Signals sent during relativistic space travel

AI Thread Summary
Amelia's journey to a planet 12 light-years away at 0.6c results in a contracted distance of 9.6 light-years, taking her 32 years in total. During her trip, Earth receives signals at a rate affected by the relativistic Doppler effect, receiving 0.5 signals per year on the way there and 2 signals per year on the return. The initial calculation suggested 40 signals, but this was incorrect due to not properly accounting for time dilation. The correct total, considering time dilation, is 32 signals, as she sends one signal each year during her 32-year journey. The discussion highlights the complexities of relativistic effects on time and signal reception.
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Homework Statement


Suppose rocket traveler Amelia has a clock made on Earth. She flies to and back from a planet 12 light-years away (as measured from rest with respect to Earth) from Earth at a speed of 0.6c. Every year she sends a signal to Earth. How many signals does Earth receive by the time she gets back?


Homework Equations


f = f'*[sqrt((1-u/c)/(1+u/c))]
(relativistic Doppler shift)
L = Lo*sqrt(1-u^2/c^2)
(relativistic length contraction)

The Attempt at a Solution


The distance to the planet for Amelia is shorter than 12 light-years. It is 9.6 light-years. So she takes 16 years (as she measures them) to get there and 16 to get back.

On the way there, by the relativistic Doppler equation I know that Earth receives her signals at a rate of 0.5 signals every Amelia-year, and on her way back Earth receives her signals at a rate of 2 signals every Amelia-year.

There are 16 Amelia-years in the trip to the planet, and 16 in the trip from the planet. So the total number of signals is

16*0.5 + 16*2 = 8 + 32 = 40.

But that is wrong, because it should be 32 signals, if she sent one every year, since her trip lasted 32 years to her.

How am I doing this wrong?
(Thanks.)
 
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You calculated the distance in Amelia's frame of reference but did not account for the slowing of time in her frame.
 
Ta-Da! Thank you, Halls of Ivy, that was kind of you. That's a load off my mind.
 
I'm dabbling over the same question but how would that time dilation effect be? Would it be affecting the 32 years time? or, since the Earth has a relativistic speed of 0.6c relative to Amelia, should we consider the effect on Earth's time?

Thanks
 
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