If you watch sci-fi movies, you’d think that flying a spaceship is just like driving a slightly more complicated car (or a Winnebago in Spaceballs). And George Lucas gave us those galactic battles with pilots who look like they’re flying fighter jets on Earth.
Well, bad news: Space is really, really different. In particular, moving a vehicle in orbit around Earth is way more complicated than that. The maneuvers you might make with a plane sometimes have the opposite effect in orbit.
To see what I mean, we’ll first just grab some basic physics and build ourselves a little model of orbital mechanics, and then I have some cool simulations of an attempted docking maneuver. Read on!
Imagine flying in a circular orbit around Earth. There are three big physics ideas we need to understand this kind of motion. First, centripetal acceleration. Recall that acceleration is a measure of how fast the velocity of an object changes.
But velocity isn’t just speed, it’s speed in a particular direction—in other words, it’s a vector. If an object is moving in a circle, its direction is constantly changing, which means it’s constantly accelerating, even if its speed is constant!
The direction of this acceleration is toward the center of the circle. (“Centripetal” means center-pointing.) The magnitude of the acceleration depends on both the magnitude of the velocity (v), i.e., the speed, and the radius (r) of the circle. This gives the following equation:
Courtesy of Rhett Allen