This is Arecibo Calling...

"Ironically, the globular cluster at which the signal was aimed won't be there when the message arrives. It will have moved well out of the way in the normal rotation of the galaxy." - It's the 25th anniversary of Earth's first attempt to phone E.T. Cornell Chronicle, Nov. 12, 1999

My estimate of the Arecibo transmission from a couple of years ago.
It looks like we may have missed...

In 1974 a ceremony was held to dedicate a major upgrade to the radio telescope at Arecibo Observatory. As part of the festivities the telescope was used to transmit a message towards Messier 13, the Great Globular Cluster of stars in the constellation Hercules.

"Scientists Hope to Reach Hypothetical Civilization in a Cluster of Stars" - New York Times, Nov. 20, 1974

Not really. This was not a serious scientific experiment that the scientists "hoped" would succeed. It would take over 20,000 years for the signal to reach the stars, and another 20,000 for a (potential) reply to return. Instead, the purpose was to draw attention to what the new transmitter was capable of. It was a publicity stunt.

They were pretty much just showing off. The signal would have been 10 million times the radio intensity emission as from our Sun. But, the audience and the press took it seriously. I have personally spoken to people who are awed and humbled by this attempt to shout at the universe.

But, what I really want to know is: "did we miss?" as the quote at the top suggests.

Objects in our Milky Way are in motion, orbiting around the galactic center. It appears that they aimed the telescope in the direction where we see M13 today but in the time that it takes for the signal to get there the cluster would have moved significantly. Perhaps outside of the telescope's beam.

A few years ago I did some back of the envelope calculations and created the image at the top showing the beam far enough from the center of the cluster that someone "out there" would find it difficult, if not impossible, to receive the signal. Assuming that they were pointing a telescope in the right direction during the correct 3 minute widow when it could be heard.

I couldn't remember where I got the numbers from for the above plot, and I wanted to double check to make sure the answer was reasonable. I looked it up and repeated the quick calculation. Here is my new plot.

Not quite a bull's eye, but there are a lot of stars in the beam.

Well, that is a very different answer. It is not quite a bull's eye, but certainly not a miss. I'm not surprised. It is terribly difficult to get accurate measurements of how far something would move in 20,000 years when the telescope was invented just 400 years ago. Depending on which source I use I could get a "hit" or a "miss" - so the verdict is uncertain.

I haven't reached the bottom of this rabbit hole. I'll need to do some more digging to find out what the spread of estimates is for distance and proper motion. For my own future reference the numbers that I used this time around are listed below.

• The cluster has a proper motion of 1.49 mas/yr in right ascension and 3.06 mas/yr in declination. (*)
• It is at a distance of 6.8 kpc, or about 22.2 thousand light years. (*)
• When transmitting the telescope has a beam width at half power of 2.7 arc minutes. (*)

I'll try to produce a better estimate of where the message lands before it arrives in about 22 millenia.

The images above are from the Digitized Sky Survey and were rendered using the Aladin Sky Atlas.

For my amateur radio friends the frequency used for the transmission was 2380 MHz with 20 MHz bandwidth and a 450 kilowatt transmitter. The gain of the antenna was 72 db. I have no idea if aliens send QSL cards and I can't even imagine how long it would take to reach Earth.

Update: July 1, 2017

I decided to recheck the calculations after reading a New York Times Magazine article titled Greetings, E.T. (Please Don’t Murder Us.) As promised three years ago here is the latest estimate.

• The proper motion is 1.79 mas/yr in right ascension and 7.07 mas/yr in declination. (*)

This is larger giving a total motion of 5.37 arc minutes for the cluster center compared to where the telescope was aimed. This is very similar to the initial estimate.

The latest recalculation.

The red circle shows the diameter at which the signal is 1/2 the power that it would be at the center of the beam, but there is also some power beyond the circle. I estimate that at the cluster center it would drop to 1/10 of full power and even lower on the other side.

A closeup of the target.

 
There are definitely cluster members within the "hotspot" of the beam, but only a small percentage of the total. The signal would also spill over into the dense core, but it would be much weaker. I would describe this as hitting the target, though not a bullseye. A large number of stars will receive a decent fraction of the transmitted energy.