1.1 What to Expect in Your First Course

Introduction

In engineering programs, courses on orbital mechanics are usually offered either at the upper-year undergraduate level, or at the graduate studies level. Prior to this, students may have only minimal exposure to the subject. In physics classes they may have heard about Kepler's laws of planetary motion, and seen a few practice problems about circular orbits; but it's unlikely that they have had any formal introduction to space flight basics. In this chapter I will suggest a preparatory roadmap that can be used to bridge this gap.

The big picture

First I will give a basic rundown of what to expect in a first orbital mechanics course. Orbital mechanics is the study of how bodies in space move under the influence of the gravitational force they exert on each other. This is a vast subject; for introductory courses, it's common to focus on the relatively straightforward scenario of a small object (for example, a spaceship) orbiting a huge object (for example, a body like the Earth or the Moon).

Basic cooking ingredients

• You can expect to see the basic Newtonian laws introduced in high school:

  • • F = m * a 

    • Fgravity = Gm1m2 / r2  (Newton's Universal Law of Gravitation)

• You should be comfortable working with the above equations either in scalar form, or with vectors in 2D and 3D. Bonus points if you are comfortable working with them using a computer. 

• You should be familiar with conic sections: the circle, ellipse, parabola and hyperbola. As the term suggests, these are traces that are created when you "slice" a section out of a cone, at various angles.

• You should be comfortable working with conic sections in both Cartesian coordinates (xy) or polar coordinates (angle and radius).

The basic plot

You can expect most courses to run this way:

Part 1:

• Spoiler alert: if you throw a small object into orbit around a large body like the Earth, the trajectory of the orbit, relative to the large body, is going to trace a conic section. The object will continue coasting happily along this trajectory, moved only by the force of gravity, until it encounters some other resistance; for example, an atmosphere, or thrust from a rocket engine.

• This strange fact was noticed by a fellow named Kepler, who observed that the planets were moving in elliptical orbits around the Sun; it was then demonstrated mathematically by Newton to be the result of the Universal Law of Gravitation 

• The first part of most courses will be dedicated to establishing this relationship; that is, the law of gravitation and the resulting conic sections we see in orbital trajectories. Or, to put it another way, to establish the relationship between Kepler's Laws and Newton's Universal Law of Gravitation. 

• The derivation usually starts with the "Two Body Problem", in which you consider the relative motion of two bodies in space under only the influence of each other's gravitational pull. After a marathon of work on this problem, a special scenario is considered: the scenario where the one body vastly outweighs the other; for example, a spacecraft orbiting a planet. By this point most of the relationships have boiled down to simple equations, in particular the Orbit Equation. 

• A word to encourage beginners in this subject: the application of the resulting orbital equations is easier than their derivation. So Part 2 is easier than Part 1. 

Part 2:

• Usually the course will then turn its attention to applying Kepler's laws to space flight, focused on the scenario of a small mass (e.g. a spaceship) orbiting a big mass (e.g. a planet) and performing various maneuvers that might be required in a space mission

• Space flight is different from driving a car or flying an airplane, where the engine(s) are continually running. It is more like a game of celestial golf. Once launched into an initial orbit, a spacecraft can spend most of its time coasting. Every now and then its rocket engines may be fired to make a trajectory adjustment. 

• Planning the sequence of maneuvers to complete the flight objective without running out of fuel is the job of a mission planner. 

• The orbital elements and orbital state vector will be introduced, which are ways of measuring the position of an orbiting object in 3D space without Cartesian coordinates

Orbital Elements and Basic Maneuvers

To describe an orbit, here are some of the terms that will be encountered:

• eccentricity: how circular an orbit is. It's usually given symbol e so don't get it confused with Euler's number (2.718...) 

• periapsis: the lowest point in the orbit

• apoapsis: the highest point in the orbit 

• orbital plane: a flat plane in which the conic section of the orbit trajectory lies

• inclination: the angle at which the orbital plane intersects the equator of the body being orbited 

And some of the basic maneuvers covered will be: 

• changing the shape (eccentricity) of the orbit

• raising or lowering periapsis or apoapsis 

• Hohmann transfers

• Plane change maneuvers

• Phasing maneuvers 

Sandbox Practice

With the knowledge outlined above, you can actually already perform a lot of interesting missions on a PC simulator like Orbiter Space Flight Simulator. To list some examples:

• launch from a surface base to an orbiting space station or spaceship

• transfer from one orbiting space station to another 

• deorbit to land at a surface base 

• suborbital flights from one surface base to another surface base 

It's easiest to run your practice flights on bodies like the Moon that have no atmosphere, so that you can, continuing in the tradition of all high school physics textbooks, neglect air resistance. 

To emphasize how valuable these simulators or video games (call them what you want) are, I will share a comic I found on the internet:

In the next section we will list resources that can be used to study all these topics.