Orbital Mechanics I

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 basic algebra, the Pythagorean theorem, basic programming, the ability to catch on to mathematical concepts quickly, 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 @ $40 each) secures your spot in the class with no ongoing obligation.

Next class begins September, 2026
more than 99% of students rate this course content and results as Super
Register

Skills you will get

From the building block prerequisites listed above, we will generally cover a first semester of calculus (with proofs), introductory orbital mechanics, introductory physics, and an introduction to Python coding as applied to orbital mechanics. The main product of the course will be a project involving a Python modeling of the launching of a spacecraft into a circular orbit from a planet with an atmosphere.

  • Definition of the calculus derivative

    i.Slopes
    ii.Infinitesimals
    iii.Derivatives

  • Properties of the derivative

    i.Intro to proofs
    ii.Sum and difference rule
    iii.Product rule

  • Derivatives of functions

    i.Derivatives of polynomials
    ii.Derivatives of rational functions

  • The Finite Difference Method

    i.Application in Excel or LibreOffice Calc
    ii.General application
    iii.Use for high-order partial differential equations

  • Orbital Mechanics Physics

    i.Position, velocity, and acceleration
    ii.Newton’s laws
    iii.Operating principle of rockets
    iv.Delta-V and fuel

  • Gravitation

    i.Vector length and direction formulae
    ii.Scalar gravity
    iii.Vector gravity

  • Orbits

    i.Why they exist
    ii.Effects of orbital maneuvers

  • The rocket equation

    i.Derivation
    ii.Use and examples

  • Orbital mechanics simulation with Python

    i.Installation
    ii.Variables and printing
    iii.If-then statements

  • More simulation with Python

    iv.For-loops
    v.Functions
    vi.numpy vectors
    vii.More advanced simulation techniques (e.g. RK45)

  • Simulating initial value problems in Python

    i.scipy.integrate.solve_ivp function
    ii.Forces acting on a spacecraft

  • Orbital spacecraft modeling

    i.Basic orbit modeling
    ii.Applying accelerations
    iii.Orbit transfers

  • Launch modeling (no drag)

    i.Tuning the engine thrust
    ii.Gravity turns

  • More launch modeling (no drag)

    iii.Residual eccentricity
    iv.Correcting residual eccentricity

  • Additional parameters

    i.Drag
    ii.Staging
    iii.Variable acceleration/thrust

  • Higher-order models

    i.Earth oblateness
    ii.Solar and lunar gravitational effects (third-body forces)

Course program:

Whole course - 3 Blocks (12 hours total) - $480 total to be paid in blocks

This 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 basic algebra,the Pythagorean theorem and basic programming (any language). 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 which will simulate the launching of a spacecraft into a circular orbit from a planet with an atmosphere. 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 - $80 total

    2 Hour-long classes @ $40 each

    Introduction to Basic Differential Calculus (with proofs)

    The definition and properties of the derivative will be covered and we will learn about taking derivatives of functions. We will begin learning about the Finite Difference Method using Excel or LibreOffice Calc.

  • 2nd Block - $200

    5 Hour-long classes @ $40 each

    Finite Difference Method and Orbital Mechanics Physics

    We will cover more advanced applications of the Finite Difference Method and we will learn about the physics involved in orbital mechanics. Our studies during this block will culminate in learning about how the rocket equation is derived and its uses.

  • 3rd Block - $200

    5 Hour-long classes @ $40 each

    Orbital Mechanics simulation with the Python programming language and major project

    We will cover basic Python installation, data structures, and numpy vectors. Then we will move into simple through advanced simulation techniques on orbital spacecraft and launch modeling. We will culminate learning about adding additional parameters to our model including drag, staging and variable acceleration/thrust. Learning about third-body forces and how to incorporate them into our model will conclude this block.

  • Your student will produce:

    After the major project:

    A python model that simulates the launching of a spacecraft into a circular orbit from a planet with an atmosphere; 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

Testimonials about our courses


See testimonials

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: $80 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.