No ET! Ever?

[Jehanne]

That's false:



And, the above is not accounting for the proper motion of stars throughout the Galaxy.  And, so, if you wanted to send a message from 100 light-years away using a directional antenna, here is the formula that you would use:



After that, you (or I), am going to have to convert lumens to watts:



Assuming 15 lm/watt, here is what I get:

1 light-year = 9460730472580800 meters

100 light years = 946,073,047,258,080,000 meters

1,000,000,000 watts = 15,000,000,000 lumens

D ^ 2 = 8.950542107481892730061252864e+35 meters squared

B = L / (4 * pi * D ^ 2)

   = 1.333619862188475648988125129197e-27 lumens / meter squared

   = 8.8907990812565043265875008613135e-29 Watts / meter squared

Sensitivity of Arecibo radio receiver:  10−26 watts per square meter.

And, so, Arecibo may be able to pick-up a very strong signal if it was looking at the right spot and the exact moment in time.

That picture you show reflects the precession of equinox.   It has nothing to do with earth's motion or proper motions of target stars and therefore does nothing to increase the difficulties of targeted transmission.

Your original claim was, "the stars are in pretty much the same positions as when they were observed by the Greeks / Ancient Chinese." (emphasis mine).

In any case, the proper motion of the Sun around the center of the Galaxy (at nearly 700 times the speed of sound), would be sufficient to cause a narrow band radio transmission to miss the Earth, not to mention the Earth's motion around the Sun (around 60 times the speed of sound).