Saros series are series of eclipses occurring a little over 18 years apart from each other. Below I visualize total solar eclipses of one Saros series (number 139 to be precise), which includes the total solar eclipse occurring in the North America on April 8, 2024. An exeligmos is a cycle of three Saros, or 54 years and 33 days which results in eclipses in the cycle to occur roughly the same local time of day and similar location (while single Saros shifts an eclipse by roughly 120 degrees in longitude.)
The implementation SolarEclipse, new in Mathematica 14.0 makes studying and visualizing eclipses much less of a chore, and is supported below by general GeoGraphics and visualization functionality, leading to a relatively compact way to study Saros series.
In[]:=
With[{s=139},​​(*seriesoftotaleclipsesoftheSarosseries*)​​SolarEclipse[{"Saros",s},EclipseType->"Total"]//​​{(*dates*)​​#,​​(*areasoftotaleclipse*)​​SolarEclipse[#,"UmbraEnvelopePolygon"]["Values"],​​(*maximumeclipsepositions*)​​SolarEclipse[#,"MaximumEclipsePosition"]["Values"],​​(*umbrasatmaximumeclipsepositions*)​​SolarEclipse[#,{"UmbraPolygon",#}]&/@#}&//​​(*extractthreeexeligmosseries,or"un-Riffle"abovedata*)​​ResourceFunction["EveryOther"][Transpose[#],3]&//​​{MapThread[​​(*areasoftotaleclipsesinexeligmosseriesinspecificcolor*)​​{GeoStyling[#2],#1[[All,2]]}&,​​{#,​​(*colorsfordifferentexeligmosseries*)​​Table[LCHColor[3/4,3/4,c,1/3],{c,1/6,1,1/3}]}],​​Dashed,GeoStyling[Black],​​Map[​​{(*pathsofexeligmos(55yearinterval)eclipses*)​​GeoPath[#[[All,3]]],​​(*umbraateacheclipsemaximum*)​​#[[All,4]],​​(*yearlabels*)​​Haloing[],Style[Text[#1["Year"],#3,{0,-3/2}],12]&@@@#}&,​​#]}&//​​GeoGraphics[#,​​GeoBackground->"CountryBorders",GeoRange->"World",GeoZoomLevel->4,​​GeoProjection->"Equirectangular",GeoGridLines->Automatic,​​PlotLabel->Style[TemplateApply["Exeligmos series of total eclipses in solar Saros `` with maximum umbras",s],24,Black],​​ImageSize->1024]&]

CITE THIS NOTEBOOK

Visualizing total solar eclipses of one Saros series​
by Jari Kirma​
Wolfram Community, STAFF PICKS, February 10, 2024
​https://community.wolfram.com/groups/-/m/t/3120094