I never heard of 3 dimensions of velocity. Can someone explain that to a layman? I always thought velocity meant speed, whether initial or continuous or decaying. Are those the 3 dimensions? If so, the word dimension has taken on new meaning to me. If not, then I would call it a varying (degree) of motion.
Velocity involves speed AND direction. So you need the x,y,z component of the vector.
Is that like the 6 Degrees of Kevin Bacon?...............
To navigate “a spacecraft needs to be able to determine its position and velocity.”
Technically, speed and velocity are different. Your velocity is your speed plus your direction of travel. In other words, velocity gives you a little more information than your speed alone.
It’s easy to see that when navigating to a specific point on the map, knowing your current position and velocity are more useful than just knowing your position and raw speed... You’re at 9th and Elm and walking at 5 mph... So what? Are you getting closer to your desired destination or farther away? You have no idea without knowing your velocity.
Velocity is even more important in deep space, where things aren’t laid out in a nice grid pattern like city streets (that can give you all kinds of hints about which direction you’re going).
Space dimensions: Sticking to earth’s surface, you could designate your position with two numbers... e.g., you could say you’re one mile east and one mile south of your house and everyone would know exactly where you were, 1.414 miles southeast of your house.
Velocity dimensions: Similarly, you could designate your velocity by saying you were travelling at 3 mph east and 4 mph north and everyone would know you were travelling at 5 mph northeast.
Congrats, you’ve just worked out your coordinates in four dimensions, two in space (1,1), and two in velocity (3,4).