Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 377

Position

The position of an object is relative in that it only makes sense when we relate it to another object, when we say it is, for example, x metres AWAY FROM another object (and give the direction); but is it relative in any other sense?

Right now my position, my location, could be stated in terms of latitude and longitude (or some other system). So I could be, say, y metres south of the north pole and x metres east of the prime meridian, or something like that (also, zero metres from the surface of the Earth).

If, for the sake of discussion, we agree on the coordinate system, which pole counts as north, which meridian is prime, and which directions are positive, which are negative, etc, etc; is there then something objective, or absolute, about my position? Is my position (x) then the same for me as it is for you  wherever you are, and the same for an astronaut on the Moon, or a rock on Mars, etc (if we all agree on the co-ordinate system)?

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,702

Re: Position

The latitude/longitude coordinate system was devised specifically for navigating on the surface of the Earth.  You can determine your latitude by observing the angle between the Pole star and the horizontal. Latitude is harder; if you can work out the right ascension amd declination of a star and you know the time and date, you can calculate the longitude, but not much help if you're on the Moon or Mars.  No one has devised a coordinate system for the Solar System yet. 

So maybe you should make one.  World fame awaits.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 377

Re: Position

Thanks, Bob.

Even though it’s not much help if you’re on the Moon or Mars, would you, on either of those, agree on my position, as something objective, something absolute?

Could the coordinate system for the Solar System simply be a vast x,y,z coordinate grid, with some agreed upon reference points?
What if we all agreed that the Sun’s north pole was the origin?

(Nb; I’m aware that the planets etc are forever changing position, etc, so I’m not thinking in terms of a practical system, to aid navigation; I’m thinking in terms of a thought experiment, to help me understand the notion of ‘position’ and in what sense/s it is relative.)

So if we imagined the Solar System at any given moment, i.e, we freeze-framed the ‘film’ of it, to stop everything (annoyingly ) moving around, we could then say I’m 90 point x million miles (insert direction, which would be agreed upon) from the origin (the Sun’s north pole).

And Astronaut A would be 90 point x million miles (insert direction) from the origin.

And you, Commander Bob, of Mars Fleet 25, would be, at Mars’s north pole, 140 point x million miles (insert direction) from me on Earth.
Etc, etc.

Would each of our positions then be objective, absolute, in those frozen slices of time, similar to points M,A,B (Me, Astronaut, Bob) on an x,y,z coordinate grid in a high school maths text book?

Last edited by paulb203 (2025-02-22 23:12:00)

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Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,702

Re: Position

What you describe sounds like a Galilean frame of reference and I'd think it would  work.  You could add equations that accurately give the position in orbit for the planets and moons and so we'd have a way of taking account of all the movements.  I'm not sure if Einstein's theory messes with that nor if the uncertainty principle throws a spanner in, but something like that got astronauts to the Moon and back, and also all those exploration rockets that have gone out to the outer planets.

Is this the moment to remind you that the Sun is part of a spiral arm of the Galaxy which is both spinning and moving through space?  It's a similar dilemma to the one that says the Earth is sitting on the back of a giant turtle.  And what holds the turtle? Another larger one. And what holds that?  "Oh, you don't get me like that", said the lady,"It's turtles all the way down". *

Bob

*https://apilgriminnarnia.com/2014/03/26/turtles/

Commander Bob, of Mars Fleet 25

Thanks for the promotion.  Do I get a smart uniform?

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 377

Re: Position

Thanks, Bob.

I'm not sure if Einstein or Uncertainty messes with it either. But it is a frozen frame of a slice of space-time we're talking about so movement doesn't come into it. And even if we can't know the exact position of something etc, that might not matter either, because I'm trying to ascertain if the positions of things are absolute, not if we can know what those positions are. Reminder; it's a thought experiment.

One of the reasons I'm asking;

This came up for me recently.

I'm on a plane which is flying across the sky. I throw a ball up and wait for it to return to my hand. Apparently that ball, in my reference frame, travels in a straight line (up, then back down into my hand, in a straight line). But for Commander Bob (not in his smart uniform as its his day off) on a mountain watching the ball through a telescope, the ball describes a parabola. Both are true apparently.

Which got me wondering about the ball's various positions, as opposed to it's motion.

Is the following correct.

The ball starts at position a, and ends up at position b. Absolutely.

Or;

The ball starts at position a, and ends up at position b, FOR ME. But it's positions are different for you, Commander B.

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Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,702

Re: Position

Both are true apparently.

  Yes, that's right.  It's all to do with frames of reference.  From the plane you will see me apparently moving backwards along with the ground, but I think I'm stationary.

So I'll see the ball end up at B as well.

So "The ball starts at position a, and ends up at position b. Absolutely." is the correct version.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 377

Re: Position

Thanks, Bob.

“From the plane you will see me apparently moving backwards along with the ground, but I think I'm stationary.”

Interesting that you use ‘apparently’ in that sentence. Why ‘apparently’? I was getting the impression that it’s more than just apparently, it was simply the reality of the situation; that in my reference frame you ARE moving backwards. And in your reference frame I AM moving forwards. Have I got that wrong? Is it only 'apparently'? Or are you using 'apparently' for 'relatively'?

“So "The ball starts at position a, and ends up at position b. Absolutely." is the correct version.”
Yet when I join up the ab dots I get a straight line; you get a parabola (?).

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Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,702

Re: Position

Every morning the Sun rises in the East and in the evening sets in the west. The Sun appears to move across the sky.  It's all relative.

If you set on a pendulum swinging to and fro you trace out a certain back and forth movement.  But if that pendulum is itself supported by another pendulum which is also swinging the resultant motion is surprising and I think you'll enjoy discovering what it is .

https://www.youtube.com/watch?v=uPbzhxYTioM

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 377

Re: Position

Thanks, Bob.
I enjoyed the pendulum video.

Relative (apparent?) motion is still a bit of a head scratcher.

But I guess that's physics for you

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Prioritise. Persevere. No pain, no gain.