α = {525/10, -133/10} π/180; (* Berlin *)
β = {-378/10, -145} π/180; (* Melbourne *)
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}; (* Plot Range *)
P[ε_, γ_] := {Cos[γ]*Cos[ε], Sin[ε], Sin[γ]*Cos[ε]};
export = Quiet[Manipulate[
plot[X_, Y_, Z_] :=
Graphics3D[{
{Opacity[0.1], Sphere[{0, 0, 0}, 1]},
{Cyan, PointSize[0.03], Point[P[α[[1]], γ + α[[2]]]]},
Text[StyleForm["Berlin", FontSize -> 9], {P[α[[1]] + 0.2, γ + α[[2]]]}],
{Dashed, Line[{P[α[[1]], γ + α[[2]]], {0, 0, 0}}]},
{Magenta, PointSize[0.03], Point[P[β[[1]], γ + β[[2]]]]},
Text[StyleForm["Melbourne", FontSize -> 9], {P[β[[1]] - 0.2, γ + β[[2]]]}],
{Dashed, Line[{P[β[[1]], γ + β[[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]]]]}},
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];
N[(τg τ[α[[1]]])/(τg τ[-β[[1]]]), 16]