Im trying to calculate the orbits of a solar system of a three particles in a plane. I have code that kind of does what I want it too but I would like this code to include the Verlet Method along with parameters of masses. The three "particles" being the Earth, Moon, and Sun. The Following is the code I have that correctly represents what I want to do:$\%$ Earth's Orbit

at $=149\mathrm{.}5963995$; $\%$ horizontal radius

bt $=149\mathrm{.}57552243$; $\%$ vertical radius

x$0$t $=0$; $\%$ x$0,$y$0$ ellipse center coordinates

y$0$t $=0$;

t $=-4*$ pi:$0\mathrm{.}01$:$4*$ pi;

xt $=$ x$0$t $+$ at $*$ cos$($t$)$;

yt $=$ y$0$t $+$ bt $*$ sin$($t$)$;

n $=$ length$($xt$)$;

$\%$ Moon's Translation around the Earth

for i $=1$:$1$:n

xt$2=$ xt$($i$)$; $\%$ Earth's position

yt$2=$ yt$($i$)$; $\%$ Moon's center

al $=38\mathrm{.}1575$; $\%$ horizontal radius $*100$

bl $=38\mathrm{.}0744275597$; $\%$ vertical radius $*100$

$\%$ Moon's Orbit

x$0$l $=$ xt$2-0\mathrm{.}025165$; $\%$ x$0,$y$0$ ellipse center coordinates focus

y$0$l $=$ yt$2$;

t $=-111*$ pi:$0\mathrm{.}01$:$111*$ pi;

xl $=$ x$0$l $+$ al $*$ cos$($t$)$;

yl $=$ y$0$l $+$ bl $*$ sin$($t$)$;

m $=$ length$($xl$)$;

xs $=2\mathrm{.}4991665$; $\%$ Sun's position

ys $=0$;

xm $=$ xl$($m $-14*$ i$)$;

ym $=$ yl$($m $-14*$ i$)$;

pts $=($yt$($i$)-$ ys$)/($xt$($i$)-$ xs$)$;

plt $=($ym $-$ yt$($i$))/($xm $-$ xt$($i$))$;

plot$($xl$,$ yl$,\text{'}$m$\text{'})\%$ Moon's orbit

hold on

plot$($xl$($m $-14*$ i$),$ yl$($m $-14*$ i$),\text{'}$ok$\text{'},$ 'MarkerSize', $5,$ 'MarkerFaceColor', $\text{'}$w$\text{'})\%$ Moon moving in its orbit

hold on

plot$($xt$,$ yt$,\text{'}$k$\text{'})\%$ Earth's orbit

hold on

plot$($xt$($i$),$ yt$($i$),\text{'}$ob$\text{'},$ 'MarkerSize', $10,$ 'MarkerFaceColor', $\text{'}$c$\text{'})\%$ Earth moving in its orbit

hold on

plot$($xs$,$ ys$,\text{'}$or$\text{'},$ 'MarkerSize', $20,$ 'MarkerFaceColor', $\text{'}$y$\text{'})\%$ fixed Sun

porcentaje $=($pts $-$ plt$)/(($pts $+$ plt$)/2)$;

per $=$ abs$($porcentaje$)$;

if per $<0\mathrm{.}1$

line$([$xt$($i$)$ xs$],[$yt$($i$)$ ys$])$

line$([$xm xt$($i$)],[$ym yt$($i$)])$

hold off

vector$($i$)=$ i;

end

hold off

axis$([-200200-200200])$

pause$(\mathrm{.}0000000001)$

end