Question on Time Dilation for Traveling Observers

[dako7]

I just had a quick question on time dilation that I'm stumped on.

There are three observers: two are traveling on separate ships traveling close to the speed of light (their speeds are the same) in opposite directions parallel to each other. One observer is standing still on a space station in between both ships. There are three large clocks, one connected to one ship, one connected to the other, and one connected to the space station. The observer on one of the ships takes out some binoculars (assuming they are able to) and looks the two other clocks in comparison to his own. What will they see?

Well, this observer would notice that the clock on the space station is moving much slower than his own, but what would they see the other ship's clock doing? Because it is traveling at the same speed, albeit in the opposite direction, would the clock be running at the same speed? Or slower?

 

[phinds]

I just had a quick question on time dilation that I'm stumped on.

There are three observers: two are traveling on separate ships traveling close to the speed of light (their speeds are the same) in opposite directions parallel to each other. One observer is standing still on a space station in between both ships. There are three large clocks, one connected to one ship, one connected to the other, and one connected to the space station. The observer on one of the ships takes out some binoculars (assuming they are able to) and looks the two other clocks in comparison to his own. What will they see?

Well, this observer would notice that the clock on the space station is moving much slower than his own, but what would they see the other ship's clock doing? Because it is traveling at the same speed, albeit in the opposite direction, would the clock be running at the same speed? Or slower?

Each observer has his own frame of reference and would see the other clocks as running slower than his own.

 

[dako7]

Awesome, thank you so much. :)

 

[ghwellsjr]

Let's call the speed of each ship relative to the station β, a fraction of the speed of light. Then each ship will see the station's clock running slower according to the Relativistic Doppler Factor:

√[(1-β)/(1+β)]

And they will each see the other ship's clock running slower by the square of this factor or simply:

(1-β)/(1+β)

And the station will see each ship's clock running slower by the first factor.

EDIT: This is assuming that the ships and the station are in line with one another and that the ships are traveling away from the station.