Motion and Asymmetry

Then new Cosmos series is in progress.
I recorded and finished watching the original Cosmos by Carl Sagan.
The final episode is "We speak for Earth"
These were his closing comments:

"Our loyalties are to the species and the planet.
We speak for Earth.
Our obligation to survive and flourish is owed not just to ourselves, but also to that Cosmos, ancient and vast, from which we spring."

The new and the original series brought up the constant speed of light and the resulting theory of relativity and light and cosmos.

So I went back to the Twin paradox and learned or re-learned why it is not a paradox.

First :  It is true that two bodies in relative motion with no acceleration would experience a doppler shift in light where the spectrum is offset.  Sideways motion would be shown in a change in the doppler shift over time.

Any orbit or rotation would experience tidal forces.

Two bodies in relative motion would see length contraction and time dilation of the other of magnitude sqrt(1-v2/c2) or sqrt( (1+v/c) / (1-v/c) ).

If one changed direction due to acceleration a frame change in Minkowski space would occur, and would occur non-simultaneously for each.
Consider the twin paradox, there is an asymmetry of events.

This is explained by : http://en.wikipedia.org/wiki/Twin_paradox

Two twins.
One travels and returns.
Travel distance 4 light years.
Travel speed v=.8c (80% of light speed).
Magnitude of time dilation and length contraction is sqrt(1-4/5*4/5) = sqrt(9/25) = 3/5 = 60%.
So for the traveling twin d=.4*60%=2.4ly. T=10years*60%=6years.

Each agrees to send a signal to the other once per year showing their clock.

Home sends one signal per year for 10 years.

Traveling sends one signal per year for 6 years.

They each receive the others signal asynchrously as follows:

Home      receives 3 signals for first 9 years at rate of 1/3 per year.
                 then       3 signals for next 1 years at rate of 3 per year.

Traveling receives 1 signals for first 3 years at rate of 1/3 per year.
                  then       9 signals for next 3 years at rate of 3 per year


The asymmetry is show by the diagram



Red lines are red shifted.  Blue lines are blue shifted.  (The rates shown are higher than the example but show the relative frequency of each.)