I went to my Starry Night Software program and cruised over to Tranquility Base. I punched in the date and time of the simulated Eagle launch; 07/21/1969 at 17:54 UT. My software gave 1 hour and 7.8 minutes as the "now" Julian based solution for the right right ascension(RA) of planet earth at that time and date("now", I presume refers to 07/21/1969). I converted to conventional decimal form and found 0.62037.
This is from the Apollo Lunar Surface Journal;
"121:08:05 Evans: And when the LM does his P22 on your transponder, well then, that'll be our last shot at the LM's position.
121:08:14 Collins: Rog. Understand. (Pause)
The LM crew will track the Command Module as it passes over the landing site for the last time prior to launch and, with the Command Module orbit well known, in principle the tracking data will help pin down the landing site. With the information available a half hour before launch - including the crew's descriptions of West Crater and Little West Crater and the returns from the laser reflectometer - at 123:55:23, Ron gives Mike a final LM location of J.5/7.7, which is only about 200 meters from the actual landing site at J.65/7.54. Mike will be too busy during that pass over the landing site to look for the descent stage."
So for the simulated launch, Collins got .5 as the RA and it ultimately proved to be .65. I got a right ascension figure of .620. So I did better with my software than that initial J.5 estimate for the right ascension that appears in the Voice Transcript record. Of course the numbers at this point do not seem to be all that critical anyway. The reason that I say this is because it would seem these are the numbers, the Julian system based numbers, the very numbers "they" are using for the launch. So for now, let's acknowledge that simple fact and see where it leads.
So the astronauts are sighting the earth! That is where the Julian figures come from. Which makes sense, because if one determines the right ascension and the declination for the earth on 07/21/1969 at 17:54 UT, the time of the simulated Eagle launch, then one would know the position of the Eagle, EXACTLY. Well exactly if you had good equipment. And in the pretend Apollo world, they did have good pretend equipment. Well it was real equipment, but they actually did not sight the earth and determine its right ascension and declination from the surface of the moon. So they have good pretend precision. Let's leave it at that.