points for the system. Whenever we find an equilibrium point in…
Jacobi and Lagrange So far we have explored the Jacobi Integral and the Lagrange points. Now, we are ready to combine the two into one of the most useful concepts in the Circular restricted 3-Body Problem (CR3BP), forbidden regions. You’ve seen them in my visualizations before, but now we’ll finally go over what they are.…
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…
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…
