# Mercury's perihelion precession [closed]

i want to plot the precession of mercury's perihelion in MatLaB .(like the image below).Help me out here ,guys. https://en.wikipedia.org/wiki/Apsidal_precession#/media/File:Perihelion_precession.svg

Update: I did plot in matlab but the figure is not matching with the desired perihelion precession . This is my code.

a=10;
b=5;
lambda=.5;
v1=1/20;
v2=3;
t=1:.2:40;
x=a^2+b^2 +a*cos(2*pi*v1*t).*cos(2*pi*v2*t)-lambda*b*sin(2*pi*v1*t).*sin(2*pi*v2*t);
y=a^2+b^2 +a*sin(2*pi*v1*t).*cos(2*pi*v2*t)-lambda*b*cos(2*pi*v1*t).*sin(2*pi*v2*t);
plot(x,y)


Something like that for example ??

EDIT 1

The parametric equations of the curve are :

\begin{align} x(t) & = \left[\sqrt{a^2-b^2}+a\cos\left(2\pi\nu_{\theta} t\right)\right] \cos\left(2\pi\nu_{\phi} t\right)-b\,\sin\left(2\pi\nu_{\theta} t\right)\sin\left(2\pi\nu_{\phi} t\right) \tag{01a}\\ y(t) & = \left[\sqrt{a^2-b^2}+a\cos\left(2\pi\nu_{\theta} t\right)\right] \sin\left(2\pi\nu_{\phi} t\right)+ b\,\sin\left(2\pi\nu_{\theta} t\right)\cos\left(2\pi\nu_{\phi} t\right) \tag{01b} \end{align}

The graph shown in the Figure is produced by GeoGebra software.

The variables and the values given are : \begin{align} a & = \text{major semi-axis} = 5 \tag{02a}\\ b & = \text{minor semi-axis} = 3 \tag{02b}\\ \nu_{\theta} & = \text{frequency of rotation of the particle on its elliptical orbit}= 3 \tag{02c}\\ \nu_{\phi} & = \text{frequency of rotation of the elliptical orbit around a focus}= 1/10 \tag{02d}\\ t & = \text{parameter of the curve representing the time} \in \left[0,1.22 \right] \tag{02e} \end{align}

The graph of the curve represents the orbit of a particle moving on an ellipse rotating around one of its focal points, simulating the motion of planet Mercury around the Sun. The values given to the variables are indicative without any relation to the values of the motion of planet Mercury.

EDIT 2

Et voilà your MatLab code and graphics

a=5;
b=3;
v1=3;
v2=1/10;
t = [0:.001:1.22];
x=(sqrt(a^2-b^2) +a*cos(2*pi*v1*t)).*cos(2*pi*v2*t)-b*sin(2*pi*v1*t).*sin(2*pi*v2*t);
y=(sqrt(a^2-b^2) +a*cos(2*pi*v1*t)).*sin(2*pi*v2*t)+b*sin(2*pi*v1*t).*cos(2*pi*v2*t);
plot(x,y)

• yeah like that one. can you give me the whole code? Nov 4, 2017 at 10:04
• @user1157 I produced it by GeoGebra software not MatLab. Take the curve equation in the Figure, give values to the variables etc. Take a look in my answer therein : Painting with a Pendulum: Would it be possible to graph the pattern? in order to understand the meaning of the variables. Nov 4, 2017 at 10:13
• you have given third brackets . should i take the modulus values in there ? still trying to code it in matlab . Nov 10, 2017 at 10:39
• @user1157 I apologize, but I don't understand what are you asking for. Nov 10, 2017 at 10:56
• updated the Question. I think i am not giving correct values to the variables. Nov 10, 2017 at 17:15