Sorry for the missed lectures on Friday and Monday. I was out sick. Assignments are due on Friday. We covered perturbations to orbital motion. We examined contributions from gravitational and nongravitational sources to the two-body motion.
Sign up for updates here: https://mailchi.mp/d95b0d174531/odcourse
Slides: L5 Slides – Perturbed Motion
Previous lectures:
We resumed today with orbital mechanics. We covered the two-body problem, introduced Kepler’s problem (time doesn’t relate well to true anomaly), and sprinted to the state transition matrix. We will resume with perturbations and additional bodies considered on Friday.
Sign up for updates here: https://mailchi.mp/d95b0d174531/odcourse
Slides: L4 Slides – Two Body Problem
Previous lectures:
Re-recorded lecture from Monday, January 28. I cover the 2D Uniform Gravitational Field (parabolic trajectory) problem solution. I also reviewed linearization and the state transition matrix because I felt that I didn’t cover them adequately in lecture 1. We will pick back up with additional review of orbital mechanics before moving on to observations.
Sign up for updates here: https://mailchi.mp/d95b0d174531/odcourse
The problem solution can be found on GitHub at https://github.com/simpsonchristo/Soln-HW1-SimpsonAerospace.
The pdf write-up of the solution and the slides can be found here:
Write-up: soln_hw1
We review orbital mechanics to prepare for orbit determination. We will cover the two body problem, orbital elements, and perturbing accelerations. We will continue on Monday. Be ready to turn in your solution for the practice problem.
Lecture Slides:
The inherent characteristics of an orbit determination (OD) problem are introduced. Dynamic state estimation, observations, linearization, and the state transition matrix are discussed. At the end, I have left a practice problem that we will review on Friday, 8 June. We throw a satellite up and watch it come down while introducing some important concepts.
Lecture Slides:
SA · ORBIT DETERMINATION · SHORT COURSE · 14JUN26
A short course.
A twelve-lecture introduction to orbit determination — from orbital mechanics and the two-body problem through coordinate systems, measurement simulation, and fitting real measurements into a state estimate. Taught by Dr. Christopher R. Simpson. Free, self-paced, with lecture notes and video.
Students and engineers who want a working understanding of how a state estimate is built from measurements. Some calculus and basic orbital mechanics help, but the course builds from first principles.
Work the lectures in order. Each builds on the last. Questions are welcome on each lecture’s video page — discussion is the point.
Originally taught Spring 2019; refreshed and re-launched 2026.
If you haven’t already signed up; please submit your email to receive notifications and updates about the course.
[contact-form][contact-field label=”Name” type=”name” required=”1″ /][contact-field label=”Email” type=”email” required=”1″ /][/contact-form]
I pick up again by reviewing the solution to the problem assigned during Lecture 1. (The link will take you to a solution using C++ on GitHub). A few common coordinate systems and reference frames are introduced, orbital perturbations are introduced, and an example problem to be solved in Lecture 4 is given to the class to start on.
[youtube https://www.youtube.com/watch?v=FlcF9AoNBUo]
Lecture 3 – Review Of Orbital Mechanics B
Lecture 2 – Orbital Mechanics Review A
If you haven’t already signed up; please submit your email to receive notifications and updates about the course.
[contact-form][contact-field label=”Name” type=”name” required=”1″ /][contact-field label=”Email” type=”email” required=”1″ /][/contact-form]
Problem 1 provides the solution for us. We are learning how to use iterative methods to estimate the state vector. In this case we will use the Newton-Raphson root-finding method to solve for the problem. An Excel sheet is provided that walks through the first three iterations as an illustration. C++ code is provided on GitHub that will solve for the final solution and show the number of iterations.
Excel – Visual Iterative Solution
I’ve been traveling and haven’t been able to finish the last part of Orbital Mechanics Review. Feel free to review Dr. Russell’s work, prior to Monday. Full solution will be posted Monday as well. If you’re answers don’t match up; start a discussion in the comments below.
Answer for the practice problem:
| X0 | 1 |
| Y0 | 8.0 |
| Xdot | 2.0 |
| Ydot | 1 |
| g | 0.5 |
| Xs | 1.0 |
| Ys | 1.0 |
If you haven’t already signed up; please submit your email to receive notifications and updates about the course.
[contact-form][contact-field label=”Email” type=”email” required=”1″ /][/contact-form]
We review orbital mechanics and Newton’s law of gravitation to prepare for orbit determination. We will cover the two body problem, orbital elements, and perturbing accelerations. We won’t finish the entire lecture today. We will continue on Monday.
[youtube https://www.youtube.com/watch?v=eBekNtOqy-k]
Lecture 2 – Orbital Mechanics Review A