Mercury Orbiting the Sun

a=6;
e=.205;
b=a*Sqrt[1-e^2];
c=Sqrt[a^2-b^2];
A[ϕ_]:=1/(2*a b Pi) (c b Sin[ϕ]+ a b ϕ)
θ[area_]:=InverseFunction[A][area]
Animate[ Show[Plot[{b{1-{x^2/a^2}}^{1/2},-{b{1-{x^2/a^2}}^{1/2}}},{x,-a,a},PlotRange->{{-a-1,a+1},{-b-1,b+1}},Axes->False,PlotStyle->{Black,Black}],Graphics[{Cyan,Line[{{-c,0},{a*Cos[θ[t]],b * Sin[θ[t]]}}], Yellow,Disk[{- c,0},{a/10,b/6}],PointSize[Large],Red, Point[{a*Cos[θ[t]],b * Sin[θ[t]]}]}]],{t,0.001,1,Pi/10000},DefaultDuration->8,AnimationRunning->False]

Demonstration of Vectors

Animate[ Show[Plot[{b{1-{x^2/a^2}}^{1/2},-{b{1-{x^2/a^2}}^{1/2}}},{x,-a,a},PlotRange->{{-a-3,a+3},{-b-3,b+3}},Axes->False,PlotStyle->{White,White}],Graphics[{ Yellow,Disk[{- c,0},{a/10,b/6}],Cyan,Arrow[{{a*Cos[θ[t]],b * Sin[θ[t]]},{-c,0}}],Blue, Arrow[{ {a Cos[θ[t]],b Sin[θ[t]]},{a Cos[θ[t]]+3Cos[3 Pi t],b Sin[θ[t]]+3Sin[3Pi t]}}],PointSize[Large],Red, Point[{a*Cos[θ[t]],b * Sin[θ[t]]}]}],Background->Black],{t,0.001,2,.00010000},DefaultDuration->10,AnimationRunning->False]

Perspective of the Sun From Mercury’s Equator

M2S[t_]:={-c-a Cos[θ[t]],-b Sin[θ[t]]}
DistanceM2S[t_]:=Norm[M2S[t]]
NormalizedM2S[t_]:=M2S[t]/DistanceM2S[t]

InitialAngle=Pi/2;
HorizonLine[t_]:={Cos[3 Pi t+ InitialAngle], Sin[3 Pi t+InitialAngle]}
cosAngle[t_]:=NormalizedM2S[t].HorizonLine[t]
sinAngle[t_]:=Det[{NormalizedM2S[t],HorizonLine[t]}]
tanAngle[t_]:=-sinAngle[t]/-cosAngle[t]
Animate[Graphics[{White,Point[{0,-1.3}],Point[{0,1.3}],Yellow, PointSize[Large], Point[{cosAngle[t],sinAngle[t]}],Orange,Circle[{cosAngle[t],sinAngle[t]},.25],{Green, Circle[{0,5/16},1/16],Line[{{0,1/4},{0,1/8}}],Line[{{-1/10,3/16},{1/10,3/16}}],Line[{{0,1/8},{-1/10,0}}],Line[{{0,1/8},{1/10,0}}],Black,Line[{{-2,0},{2,0}}]}}],{t,0,2},DefaultDuration->15,AnimationRunning-> False]

Sunrise from Window Perspective

perihelion=46001200;
aphelion=69816900;
a=.5 (aphelion+perihelion);
c=a-perihelion;
b=Sqrt[a^2-c^2];
A[ϕ_]:=1/(2*a b Pi) (c b Sin[ϕ]+a b ϕ);
θ[area_]:=InverseFunction[A][area];
M2S[t_]:={-c-a Cos[θ[t]],-b Sin[θ[t]]};
DistanceM2S[t_]:=Norm[M2S[t]];
NormalizedM2S[t_]:=M2S[t]/DistanceM2S[t];
InitialAngle=Pi/2;
HorizonLine[t_]:={Cos[3 Pi t+InitialAngle],Sin[3 Pi t+InitialAngle]};
cosAngle[t_]:=NormalizedM2S[t].HorizonLine[t];
sinAngle[t_]:=Det[{NormalizedM2S[t],HorizonLine[t]}];
tanAngle[t_]:=-sinAngle[t]/-cosAngle[t];
radSun=695500;
sunSize[t_]:=2 ArcTan[radSun/DistanceM2S[t]];
sunDegrees[t_]:=sunsize[t]*360/2 Pi;






Animate[Graphics[{Red,PointSize[2sunSize[t]],Point[{0,tanAngle[t]}],Black,Line[{{Tan[Pi/10],0},{-Tan[Pi/10],0}}],Line[{{-Tan[Pi/10],-Tan[Pi/10]},{-Tan[Pi/10],Tan[Pi/10]}}],Line[{{Tan[Pi/10],-Tan[Pi/10]},{Tan[Pi/10],Tan[Pi/10]}}],Line[{{Tan[Pi/10],Tan[Pi/10]},{-Tan[Pi/10],Tan[Pi/10]}}]},PlotRange->{{-Tan[Pi/10],Tan[Pi/10]},{0,Tan[Pi/10]}}],{t,.25,.75},DefaultDuration->15,AnimationRunning->False]

Sunset from Window Perspective

Animate[Graphics[{Red,PointSize[2sunSize[t]],Point[{0,-tanAngle[t]}],Black,Line[{{Tan[Pi/10],0},{-Tan[Pi/10],0}}],Line[{{Tan[Pi/10],0},{-Tan[Pi/10],0}}],Line[{{-Tan[Pi/10],-Tan[Pi/10]},{-Tan[Pi/10],Tan[Pi/10]}}],Line[{{Tan[Pi/10],-Tan[Pi/10]},{Tan[Pi/10],Tan[Pi/10]}}],Line[{{Tan[Pi/10],Tan[Pi/10]},{-Tan[Pi/10],Tan[Pi/10]}}]},PlotRange->{{-Tan[Pi/10],Tan[Pi/10]},{0,Tan[Pi/10]}}],{t,.25,.75},DefaultDuration->15,AnimationRunning->False]