Calculations with Mayan cycles of synodic months

Read in the file of new moon dates from 1502 through 2025.
In[]:=
moonfile=FileNameJoin[NotebookDirectory[],"newmoons.wl"];
In[]:=
Get[moonfile];
In[]:=
First[newmoons]
Out[]=
Sat 18 Jan 1502 18:53:37GMT-6
In[]:=
Last[newmoons]
Out[]=
Fri 19 Dec 2025 19:43:20GMT-6
Make a list of the lengths of the synodic months in that period .
In[]:=
lunarmonths=Table[DateDifference[newmoons[[i-1]],newmoons[[i]]],{i,2,Length[newmoons]}];
Statistics of the months
In[]:=
meanMonth=Mean[lunarmonths]
Out[]=
29.5306
days
In[]:=
maxMonth=Max[lunarmonths]
Out[]=
29.8326
days
In[]:=
minMonth=Min[lunarmonths]
Out[]=
29.2719
days
In[]:=
stdevMonth=StandardDeviation[lunarmonths]
Out[]=
0.143298
days
In[]:=
UnitConvert[stdevMonth,"Hours"]
Out[]=
3.43915
h
In[]:=
UnitConvert[maxMonth-minMonth,"Hours"]
Out[]=
13.4581
h
The Mayan cycle of 405 synodic months was intended to be 11,960 days long. Get the average length of a synodic month according to this system.
In[]:=
mayancycle=Quantity[11960,"Days"]
Out[]=
11960
days
In[]:=
mayancycle/405//N
Out[]=
29.5309
days
In[]:=
UnitConvert[mayancycle,"Years"]//N
Out[]=
32.7671
yr
Calculate the length, in days, of all the Mayan cycles in the list of new moons.
In[]:=
cycles=Table[DateDifference[newmoons[[i]],newmoons[[i+405]]],{i,1,Length[newmoons]-405}];
Statistics of the cycles
In[]:=
Max[cycles]
Out[]=
11960.3
days
In[]:=
Min[cycles]
Out[]=
11959.5
days
In[]:=
Mean[cycles]
Out[]=
11959.9
days
In[]:=
UnitConvert[mayancycle-Mean[cycles],"Minutes"]
Out[]=
160.959
min
In[]:=
UnitConvert[mayancycle-Min[cycles],"Hours"]
Out[]=
10.8832
h
In[]:=
UnitConvert[Max[cycles]-mayancycle,"Hours"]
Out[]=
6.63467
h