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We can use the "new moon" -- the transition between waning and waxing -- to not only find the beginning of the new month, but also the beginning of the new year. The new year was the month starting the first day of Nisannu, just like the Hebrew "sacred" new year was started on the first day of Nisan.
The new year started Nisannu the 1st, and the month Nisannu was the month that started closest to the spring equinox. Therefore the first full moon after the spring equinox should always be within a day of Nisan 14. That's because there are 29.5 days in a lunar month, so months typically alternated between 29 and 30 days for an average of 29.5. The middle of a 29-day month could land closer to the 14th, and the middle of a 30-day month could land closer to the 15th. Also, it depended on whether there was a delay in actually seeing the new moon sliver which could easily delay by a day.
Note the Watchtower's comment on Nisan 14 here:
*** w76 2/1 p. 73 “Keep Doing This in Remembrance of Me” ***
According to our present method of calculation, the Memorial date approximates the nearest full moon after the spring equinox. For example, in 1975 the Memorial date, as calculated fourteen days from the new moon (nearest the spring equinox) visible in Jerusalem, was Thursday, March 27, after sundown. Appropriately, there was also a full moon on Thursday, March 27, 1975. The date for Memorial in 1976, calculated by our present method, falls on Wednesday, April 14, after sundown. The full moon also occurs on this same date. So if, in the future, any of Jehovah’s people should be out of touch with the governing body, they could determine the Memorial date with fair accuracy from local calendars that show the first full moon after the spring equinox. The celebration would then take place after sundown of the day on which the full moon occurs.
So a fun experiment is to see if you can use just observation in the software program to find the date of the new year. You can probably find Nisannu just by looking for the exact time the phase changes from waning to waxing (the new sliver) and find the one closest to the Spring Equinox. That always puts the first full moon after the spring equinox in March or April, and very rarely, early in May.
If you scroll through the dates, you find the first new moon is on January 23, -567. The next one is on February 22nd. Still too early. The next one is on March 23rd. A good candidate. And the next one is on April 23rd. Also a good candidate. And we have to know something about Babylonian observations to figure out which one of those last two is the best candidate. But we can take a good guess and see if it matches the scholars later. 
After guessing, we can check it against page 26 of Parker and Dubberstein: https://isac.uchicago.edu/sites/default/files/uploads/shared/docs/saoc24.pdf
P & D had the advantage of checking hundreds of dated clay tablets to be able to know which years had the leap month, and that produced a much more sure version of the Babylonian calendar. 
What Stellarium will let you do is see how much the sun's glare might have interfered with the ability to see a new moon sliver. If it couldn't be seen, the month started the next day. Also, they new it was due if the previous month had 30 days. But some months would have only 29 which would pretty much mean the next month should have 30.

@xero, i don't know how far along you are but Stellarium is a great tool for this, and I see you are using the Mul.Apin Sky Culture. It saves time from having to keep track of the Babylonian star names yourself.
I suspect there will be some others here who might try the Stellarium software, too. If so, they should know that it's good to get more than use the online web version. It's great, but the desktop version gives you everything you need.
It's free. Although you are allowed to donate. 
You can download and install the latest version 23.3 or 23.4 from here: https://stellarium.org/release/2023/09/25/stellarium-23.3.html
Once installed, you will want to change the location to somewhere near Babylon. The city @xero picked is below:

Once you install it, you can hover your mouse over the bottom left edge of the screen and select the icon just under the clock:
"Sky and Viewing Options [F4]"
Then select "Sky Culture" from the top of that newly opened window, and pick Babylonian -- MUL.APIN:

Now when you close that window, pick the clock icon you saw earlier. 
Start with any BCE date you like, but I think most people will try either 588 BCE or 568 BCE if the first thing they want to check is VAT 4956:
Along the bottom of the screen, if you hover the mouse over the bottom left edge of the screen you will see some other options:

The first two highlighted ones will toggle the borders of the constellations on, which is helpful. The second one toggles the names on and off. But you will also probably want to experiment with the imagery and the horizon/landscape settings which you can make disappear or make  almost transparent. You can also use the arrow keys and Page Up and Page Down to zoom in and out and turn the orientation so that you are facing due West which is my favorite place to start. 
The last thing to do after orienting your screen is to go back to that Clock icon and set the year, month, day, and time. If you want to check 568 BCE first, then type the following into the date and time boxes. For purposes of VAT 4956 I would start on January 1, 568 BCE. In astronomy dates 568 BCE is written as -567, due to the zero year issue. So that's actually written as -567:01:01 -- 00:00:01. You don't have to spin it all the way back; you can type numbers into the fields. Here I will set it for 4:45 in the afternoon.

16:45 (4:45pm) is pretty close to sundown on January 1, but you can "spin" the dial forward to just after sundown so that you can actually see the visible stars:

If you make it even later after sundown, the glow of the sun is gone, and you can see more constellations fall below the horizon. Just for fun I have also toggled the ecliptic lines which might come in handy for later:

That's pretty much the set-up although there's a ton of other things to play with.
 

One more important thing is to click on the Moon (also called SIN in this Sky Culture, because the Moon god was named SIN). You will be able to see one of the lines of information showing the phase of the moon which will be very important. At this time on January 1st, the phase is: "Moon Age: 8.1 days old (Waxing Gibbous)"
That means that at 7pm, when I took this screenshot, it was now 8.1 days since the new moon sliver began, and the sliver was "waxing" or growing bigger (prior to the full moon). After the full moon the phase becomes "Waning Gibbous," getting smaller again until the moon disappears and starts a new sliver (new moon) for a new month.
 

It might be good to read at least the first page of this work: https://www.jstor.org/stable/41670130
You won't need a log-in to JSTOR for it, because it's all on the preview page.
Basically, the point is that a "cubit" is indeed a unit of angular measure, but the paper uses a more stringent method of measuring it accurately by looking at the 200 or so planetary references in Babylonian documents, since planets move slower than the moon and some planets were only visible for a short period of time, and therefore we can know the time window of the observation more accurately.  
Basically, as you can see in the summary of the document, the cubit had been considered to be about 2 degrees, and a finger would be 1/24th of a cubit. The paper will more accurately offer evidence of 2.2 degrees per cubit, a difference of only 10%. 

Also, on the question of what is in front of or behind, the following will likely make the most sense to you after you have looked at enough observations and compared them with your Stellarium screen (or any other software that does this).a
Even though it's easier to envision the horizon rather than the ecliptic, it still generally works out that words Babylonians used in their "astronomy" mapped as follows:
North=Above, South=Below, East=Behind, West=In Front.  For the parts of the sky closest to the horizon, especially towards the west,  it therefore works out like the old "Western" movie cliche, where "the sun sinks slowly into the west." So it's easy to imagine that most of the heavenly objects are sinking in that direction therefore the sun was in front of all the stars that will also "sink" in that general direction. Therefore all the stars along MOST of the sky that are still farther east are behind, heading racing toward the horizon. And they will also be in the same "in front" or "behind" positions when  they appear to come up on the eastern horizon the next morning. 

@xero, i don't know how far along you are but Stellarium is a great tool for this, and I see you are using the Mul.Apin Sky Culture. It saves time from having to keep track of the Babylonian star names yourself.
I suspect there will be some others here who might try the Stellarium software, too. If so, they should know that it's good to get more than use the online web version. It's great, but the desktop version gives you everything you need.
It's free. Although you are allowed to donate. 
You can download and install the latest version 23.3 or 23.4 from here: https://stellarium.org/release/2023/09/25/stellarium-23.3.html
Once installed, you will want to change the location to somewhere near Babylon. The city @xero picked is below:

Once you install it, you can hover your mouse over the bottom left edge of the screen and select the icon just under the clock:
"Sky and Viewing Options [F4]"
Then select "Sky Culture" from the top of that newly opened window, and pick Babylonian -- MUL.APIN:

Now when you close that window, pick the clock icon you saw earlier. 
Start with any BCE date you like, but I think most people will try either 588 BCE or 568 BCE if the first thing they want to check is VAT 4956:
Along the bottom of the screen, if you hover the mouse over the bottom left edge of the screen you will see some other options:

The first two highlighted ones will toggle the borders of the constellations on, which is helpful. The second one toggles the names on and off. But you will also probably want to experiment with the imagery and the horizon/landscape settings which you can make disappear or make  almost transparent. You can also use the arrow keys and Page Up and Page Down to zoom in and out and turn the orientation so that you are facing due West which is my favorite place to start. 
The last thing to do after orienting your screen is to go back to that Clock icon and set the year, month, day, and time. If you want to check 568 BCE first, then type the following into the date and time boxes. For purposes of VAT 4956 I would start on January 1, 568 BCE. In astronomy dates 568 BCE is written as -567, due to the zero year issue. So that's actually written as -567:01:01 -- 00:00:01. You don't have to spin it all the way back; you can type numbers into the fields. Here I will set it for 4:45 in the afternoon.

16:45 (4:45pm) is pretty close to sundown on January 1, but you can "spin" the dial forward to just after sundown so that you can actually see the visible stars:

If you make it even later after sundown, the glow of the sun is gone, and you can see more constellations fall below the horizon. Just for fun I have also toggled the ecliptic lines which might come in handy for later:

That's pretty much the set-up although there's a ton of other things to play with.
 

It might be good to read at least the first page of this work: https://www.jstor.org/stable/41670130
You won't need a log-in to JSTOR for it, because it's all on the preview page.
Basically, the point is that a "cubit" is indeed a unit of angular measure, but the paper uses a more stringent method of measuring it accurately by looking at the 200 or so planetary references in Babylonian documents, since planets move slower than the moon and some planets were only visible for a short period of time, and therefore we can know the time window of the observation more accurately.  
Basically, as you can see in the summary of the document, the cubit had been considered to be about 2 degrees, and a finger would be 1/24th of a cubit. The paper will more accurately offer evidence of 2.2 degrees per cubit, a difference of only 10%. 

Also, on the question of what is in front of or behind, the following will likely make the most sense to you after you have looked at enough observations and compared them with your Stellarium screen (or any other software that does this).a
Even though it's easier to envision the horizon rather than the ecliptic, it still generally works out that words Babylonians used in their "astronomy" mapped as follows:
North=Above, South=Below, East=Behind, West=In Front.  For the parts of the sky closest to the horizon, especially towards the west,  it therefore works out like the old "Western" movie cliche, where "the sun sinks slowly into the west." So it's easy to imagine that most of the heavenly objects are sinking in that direction therefore the sun was in front of all the stars that will also "sink" in that general direction. Therefore all the stars along MOST of the sky that are still farther east are behind, heading racing toward the horizon. And they will also be in the same "in front" or "behind" positions when  they appear to come up on the eastern horizon the next morning. 

It might be good to read at least the first page of this work: https://www.jstor.org/stable/41670130
You won't need a log-in to JSTOR for it, because it's all on the preview page.
Basically, the point is that a "cubit" is indeed a unit of angular measure, but the paper uses a more stringent method of measuring it accurately by looking at the 200 or so planetary references in Babylonian documents, since planets move slower than the moon and some planets were only visible for a short period of time, and therefore we can know the time window of the observation more accurately.  
Basically, as you can see in the summary of the document, the cubit had been considered to be about 2 degrees, and a finger would be 1/24th of a cubit. The paper will more accurately offer evidence of 2.2 degrees per cubit, a difference of only 10%. 

Also, on the question of what is in front of or behind, the following will likely make the most sense to you after you have looked at enough observations and compared them with your Stellarium screen (or any other software that does this).a
Even though it's easier to envision the horizon rather than the ecliptic, it still generally works out that words Babylonians used in their "astronomy" mapped as follows:
North=Above, South=Below, East=Behind, West=In Front.  For the parts of the sky closest to the horizon, especially towards the west,  it therefore works out like the old "Western" movie cliche, where "the sun sinks slowly into the west." So it's easy to imagine that most of the heavenly objects are sinking in that direction therefore the sun was in front of all the stars that will also "sink" in that general direction. Therefore all the stars along MOST of the sky that are still farther east are behind, heading racing toward the horizon. And they will also be in the same "in front" or "behind" positions when  they appear to come up on the eastern horizon the next morning. 

-589 [astron.] -- "July 26," 590 B.C.E. 😉

FYI I'm taking the time to map out the 13 positions

"While not all of these sets of lunar positions
match the year 568/567 B.C.E., all 13 sets match cal-
culated positions for 20 years earlier, for the year
588/587 B.C.E"

So I can see for myself.
 
 

My apologies. But I have removed some more of the "Vicar of Warwick" saga and other posts from xero's Nineveh topic over to here because it's just not close enough to the chronology topic that started there. These posts are not really about forum participants we have known either, but this has already become kind of a catch-all for unnecessary dialogues.
@Pudgy @BTK59 @George88 @Srecko Sostar

As everyone can now see, I didn't make anything up. I simply quoted correctly from what you had just posted a minute or so earlier.
I never expected you to admit a mistake. This is a tiny one, but the bigger the mistake the more you dig in your heels and try to project it onto the other person. You should be aware, however, that almost by definition, that a person who is known for projecting their faults and insecurities onto others, ends up revealing a lot more about themselves.
No. It had everything to do with my remark. Jesus spoke of the resurrection at the last day, but persons in the first century were believing the times and seasons were in their own jurisdiction and claiming that the resurrection had already occurred, just as you posted. The exact same thing happens with the 1914 doctrine, because we tie that to the claim that the first resurrection has already occurred:
*** w07 1/1 p. 28 par. 11 “The First Resurrection”—Now Under Way! ***
That would indicate that the first resurrection began sometime between 1914 and 1935. Can we be more precise?
 
I'm hearing an echolalia. You are repeating what I was saying above, except that you are projecting it back as if you have never been able to admit a mistake and must try to make your mistake stick to the person who pointed it out. 
Please keep in mind how others perceive a person who is bent on projecting their errors onto others. It's almost like confession. Note again that it was the Watchtower that linked the first resurrection to the 1914 chronology. (See above.)
I think everyone is aware that subtext of every discussion of Neo-Babylonian chronology is always the 1914 doctrine. 

My apologies. But I have removed some more of the "Vicar of Warwick" saga and other posts from xero's Nineveh topic over to here because it's just not close enough to the chronology topic that started there. These posts are not really about forum participants we have known either, but this has already become kind of a catch-all for unnecessary dialogues.
@Pudgy @BTK59 @George88 @Srecko Sostar

…

You REALLY need to take a “Reading Comprehension” course, Georgie.
What part of “… for the record…” did you not understand?

… and so (cues the organist) … that ends another thrilling episode of “The Vicar of Warwick”. where the Vicar and ex-Bethelite Quasimodo whack-a-mole each other back and forth with great blows, none seeming to have any effect.
At all.
Tune in to the NEXT episode of season 15, when Quasimodo, loosing patience, finally pulls the lever, consigning the Vicar to the bowels of Twitter, now known as “X”.
(organ music stops as organist stands up and joins in thunderous applause …).
fade to black.

It's when we adopted the name, "Jehovah's Witnesses". 7/26/1931

As everyone can now see, I didn't make anything up. I simply quoted correctly from what you had just posted a minute or so earlier.
I never expected you to admit a mistake. This is a tiny one, but the bigger the mistake the more you dig in your heels and try to project it onto the other person. You should be aware, however, that almost by definition, that a person who is known for projecting their faults and insecurities onto others, ends up revealing a lot more about themselves.
No. It had everything to do with my remark. Jesus spoke of the resurrection at the last day, but persons in the first century were believing the times and seasons were in their own jurisdiction and claiming that the resurrection had already occurred, just as you posted. The exact same thing happens with the 1914 doctrine, because we tie that to the claim that the first resurrection has already occurred:
*** w07 1/1 p. 28 par. 11 “The First Resurrection”—Now Under Way! ***
That would indicate that the first resurrection began sometime between 1914 and 1935. Can we be more precise?
 
I'm hearing an echolalia. You are repeating what I was saying above, except that you are projecting it back as if you have never been able to admit a mistake and must try to make your mistake stick to the person who pointed it out. 
Please keep in mind how others perceive a person who is bent on projecting their errors onto others. It's almost like confession. Note again that it was the Watchtower that linked the first resurrection to the 1914 chronology. (See above.)
I think everyone is aware that subtext of every discussion of Neo-Babylonian chronology is always the 1914 doctrine. 

As everyone can now see, I didn't make anything up. I simply quoted correctly from what you had just posted a minute or so earlier.
I never expected you to admit a mistake. This is a tiny one, but the bigger the mistake the more you dig in your heels and try to project it onto the other person. You should be aware, however, that almost by definition, that a person who is known for projecting their faults and insecurities onto others, ends up revealing a lot more about themselves.
No. It had everything to do with my remark. Jesus spoke of the resurrection at the last day, but persons in the first century were believing the times and seasons were in their own jurisdiction and claiming that the resurrection had already occurred, just as you posted. The exact same thing happens with the 1914 doctrine, because we tie that to the claim that the first resurrection has already occurred:
*** w07 1/1 p. 28 par. 11 “The First Resurrection”—Now Under Way! ***
That would indicate that the first resurrection began sometime between 1914 and 1935. Can we be more precise?
 
I'm hearing an echolalia. You are repeating what I was saying above, except that you are projecting it back as if you have never been able to admit a mistake and must try to make your mistake stick to the person who pointed it out. 
Please keep in mind how others perceive a person who is bent on projecting their errors onto others. It's almost like confession. Note again that it was the Watchtower that linked the first resurrection to the 1914 chronology. (See above.)
I think everyone is aware that subtext of every discussion of Neo-Babylonian chronology is always the 1914 doctrine. 

You posted it just a matter of a minute or so before I quoted it. Surprised you didn't remember posting it just a minute earlier. It was part of what you said here, quoting the scripture. I'll highlight it in red:
f

No. It suspect it was just an issue with your memory. No biggie. We are all getting a bit older every day. No need to be paranoid about a manipulated piece. I don't do that. I have the power to delete comments, but I don't have the power to "add" them, LOL. Since there are none of those instances, it couldn't be one of them. Besides, even if I really had made a mistake and taken it from another post, it wouldn't be fraud and deception. It would have just been a mistake. 
In this case it was your mistake, not mine, but I am not so paranoid or anxious to accuse others so as to think it would have been fraud or deception. I do think it's a matter of "wishful thinking" on your part, though. You probably "wish" you could accuse me of fraud and deception and actually find evidence for that, even if you have to grasp at straws to do it. This is the same danger I have been talking about when promoting teachings with no evidence, or very weak and faulty evidence. People are always willing to grasp at straws to try to sow doubt on the evidence that doesn't fit their agenda, or they try the old standby ad hominem against the person presenting it.  
This is exactly what I wish would change. And of course you will continue with the accusations because, if you are anything like your other personas here, you never admit a mistake.

You posted it just a matter of a minute or so before I quoted it. Surprised you didn't remember posting it just a minute earlier. It was part of what you said here, quoting the scripture. I'll highlight it in red:
f

No. It suspect it was just an issue with your memory. No biggie. We are all getting a bit older every day. No need to be paranoid about a manipulated piece. I don't do that. I have the power to delete comments, but I don't have the power to "add" them, LOL. Since there are none of those instances, it couldn't be one of them. Besides, even if I really had made a mistake and taken it from another post, it wouldn't be fraud and deception. It would have just been a mistake. 
In this case it was your mistake, not mine, but I am not so paranoid or anxious to accuse others so as to think it would have been fraud or deception. I do think it's a matter of "wishful thinking" on your part, though. You probably "wish" you could accuse me of fraud and deception and actually find evidence for that, even if you have to grasp at straws to do it. This is the same danger I have been talking about when promoting teachings with no evidence, or very weak and faulty evidence. People are always willing to grasp at straws to try to sow doubt on the evidence that doesn't fit their agenda, or they try the old standby ad hominem against the person presenting it.  
This is exactly what I wish would change. And of course you will continue with the accusations because, if you are anything like your other personas here, you never admit a mistake.

For the record, I do not claim that the resurrection has already taken place. That's part of the 1914 doctrine.

For the record, I do not claim that the resurrection has already taken place. That's part of the 1914 doctrine.

For the record, I do not claim that the resurrection has already taken place. That's part of the 1914 doctrine.