Posted on 03/22/2021 7:55:09 AM PDT by Red Badger
A 3 dimensional velocity vector would be (speed in x direction, speed in y direction, speed in z direction), if the 3 spatial dimensions are (x,y,z).
More mathematically, instead of speed in x direction, you would say change of location in the x direction with respect to time.
So, velocity would be (dx/dt, dy/dt, dz/dt), where d essentially means ‘change in’.
To summarize, what they are saying as that they know not only your current position in space, they also know how fast you are moving in each of the 3 dimensions, x,y,z, where x is left to right, y is forward-backward, and z is up-down.
Cosmos crashed and burned before getting past Saturn. You can see the debris plume on Europa.
Right, I was focusing on weakness/degredation of signal, which relays can solve.
Still sounds like trajectory to me. Guess I don’t have the brain power to get it.
It is a trajectory, but it includes speed as well as direction.
All blackholes are wormholes but all wormholes are not blackholes.
You just made my point by describing x,y,z dimensions. How fast you're traveling within those known dimensions is called speed, no matter the angle or trajectory. If they want to call velocity by another term, fine, but most believe it to be the speed of a given object.
So, is the speed of light a velocity or just 186,000 miles per second as in speed? Yes, even light can be bent as in a prism or other within our perception and calculated physics. Maybe that's where they get the other 3 dimensions. This is all probably beyond my little brainpan.
Speed in a specified direction is velocity, as velocity always includes direction. In space, which is 3-dimensional, you have to say how fast you are moving in each of those 3 spatial dimensions. That is a 3-dimensional velocity (speed in x, speed in y, speed in z). The ‘speed’ in the direction of travel is the magnitude of the 3-dimensional vector (square root of the sum of the squares of the speed in each direction).
speed in x, speed in y, speed in z is a 3-dimensional velocity vector. You can compute the angle of travel from those values by trigonometry.
Light is another thing altogether and requires relativistic physics. It is just weird.
I think I just read 3 of his "juvenile" novels (when in grade school) so they were tamer: Red Planet, Tunnel in the Sky, and Time for the Stars. The last is the one using the concept of telepathy. In Tunnel in the Sky one of the characters is a Zulu woman--when I read that I don't think I realized that that meant she was black.
It’s kind of a joke in parts of the SciFi readers’ community. After SIASL Heinlein kind of went off the deep end. ‘Time Enough for Love” is a real slog to get through with Lazarus Long very obviously being Heinlein’s alter ego. He became almost as unreadable as Asimov’s later output.
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).
I thought Farnhams Freehold was odd as well.
Oops, not due northeast, but at 53.13° wrt the east-west axis... a little trig mistake there.
Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.