Measuring relative speeds in SR Suppose I have a galactic ruler spanned from earth to Alpha Centauri. With marked units, so one can read off the distance starting with 0 at earth until 4 light-years at Alpha Centauri.
Now according to relativity, if I fly with my spaceship at 97% of the speed of light from earth to Alpha Centauri this will only take about 1 year.
At first glance, this would seem I am going 4 lightyears within a year to contradict the no faster than light travel. However, this is explained by length contraction. So this means basically that from my frame of reference I cannot trust the hatch marks of the ruler at all.
This brings me to my question:
How would I even measure the relative speed to the ruler if I cannot trust these lengths? The same goes for a person on earth?
Both parties would measure the same relative speed as can be computed! from SR. But how would we measure it?
The fact that both parties measure the same value for the relative speed - is this an assumption that goes into deriving SR or is it a consequence as well?
 A: Usually the easiest way to measure speed is with Doppler radar. For an inertial observer this gives the same velocity as you would get with a system of rods at rest and synchronized clocks.
A: You send a light signal forwards towards a particular mark on the giant ruler at time, say, $t_1$ seconds. At  $t_2$ seconds you see the mark illuminated by your light flash. So the round trip there and back took $t_2-t_1$ .
The flashes take the same time on each leg because you are stationary, so you know the mark was $c(t_2-t_1)/2$ metres away at time $(t_2+t_1)/2$.
Wait a short but arbitrary time to $t_3$, then send another flash to the same mark, and it comes back at  $t_4$. Now you have a second distance measurement, $c(t_4-t_3)/2$, presumably shorter than the first as the mark is moving towards you, at a later time $(t_4+t_3)/2$.  The ratio of the differences gives you the velocity.
A: Let's say that to an observer on earth, at rest with respect to the ruler, you pass mark $x_1$ at time $t_1$ and mark $x_2$ at time $t_2$. So he measures you speed as ($x_2$-$x_1$)/($t_2$-$t_1$).
Let's say you do the same with the same two marks. So you would pass $x_1'$ at time $t_1'$ and $x_2'$ and time $t_2'$ and measure your speed relative to the ruler as ($x_2'$-$x_1'$)/($t_2'$-$t_1'$).
As the ruler is at rest in the earth's frame of reference, as you say it's length is contracted in your moving frame. So ($x_2'$-$x_1'$) = ($x_2$-$x_1$)/$\gamma$. But we have to also take account of time dilation. Your time measurement, ($t_2'$-$t_1'$), is a proper time interval as your clock is at rest in your frame of reference. So we have ($t_2'$-$t_1'$) = ($t_2$-$t_1$)/$\gamma$.
As a result, ($x_2'$-$x_1'$)/($t_2'$-$t_1'$) will equal ($x_2$-$x_1$)/($t_2$-$t_1$) and both you and the earth observer will measure the same relative speed.
Here $\gamma$ is the usual $1/\sqrt(1-v^2/c^2)$.
