Solstice

lat = 55.95; long = -3.2;
decl[d_: Integer,
   h_: Real](*declination of the sun in rad on day d after Jan 1 at h \
hrs*):= .006918 - .399912 Cos[\[Gamma][d, h]] +
   0.070257 Sin[\[Gamma][d, h]] - .006758 Cos[
     2 \[Gamma][d, h]] + .000907 Sin[2 \[Gamma][d, h]] - .002697 Cos[
     3 \[Gamma][d, h]] + .00148 Sin[3 \[Gamma][d, h]];
hra[d_, h_,
   long_](*hour angle in rad*):= \[Pi] ((60 h + tcf[d, h, long])/4 -
      180)/180;
tcf[d_, h_, long_](*time correction factor in min*):=
  eot[d, h] - 4  long + 60 (Round[long/15](*theoretical timezone*) );
eot[d_, h_](*equation of time in min*):=
  229.18 (0.000075 + 0.001868 Cos[\[Gamma][d, h]] -
     0.032077 Sin[\[Gamma][d, h]] - 0.014615 Cos[2 \[Gamma][d, h]] -
     0.040849 Sin[2 \[Gamma][d, h]]);
az[d_, h_, lat_, long_](*azimuth of the sun in rad*):=
  Module[{a},
   a = ArcTan[(Tan[decl[d, h]] Cos[lat Degree] -
       Sin[lat Degree] Cos[hra[d, h, long]]), -Sin[hra[d, h, long]]];
   If[a < 0, a + 2 \[Pi], a]];
n = 8;
psuns = Table[(\[Pi]/2 -
        alt[365 Floor[t]/n, Sign[lat] 12, Abs@lat, long]) {Sin[#],
       Cos[#]} &[az[Floor[t] 365/n, Sign[lat] 12, Abs@lat, long]], {t,
     0, n}];
Manipulate[
 Module[{psun, \[Tau]},
  \[Tau] = t - Floor[t];
  psun = (\[Pi]/2 -
        alt[365 Floor[t]/n, Sign[lat] 24 \[Tau], Abs@lat,
         long]) {Sin[#], Cos[#]} &[
    az[Floor[t] 365/n, Sign[lat] 24 \[Tau], Abs@lat, long]];

  Show[
   Graphics[{White, Disk[{0, 0}, 1.65]
     },
    Background -> Black, PlotRange -> 1.66],
   ParametricPlot[
    With[{shr = Sign[lat] (hour)},
     (\[Pi]/2 - alt[d, shr, Abs@lat, long]) {Sin[#], Cos[#]} &[
      az[d, shr, Abs@lat, long]]
     ]
    , {d, 0, 365}, {hour, 0, 24}, PlotPoints -> 12,
    PlotStyle -> Directive[Opacity[0.1], Red], MeshStyle -> Orange],
   Graphics[{
     Yellow, Disk[psun, 0.05],
     Darker@Yellow,
     Table[Disk[p, 0.05], {p, psuns[[;; Floor[t + 0.5]]]}],
     Line[psuns[[;; Floor[t + 0.5]]]]
     }]
   ]
  ],
 {t, 0, n}]