What is Orbit Determination When we are dealing with two bodies, we can determine their orbital paths exactly using a certain set of orbital elements. If you want to learn more about these orbital elements you can find my post on them here and how to use them to determine an orbital path here. If…
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…
Power Series Approximation A Taylor series is a useful tool in analyzing functions. It allows us to break up those function into an infinitely long, easier to deal with, polynomial. The general formula of a Taylor series is, for some function r(t) Note: The vertical line with a zero at the bottom means evaluate this…
Things Always Come in 3’s If two wrongs don’t make a right, try three. -Laurence J. Peter Lot’s of things come in threes, there’s even a whole website devoted to three’s. Is there a reason we’re fixated on groupings of three? Probably, but that seems like a psychology question and this post is about…
Review of Constants of Integration In Last week’s post we played around with the equation of motion to transform it into forms that we could integrate. Through that we identified 5 different constants of integration. There’s actually also a sixth that I didn’t go over last time called mean angular motion and denoted by symbol, n.…
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…
