Different Simultaneity for telescopes in space and earth?

[ofirg]

I was just wondering. According to Lorentz transformations, if two events are simultaneous in one reference frame, they will generally not be simultaneous in another.
The time difference that I get between the two events in the other reference frame is

$\Delta t^{`} = \gamma\beta\Delta x \approx {\Large \frac{\beta^{3}}{2}} \Delta x$

Where the approximation assumes $\beta \ll 1$

Now, for space born objects $\beta \approx 3 \cdot 10^{-5}$ so

$\Delta t^{`} \approx 10^{-14} \Delta x$ where $\Delta x$ is in light time.

If one takes a distance of 100 Mpc then $\Delta t^{`} \approx 10 sec$

So If I have two distant transient sources that give a signal at more or less the same time on earth, a space telescope will observe them at a noticeable time difference?

 

[Orodruin]

No. You can never observe distant sources as they are "simultaneously" to the observation due to light travel time. Telescopes at the same event in motion wrt each other will observe distant objects in the same state (modulo redshifts and aberration).

 

[ofirg]

Thanks For the reply.

I see now that I mixed up the times that the telescopes will assign to the events themselves ( the time that the sources output the signal) which will be different And the time of observation, which will be the same.