In Orbit You Have to Slow Down to Speed Up

If you watch sci-fi movies, you’d deliberation that flying a spaceship is conscionable for illustration driving a somewhat much analyzable car (or a Winnebago successful Spaceballs). And George Lucas gave america those galactic battles pinch pilots who look for illustration they’re flying combatant jets connected Earth.

Well, bad news: Space is really, really different. In particular, moving a conveyance successful orbit astir Earth is measurement much analyzable than that. The maneuvers you mightiness make pinch a level sometimes person nan other effect successful orbit.

To spot what I mean, we’ll first conscionable drawback immoderate basal physics and build ourselves a small exemplary of orbital mechanics, and past I person immoderate cool simulations of an attempted docking maneuver. Read on!

Circular Orbits

Imagine flying successful a information orbit astir Earth. There are 3 large physics ideas we request to understand this benignant of motion. First, centripetal acceleration. Recall that acceleration is simply a measurement of really accelerated nan velocity of an entity changes.

But velocity isn’t conscionable speed, it’s velocity successful a peculiar direction—in different words, it’s a vector. If an entity is moving successful a circle, its guidance is perpetually changing, which intends it’s perpetually accelerating, moreover if its velocity is constant!

The guidance of this acceleration is toward nan halfway of nan circle. (“Centripetal” intends center-pointing.) The magnitude of nan acceleration depends connected some nan magnitude of nan velocity (v), i.e., nan speed, and nan radius (r) of nan circle. This gives nan pursuing equation: