Question about relativity

[discountbrains]

Suppose there are two spaceships A and B both
traveling from planet X to planet Yand A is ahead
of B. A and B are both traveling at 0.999 times the
speed of light (or whatever-very close to the speed
of light) and the distance between them is 1/3 the
distance from X to Y.
We know that from Einstein' s equations

... presumably the equations for special relativity.

that there would be a contraction in the distance
from A to B in the direction they are traveling.

... but still 1/3 ...

Now the distance from X to Y is the sum of the
(distance from X to B) + (the distance from B to
A) + (the distance from A to Y) which is less than
the distance from planet X to planet Y to an observer
on planet Z stationary to X and Y.

... or just leave them on X or Y ...

So, which is it: the correct distance from planets
X to Y is what those on planet Z see or is it what
someone on one of the spaceships observes?

Yes.  "Correct" is what one measures, and a moving observer, using any of
the available methods, gets a shorter distance than the observer at rest.

How could they be both?

That is why it is called "relativity".
How can you view an entire skyscraper between your thumb and index finger?
Isn't it dozens of stories high?  So is it viewable in a few inches, or is
it dozens of stories?
How can two different people take two different times to get from X to Y?
Does the path taken make any difference?

I think I might have just thought of the answer to my own question: Without going into the math details it looks like the distance observed from the spaceships from A to Y and from B to X would be greater than they actually are. Just as a trick with math produced this paradox the same math trick could be used to calculate these distances and the sum of the distances would stay constant.

So. I didn't come up with some astounding paradox.

[discountbrains]

Suppose there are two spaceships A and B both
traveling from planet X to planet Yand A is ahead
of B. A and B are both traveling at 0.999 times the
speed of light (or whatever-very close to the speed
of light) and the distance between them is 1/3 the
distance from X to Y.
We know that from Einstein' s equations

... presumably the equations for special relativity.

that there would be a contraction in the distance
from A to B in the direction they are traveling.

... but still 1/3 ...

Now the distance from X to Y is the sum of the
(distance from X to B) + (the distance from B to
A) + (the distance from A to Y) which is less than
the distance from planet X to planet Y to an observer
on planet Z stationary to X and Y.

... or just leave them on X or Y ...

So, which is it: the correct distance from planets
X to Y is what those on planet Z see or is it what
someone on one of the spaceships observes?

Yes.  "Correct" is what one measures, and a moving observer, using any of
the available methods, gets a shorter distance than the observer at rest.

How could they be both?

That is why it is called "relativity".
How can you view an entire skyscraper between your thumb and index finger?
Isn't it dozens of stories high?  So is it viewable in a few inches, or is
it dozens of stories?
How can two different people take two different times to get from X to Y?
Does the path taken make any difference?
"Spacetime Physics", by Taylor and Wheeler.
David A. Smith

No, try Harry Potter by J. K. Rowling, it's more informative.- Hide quoted text -

I think I found the answer to my question myself. Without giving the
math details it looks like by using the same math trick as before one
can show that the distance from A to Y and B to X would also appear to
by greater than from an observer at rest and the sum of the distances
would remain constant.