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Circular-Restricted Three-Body Problem (CRTBP) - Sun_Earth_Moon (using symbolic toolbox)

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Circular-Restricted Three-Body Problem (CRTBP) - Sun_Earth_Moon (using symbolic toolbox)

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Simulation the Hill’s Problem of 3-body system in MATLAB

moony(t,z)
function dz = moony(t,z)
% function to be integrated

% The constants required in the calculation

Me= 5.9742E27;               % Mass of earth
Ms= 1.9889E30;               % Mass of sun
R= 1.49598E11;               % Orbital radius of earth
% r= 3.85E8;                 % Orbital radius of moon
G= 6.67E-11;                 % Gravitational Constant
% TT=3.155E7;                % orbital time of earth
w= sqrt(G*(Me+Ms)/R^3);      % Angular velocity
de= Ms*R/(Ms+Me);            % Distance between earth and centre of mass
ds= Me*R/(Ms+Me);            % Distance between sun and centre of mass
% vv=sqrt(G*Me/r);           % average velocity of moon


dz = zeros(4,1);

% Equation for coordinates of sun and earth
xs= ds*cos(w*t);
ys= ds*sin(w*t);
xe=-de*cos(w*t);
ye=-de*sin(w*t);


% Differential equation for the coordinates of moon
a= sqrt(((xs - z(1))^2) + ((ys - z(3))^2));
b= sqrt(((xe - z(1))^2) + ((ye - z(3))^2));

Gs= G*Ms/power(a,3);
Ge= G*Me/power(b,3);

p = Gs*(xs-z(1)) + Ge*(xe-z(1));
q = Gs*(ys-z(3)) + Ge*(ye-z(3));

% % Writing Equation for gravitational acceleration on moon
% 
% a= sqrt(((ds*cos(w*t) - z(1))^2) + ((ds*sin(w*t) - z(3))^2));
% b= sqrt(((de*cos(w*t) + z(1))^2) + ((de*sin(w*t) + z(3))^2));
% p = (G*Ms*(ds*cos(w*t)-z(1)))/power(a,3) - (G*Me*(de*cos(w*t)+z(1)))/power(b,3);
% q = (G*Ms*(ds*sin(w*t)-z(3)))/power(a,3) - (G*Me*(de*sin(w*t)+z(3)))/power(b,3);

% Giving the values to function dz

dz(1) = z(2);
dz(2) = p;
dz(3) = z(4);
dz(4) = q;

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