1
$\begingroup$

I want to add moon(Blue) that orbiting earth(Red). while Earth is orbiting Sun. this is my code so far that consist of earth, sun and moon. how to write a code so that Moon is orbiting earth instead of sun? Tmoon is formula of period of the moon and earth. T is Period for sun and Earth. e is eccentricity. a is Semimajor.

(*"Measuring the Earth-Sun system";*)

h = 0; k = 0; G = 6.63*10^(-11);
e = 0.0167086;
a = 1.496*10^(11); b = a*Sqrt[1 - e^2];
MS = 1.989*10^30(*mass Sun*) ;
ME = 5.9723*10^(24)(*Mass Earth*);
MM = 0.07346*10^(24)(*Mass Moon*);
T = 2 Pi*Sqrt[a^3/(G*(MS + ME))](*Formula Period and semimajor for circulating around central object*);
Tmoon = 2 Pi*Sqrt[aMoon^3/(G*(MM + ME))];
omega0 = 2 Pi/T;
omega1 = 2 Pi/Tmoon;
aMoon = (3.844*10^(8))*10^(2);
bMoon = aMoon*Sqrt[1 - eMoon^2];
eMoon = 0.0549;

(*** define linear eccentricity f *)
f1 = Sqrt[a^2 - b^2]; f2 = -f1;
f1Moon = Sqrt[aMoon^2 - bMoon^2]; f2Moon = -f1Moon;
(*f1=f1+h;f2=h+f2;*)
F1 = {f1 + h, k}; F2 = {f2 + h, k};
F1Moon = {f1Moon + h, k}; F2Moon = {f2Moon + h, k};
(*** end of define focal points*)

(* Define the end points of major and minor axes *)
esMl = {h - a, k}; esMr = {a + h, k};
esmu = {h, b + k}; esmd = {h, k - b};
lsM = Graphics[Line[{esMl, esMr}]];
lsm = Graphics[Line[{esmu, esmd}]];

(**** for the E-Sun ****)
x[t_] := a*Cos[omega0*t] + h;
xMoon[t_] := aMoon*Cos[omega1*t] + h;
y[t_] := b*Sin[omega0*t] + k;
yMoon[t_] := bMoon*Sin[omega1*t] + k;
prp1 = ParametricPlot[{x[t], y[t]}, {t, 0, T}, 
   PlotRange -> {{h - a, h + a}, {k - b, k + b}}];
prp1Moon = 
  ParametricPlot[{xMoon[t], yMoon[t]}, {t, 0, T}, 
   PlotRange -> {{h - aMoon, h + aMoon}, {k - bMoon, k + bMoon}}];
pp2 = Graphics[{PointSize -> 0.03, Point[{h, k}]}];
pp2Moon = Graphics[{PointSize -> 0.03, Point[{h, k}]}];
ppf = Graphics[{PointSize -> 0.02, Point[{F1, F2}]}];
ppfMoon = Graphics[{PointSize -> 0.02, Point[{F1Moon, F2Moon}]}];
(**** for the E-Sun ****)

(*"Simulate the motion of a moving point overlapping on the ellipse \
using Manipulate";*)
Manipulate[
 gp = Graphics[{Red, PointSize -> 0.02, Point[{x[t], y[t]}]}];
 gpMoon = 
  Graphics[{Blue, PointSize -> 0.02, Point[{xMoon[t], yMoon[t]}]}];
 Show[{prp1, prp1Moon, ppf, ppfMoon, pp2, pp2Moon, lsM, gp, gpMoon}]
 (*Show[{prp1,ppf,pp2,lsM,gp}]*)
 ,
 {t, 0.0, 10 T, 0.005 T}
 ]

enter image description here

All help is much appreciated

$\endgroup$
  • $\begingroup$ If you don't want to use PlanetaryMoonData[] or PlanetData[], do you at least have a reference for computing the heliocentric coordinates of the Moon? $\endgroup$ – J. M. is away Mar 24 '16 at 15:17
  • $\begingroup$ thanks for the info. already add the necessary reference $\endgroup$ – Nabil Mar 24 '16 at 15:33
2
$\begingroup$
h = 0; k = 0; G = 6.63*10^(-11);
e = 0.0167086;(*eccentricity Earth*)
a = 1.496*10^(11)(*semimajor Earth*);
MS = 1.989*10^30 ;(*Mass Sun*)
ME = 5.9723*10^(24);(*mass Earth*)
T = 2 Pi*Sqrt[a^3/(G*(MS + ME))];
omega0 = 2 Pi/T;

MM = 0.07346*10^(24);(*Mass Moon*)
aMoon = 3.844*10^(8)*(10^(2));(*semimajor Moon*)
(*bMoon=aMoon*Sqrt[1-eMoon^2];*)
eMoon = 0.0549;(*eccentricity Moon*)
Tmoon = 2 Pi*Sqrt[aMoon^3/(G*(MM + ME))];
omega3 = 2 Pi/Tmoon;



f1 = e*a; f2 = -f1;
b = Sqrt[a^2 - f1^2];

f1 = f1 + h; f2 = h + f2;
F1 = {f1, k}; F2 = {f2, k};

x[t_] := a*Sin[-omega0*t] + h;

y[t_] := b*Cos[-omega0*t] + k;

prp1 = ParametricPlot[{x[t], y[t]}, {t, 0, T}];

pp2 = Graphics[{PlotRange -> {{h - a - aMoon, 
       h + a + aMoon}, {k - b - aMoon, k + b + bMoon}}, Brown, 
    PointSize -> 0.03, Point[{h, k}]}];

ppf = Graphics[{PointSize -> 0.02, Point[{F1, F2}]}];


f5 = eMoon*aMoon; f6 = -f5;
bMoon = Sqrt[aMoon^2 - f5^2]; f6 = -f5;
f5 = f5 + x[t]; f6 = x[t] + f6;
F5 = {f5, y[t]}; F6 = {f6, y[t]};

x2[t_] := aMoon*Cos[omega3*t] + x[t]; 
y2[t_] := bMoon*Sin[omega3*t] + y[t];


Manipulate[
 gp = Graphics[{{Red, PointSize -> 0.02, Point[{x[t], y[t]}]}, {Blue, 
     PointSize -> 0.02, Point[{x2[t], y2[t]}]}}, Frame -> True, 
   PlotRange -> {{h - a - aMoon, h + a + aMoon}, {k - b - aMoon, 
      k + b + bMoon}}];

 Show[prp1, ppf, pp2, gp]

 ,
 {t, 0.0, T, 0.01 T}
 ]

enter image description here

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.