(* Input *)

α = {0, -104} π/180;                                                     (* Singapur          *)
β = {+30, +95} π/180;                                                    (* Houston           *)
ψ = {+60, +25} π/180;                                                    (* Helsinki          *)
δ = {90, 0} π/180;                                                       (* Nordpol           *)
ω = 72921*^-9/sek;                                                       (* Erddrehung        *)
r = 6371000 m;                                                           (* Erdradius         *)
G = 667384*^-16 m^3 kg^-1 sek^-2;                                        (* Newtons Konstante *)
M = 5972 10^21 kg;                                                       (* Erdmasse          *)
c = 299792458 m/sek;                                                     (* Licht             *)

R = {-1.3, 1.3};                                                         (* Plotrange         *)
P[ε_, γ_] := {Cos[γ]*Cos[ε], Sin[ε], Sin[γ]*Cos[ε]};                     (* Ortskoordinaten   *)

export = Quiet[Manipulate[
plot[X_, Y_, Z_] :=
Graphics3D[{

{Opacity[0.1], Blue, Sphere[{0, 0, 0}, 1]},

{Red, PointSize[0.03], Point[P[α[[1]], γ + α[[2]]]]},
Text[StyleForm["Singapur", FontSize -> 9], {P[α[[1]] + 0.2, γ + α[[2]]]}],
{Dashed, Line[{P[α[[1]], γ + α[[2]]], {0, 0, 0}}]},

{Orange, PointSize[0.03],  Point[P[β[[1]], γ + β[[2]]]]},
Text[StyleForm["Houston", FontSize -> 9], {P[β[[1]] + 0.2, γ + β[[2]]]}],
{Dashed, Line[{P[β[[1]], γ + β[[2]]], {0, 0, 0}}]},

{Green, PointSize[0.03],  Point[P[ψ[[1]], γ + ψ[[2]]]]},
Text[StyleForm["Helsinki", FontSize -> 9], {P[β[[1]] + 0.2, γ + ψ[[2]]]}],
{Dashed, Line[{P[ψ[[1]], γ + ψ[[2]]], {0, 0, 0}}]},

{Cyan, PointSize[0.03],  Point[P[δ[[1]], γ + δ[[2]]]]},
Text[StyleForm["Nordpol", FontSize -> 9], {0, 1 + 0.2, 0}],
{Dashed, Line[{P[δ[[1]], γ + δ[[2]]], {0, 0, 0}}]},

{Opacity[0.01], Cylinder[{{0, Sin[α[[1]]], 0}, {0, Sin[α[[1]]] + 0.001, 0}}, Cos[α[[1]]]]},
{Opacity[0.01], Cylinder[{{0, Sin[β[[1]]], 0}, {0, Sin[β[[1]]] + 0.001, 0}}, Cos[β[[1]]]]},
{Opacity[0.01], Cylinder[{{0, Sin[ψ[[1]]], 0}, {0, Sin[ψ[[1]]] + 0.001, 0}}, Cos[ψ[[1]]]]},
{Opacity[0.01], Cylinder[{{0, Sin[δ[[1]]], 0}, {0, Sin[δ[[1]]] + 0.001, 0}}, Cos[δ[[1]]]]}}
,
ViewPoint -> {X, Y, Z},
ImageSize -> 260,
PlotRange -> {R, R, R}];

p1 = plot[0, 2, -4]; p2 = plot[0, 4, -2];
{p1, p2}, {γ, 2 π, 0}, ControlPlacement -> Top]]

τg = Sqrt[1 - (2 G M)/(r c^2)]; τ[ε_] := Sqrt[1 - (ω Cos[ε] r)^2/c^2];

"t_Nordpol/t_Feldfrei" -> N[(τg τ[δ][[1]]), 16]
"t_Äquator/t_Feldfrei" -> N[(τg τ[α][[1]]), 16]
"t_Nordpol/t_Äquator"  -> N[(τg τ[δ[[1]]])/(τg τ[α[[1]]]), 16]

(* Output *)

t_Nordpol/t_Feldfrei -> 0.9999999993039402
t_Äquator/t_Feldfrei -> 0.9999999993027394
t_Nordpol/t_Äquator  -> 1.0000000000012007