In orbit you have to slow down to speed up

If you are watching In science fiction movies, you might think that flying on a spaceship is just like driving a more complicated car (or a Winnebago in… Space balls). George Lucas gave us those galactic battles with pilots who look like they are flying fighter planes on the ground.

Well, the bad news: space is really different. In particular, moving a vehicle into Earth orbit is much more complicated than that. Sometimes the maneuvers you might make with the plane have the opposite effect in orbit.

To understand what I mean, we’ll first take some basic physics and build ourselves a little model of orbital mechanics, and then I’ll do some fancy simulations of trying a docking maneuver. Read on!

Circular orbits

Imagine that you are flying in a circular orbit around the Earth. There are three big physics ideas we need to understand this type of motion. Firstly, Gravitational acceleration. Remember, acceleration is a measure of how quickly an object’s speed changes.

But speed is not just speed, it is specifically speed direction– In other words, it’s a vector. If an object is moving in a circle, its direction is constantly changing, which means it is constantly accelerating, even if its speed is constant!

The direction of this acceleration is towards the center of the circle. (“Centrifugal” means pointing to the center.) The magnitude of the acceleration depends on the magnitude of the velocity (T)(i.e. speed) and radius (p) from the circle. This gives the following equation:

Courtesy of Rhett Allen