# Clock watching in orbit

#### Spruce

When an accelerating astronaut is in very close orbit around a stationary observer the astronaut will see the observer's clock run fast. From this fact, I conclude the astronaut will see any light sent from the observer as blue-shifted. From the observer's view, everything is reversed i.e. the accelerating astronaut's clock is seen to run slow, and light from the astronaut is seen as red-shifted. Does anyone agree? I can't find any answers in textbooks.

#### Spruce

When an accelerating astronaut is in very close orbit around a stationary observer the astronaut will see the observer's clock run fast. From this fact, I conclude the astronaut will see any light sent from the observer as blue-shifted. From the observer's view, everything is reversed i.e. the accelerating astronaut's clock is seen to run slow, and light from the astronaut is seen as red-shifted. Does anyone agree? I can't find any answers in textbooks.
Wow! This question has been sitting unloved for 11 months. Well everybody, a published writer of physics textbooks makes this very case in 'Do Moving Clocks Always Run Slowly' http://math.ucr.edu/home/baez/physics/Relativity/SR/movingClocks.html

You might say the observer sees the astronaut in slow motion (while deducing length contraction for the astronaut). Conversely the astronaut sees the observer in fast motion (while deducing length EXPANSION for the observer).

I wonder why this example is so hard to find in textbooks? Do the facts confuse physicists?

#### ChipB

PHF Helper
I think perhaps the reason why you don't find this in text books is because it's an application of general relativity, whereas most physics texts used by undergraduates in college limit themselves to special relativity only.

#### Spruce

I think perhaps the reason why you don't find this in text books is because it's an application of general relativity, whereas most physics texts used by undergraduates in college limit themselves to special relativity only.
This is general relativity? Indulge me while I think freely. Hmmm.

Suppose the clock we are watching from our stationary position is our familiar "light-clock". As it spins, the double diagonal path traveled by a photon between its mirrors "lengthens". Further suppose that when the photon completes each cycle of reflection it is "split" and sent to us. We should receive a lower frequency of photons, due to special (not general) relativity. Therefore the light will be red -shifted.

It would be interesting to find out if a spinning light source appears red-shifted. Perhaps that question is for general relativity. Hopefully the answer is that it does, to ensure consistency with special relativity.

#### ChipB

PHF Helper
This is general relativity? Indulge me while I think freely. Hmmm.

Suppose the clock we are watching from our stationary position is our familiar "light-clock". As it spins, the double diagonal path traveled by a photon between its mirrors "lengthens". Further suppose that when the photon completes each cycle of reflection it is "split" and sent to us. We should receive a lower frequency of photons, due to special (not general) relativity. Therefore the light will be red -shifted.
That's what we on the ground in our inertial frame of reference would see, as typically described in introductory texts for special relativity. But it ignores the effect of gravitational blue-shifting as described in general relativity, so it's not clear what the final result actually is.

Here's a nice article on gravitational red-shifting and blue-shifting. In essence an observe who is "uphill" from the light source (at higher gravitational potential) perceives that it's red-shifted while an observer "downhill" sees it blue-shifted.
http://en.wikipedia.org/wiki/Gravitational_redshift

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#### Spruce

But it ignores the effect of gravitational blue-shifting as described in general relativity, so it's not clear what the final result actually is.
Nice Wikipedia article with a nice image.

But yes, the perceived frequency as viewed in an inertial frame will also depend on the mass of the light-clock itself, as well as its rotational speed. For example, if the light-clock has the mass of a planet then the final perceived wavelength will be even longer, i.e. even more red-shifted. Conversely, if the observer is the mass of a planet the final perceived wavelength will be a little shorter i.e. less red-shifted.

I just think it's neat how frequency and wavelength can be "quantized" by the cycle rate of a light-clock, when mass is considered negligible. It makes me visualise special relativity as "general relativity minus the mass".