Tag Archives: orbit determination

Spring 2019/Lecture 5/Perturbed Motion – 6 Feb 2019

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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.

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Slides: L5 Slides – Perturbed Motion

[youtube https://www.youtube.com/watch?v=HZjksLbF4go&w=560&h=315]

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Spring 2019/Lecture 4/Two Body Problem – 30 Jan 2019

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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.

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Slides: L4 Slides – Two Body Problem

[youtube https://www.youtube.com/watch?v=Mx6PEYk_RQE&w=560&h=315]

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OD – HW 1 Solution

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Solution to Homework 1

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.

Homework Solution 1

Excel – Visual Iterative Solution

C++ Solution

 

Lecture 2 – Orbital Mechanics Review A

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Lecture

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]

Previous Lectures

Lecture 1

Resources

Lecture 2 – Orbital Mechanics Review A

Lecture 1 – Orbit Determination Concepts (slides)

AppendixA-ProbabilityAndStatistics

Lecture 1 – Orbit Determination Concepts

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Lecture

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.

[youtube https://www.youtube.com/watch?v=0g0QzppL1Ow]

Resources

Lecture 1 – Orbit Determination Concepts (slides)

AppendixA-ProbabilityAndStatistics