Orbital Mechanics II
Are you interested in space travel? Have you ever wondered why movement in space is different from movement on Earth? If you are intellectually curious and interested in these questions, and if you have the background of Orbital Mechanics I which includes vector algebra, basic differential calculus, basic Python, the ability to catch on to mathematical concepts quickly, basic trigonometry, and the willingness to participate in class and complete homework, then this class is for you!
No age requirement - any student having the prerequisites is welcome!
Only payment for the first block (2 classes @ $75 each) secures your spot in the class with no ongoing obligation.
Skills you will get
From these building block prerequisites, we will generally cover integral calculus, introductory differential equations, orbital elements, orbit determination, interplanetary and interstellar trajectories, and satellite navigation. The main product of the course will be a project involving a Python modeling of a custom satellite navigation system around a gravitationally rounded object (the choice of which will be up to the student).
-
Reimann sums and integrals
i.Physical intuition of the integral
ii.Definition of the Reimann sum
iii.Evaluating Reimann sums
iv.Solids of revolution
-
Integration methods
i.Basic operations
ii.Integration by parts
iii.u-substitution
-
Integrals of functions
i.Integrals of polynomials
ii.Integrals of trigonometric functions
iii.x^-1 and e^x -
Newton's method for solving nonlinear equations
i.Application in Excel or LibreOffice Calc
ii.General application
iii.Use for multidimensional problems
-
Differential Equations
i.Types of differential equations
ii.Finite difference and Runge-Kutta methods
iii.Initial value problems
-
Gravitation
i.Review of gravitation
ii.Solving the simplified two-body problem
-
Orbits
i.Orbital parameters and their derivations
ii.Orbital periods
iii.Orbit analytical propagation
-
Reference frames
i.Rotation matrices
ii.Why we need reference frames
ii.Ways to get around needing these in your code
-
Orbital parameters and orbit position and velocity
i.How to get parameters from position and velocity
ii.How to get position and velocity from parameters
iii.Edge cases, and how to get around them
-
Analytical orbit propagation
i.Applying Newton's method to orbits
ii.Handling numerical instabilities
-
Hyperbolic orbits
i.Hyperbolic trigonometry
1.Motivation
2.Hyperbolic trig functions
3.Derivatives and integrals
ii.Velocity-at-infinity
iii.Nonstandard eccentricity and semi-major axis meanings
-
Interplanetary and interstellar orbits
i.Patched conics
ii.General approximations
iii.Interplanetary trajectories
iv.Relativistic brachistochrone
v.Interstellar travel
vi.Advanced propulsion
-
Satellite navigation
i.Atomic clocks and position determination through light delay
ii.Coverage radius
iii.Orbit constellations
iv.Global Navigation Satellite System (GLONASS)
-
-
-
Course program:
Whole course - 3 Blocks (12 hours total) - $480 total to be paid in blocksThis course was modeled after a junior-level university aerospace engineering course on orbital mechanics. It was designed to be accessible to students who are intellectually curious and have the background of vector algebra, basic differential calculus and basic Python. Homework is assigned almost every week and due the following week. No exams are given, but the materials in the course will contribute toward the main product of the course which is a project involving a Python modeling of a custom satellite navigation system around a gravitationally rounded object (the choice of which will be up to the student). The grade in the class will be based upon a weighted homework average and attendance. For more detail regarding homework, homework corrections and the late policy, please see the "Our philosophy"page as well as the syllabus which you will receive upon registration.
-
1st Block - $150 total
2 Hour-and-a-half long classes @ $75 eachIntroduction to Basic Integral Calculus (with proofs)
Reimann sums and integrals will be covered, along with solids of revolution, and basic integration methods such as integration by parts and u-substitution. We will begin learning about Newton's method for solving non-linear equations using Excel or LibreOffice Calc.
-
2nd Block - $375
5 Hour-and-a-half-long classes @ $75 eachMore advanced math and how it applies in orbital mechanics
We will cover differential equations, gravitation, orbits and reference frames.
-
3rd Block - $375
5 Hour-and-a-half-long classes @ $75 eachOrbital determination with the Python programming language, advanced topics and major project
We will orbital parameters and orbit position and velocity. Then we will move into analytical orbit propagation and hyperbolic orbits. We will culminate learning about advanced topics such as interplanetary and interstellar orbits, and satellite navigation. The students will incorporate all of their knowledge into a major project involving a Python modeling of a custom satellite navigation system around a gravitationally rounded object of the student's choice.
Your student will produce:
After the major project:
A Python modeling of a custom satellite navigation system around a gravitationally rounded object of the student's choice; and a certified certificate of completion with the student's name, course name, synopsis of course content, date, instructor name, and grade earned in the course
Registration
Registration for this course is now open. You will receive detailed information by email with next steps to secure your spot in the class.
Price: $150 for the first block of two classes to reserve your spot with no ongoing obligation
We will be back in touch to clarify further details. Thank you for your interest.