Can Atomic Clocks Accurately Measure Time in Accelerating Bodies?

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mrzero
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First I'm not a native English speaker so sorry for grammar errors .

Ok let's start my hobby is to learn things and I tried to study relativity while I where reading some example of time dilation in atomic clocks. However I remembered something the speed of a electromagnetic wave is equal to C (speed of light in a vacuum). Since Atomic clock use EM radiation from a atom to measure time is such a clock and the clock starts accelerating the EMW impulse will travel slower or faster to the recover depending on the vector of EMW movement to the vector of acceleration. And using a EMW based clock( atomic clock) co measure any thing becomes pointless. I mean if the recover is "running away" from the EMW then the clock will tick slower and if its running to meat the EMW the clock tics faster.

My question is this how can any normal person knowing that the speed of light (and EMW) is constant use a atomic clock to measure time in a accelerating body (or am I miss understanding something if yes please correct me).
 
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Thank you for the info :D.

I have a similar question regarding this relativistic Doppler effect :

For my understanding you can use this relativistic Doppler effect to measure the velocity and vector of the object such EMV emitters are placed in (similar to gyroscopes and in all 8 or more directions ) am I right about this ?