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This should be an easy question, but I don't know the correct syntax. I'm trying to create an animation based on NightHemisphere during a year. For each day, the instant correspond to the time of the Sunset at Paris Looking on previous answers, I have constructed this function that works:

f := Function[x, DateObject[{2022, 1, 1}] + Quantity[(x - 1), "Days"]];
tg = Table[Show[
    GeoGraphics[
     NightHemisphere[
      Sunset[GeoPosition[{48.858042`, 2.2910492`}], DateObject[f[n]], 
       TimeZone -> +1]], GeoRange -> "World", 
     GeoCenter -> GeoPosition[{0, 0}]],
    ImageSize -> Large], {n, 1, 365}];
Export["sunset_paris.gif", tg]

Now I want to add a disk representing the position of the Earth place just below the Sun at that time, as it appears in, for instance, in https://www.timeanddate.com/worldclock/sunearth.html but I don't know how to transform SunPosition[] or other function to the position of this place. SunPosition gives the astronomical position of the Sun as seen from a location, while I'm looking for a point on Earth. Any help is welcome.

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4
  • $\begingroup$ Instead of f := Function[x, DateObject[{2022, 1, 1}] + Quantity[(x - 1), "Days"]] you can simply write f[x_] := DayPlus[{2022, 1, 1}, x - 1] $\endgroup$
    – Roman
    Feb 22, 2022 at 21:10
  • $\begingroup$ Welcome to Mathematica.SE! I hope you will become a regular contributor. To get started, 1) take the introductory tour now, 2) when you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge, 3) remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign, and 4) give help too, by answering questions in your areas of expertise. $\endgroup$
    – bbgodfrey
    Feb 22, 2022 at 21:31
  • $\begingroup$ Thanks, @Roman, I'm new to the DateObject syntax and I didn't know that you can write the 56th of January. $\endgroup$ Feb 23, 2022 at 6:58
  • $\begingroup$ Perhaps I am confused; when I run Jose's excellent answer ((mathematica.stackexchange.com/a/264104/79614)) the sublunar plot behaves as expected, but the subsolar disk seems to make a straight line in stead of the expected sinusoid (from tropic to tropic since we considere a whole year). Is there something I am not seeing right? Cheers, Pieter $\endgroup$
    – Coti
    Aug 25, 2022 at 17:21

2 Answers 2

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First provide a latitude at which you want your disk (representing the sun) to locate on your plots - let say at $x^\circ\;\mathrm{N}$. And I'm going to define a function:

zenithPole[n_] := QuantityMagnitude[
    First@SunPosition[GeoPosition[{90, 0}], DateObject[{2022, 1, n}, TimeZone -> 1]]
]

(*at 2022-01-01 00:00*)
zenithPole[1]

(* 344.18 *)

which outputs the azimuth angle of the sun, seen from the north pole GeoPosition[{90, 0}], at time {DateObject[{2022, 1, n}, TimeZone -> 1}. And I will subtract this from 360 (*degree*), then that's the longitude of every geoposition in which the zenith is. To see for yourself if this is true,

zenith[x_,n_] := SunPosition[
    GeoPosition[{x, 360 - zenithPole[n]}]
, DateObject[{2022, 1, n}, TimeZone -> 1]]

(*at 2022-01-01 00:00*)
zenith[0,1] (*at the equator*)
zenith[2.2910492`,1] (*at E 2.2910492`*)

(*
  {180.00°, -66.98°}
  {180.00°, -69.27°}
*)

As you can see, the sun is right at the zenith. So the location you want is GeoPosition[{x, 360 - zenithPole[n]}], where the x is the latitude where you want your disk to be at.

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We can compute those locations as follows:

subSolarPoint[date_] := GeoPosition[Reverse[SunPosition[date, CelestialSystem -> "Equatorial"] - {SiderealTime[GeoPosition[{0, 0}], date], 0}]]

subLunarPoint[date_] := GeoPosition[Reverse[MoonPosition[date, CelestialSystem -> "Equatorial"] - {SiderealTime[GeoPosition[{0, 0}], date], 0}]]

Then evaluate:

paris = GeoPosition[Entity["City", {"Paris", "IleDeFrance", "France"}]];

sunsets = Table[
   Sunset[paris, DateObject[{2022, 1, n}, TimeZone -> 1]],
   {n, 1, 365}
];

tg = Table[
    GeoGraphics[{
        NightHemisphere[s],
        GeoStyling[Yellow], GeoDisk[subSolarPoint[s], Quantity[100, "Miles"]], 
        GeoStyling[Black],  GeoDisk[subLunarPoint[s], Quantity[100, "Miles"]]
    }, GeoRange -> "World", ImageSize -> Large],
    {s, sunsets}
];

ListAnimate[tg]
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  • $\begingroup$ That worked perfectly. Thanks! $\endgroup$ Feb 23, 2022 at 6:59

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