can you help me optimize and make the following code run faster. I also would like to stabalize venus orbIt. The simulation will shiw when Theia collidse with

# Adjust rendering parameters

#mpl$.$rcParans$[\text{'}$agg$.$path.chunksize'$]=10000$

# Constants

$G=6\mathrm{.}67430e-11$ # Gravitational constant $(($:$m^3(kg)k{g}^{-1}{s}^{-2}\}$

n$\_$sun $=1\mathrm{.}989e30,$ # Mass of the Sun $(kg)$ n$\_$earth $=5\mathrm{.}972e24,$ # Mass of Earth $(kg)$

m$\_$earn $=5\mathrm{.}972e24$ # Mass of Earth $(kg)$ m$\_$theia $=3\mathrm{.}2846e24$ # Mass of venus $(kg)$ m Mass of Theia $(kg)$

def acceleration$(t,$ state$)$:

if np$.$sqrt$(($x$\_$earth $-$ x$\_$theia$){?}^{2}2+($y$\_$earth $-$ y$\_$theia$){?}^{2}2)<mtext></mtext><mn>1</mn>$e$6$:

Define a coltision threshold print$("$Alert: Earth and Theia are colliding!"$)$

if np$.$isclose$($x$\_$earth, x$\_$theia$)$ and np$.$isclose$($y$\_$earth, y$\_$theia$)$

ip$\mathrm{.}1$sclose$($x$\_$earth, X$\_$theia$)$ and np$.$isclose$($y$\_$earth, y$\_$theia$)$:

return np$.$array$([$vx$\_$earth, vy$\_$earth, ax$\_$earth, ay$\_$earth,

vx$\_$venus, vy$\_$venus, ax$\_$venus, ay$\_$venus, vx$\_$theia, vy$\_$theia, ax$\_$theia, ay$\_$theia$])$

# Initial conditions

x$0\_$earth, y$0\_$earth $=1\mathrm{.}496e11,$ vxo$\_$earth, vyo$\_$earth $=0,-29780$

xo$\_$venus, $y\_$venus $=1\mathrm{.}082e11,$ vxo$\_$venus, vyo$\_$venus $=0,-35260$

initial$\_$state earth, yo$\_$earth, vxo$\_$earth, vyo$\_$earth

# Time paraneters

t$\_$start$\_$years, t$\_$end$\_$years $=0,300000000$

# Solve the ODE with tqdm

# Adjust integration parameters

method $=\text{'}$RK$45\text{'}$

tolerance $=1e-6,$ # Tolerance for error control

# Solve the ODE with updated parameters

solution $=$ solve$\_$ivp$($acceleration$,$ t$\_$span, initial$\_$state, method$=$method,

rtol$=$tolerance, atol$=$tolerance, max$\_$step$=$max$\_$step$)$

# Extracting positions

earth$\_$positions $=$ solution. $y[$:$2]$ venuspositions $=$ solution. $y[4$:$6]$

venus$\_$positions $=$ solution.y $4$:$6$ theia$\_$positions $=$ solution.y$[8$:$10]$

# Find when Earth and Theia have the same position

same$\_$position$\_$index $=$ np$.$argmin$($np$.$linalg, norm$($earth$\_$positions.

theia$\_$positions, axis $=0)$ same$\_$position$\_$time $=$ solution.t $[$same$\_$position$\_$index$]$

# Handling division by zero

final$\_$velocity$\_$theia $=np.$linalg.norm$($solution$.$y$[10$:$12,$ same$\_$position$\_$index$])$

if np$.$allclose$($acceleration$($same position$\_$time, solution.y$[$:

same$\_$position$\_$index$]),($:${?}^0\}$

else: final$\_$acceleration$\_$theia $=$ np$.$linalg.norm$($acceleration$($same$\_$position$\_$time,

final$\_$acceleration$\_$theia$\_=$

np$.$linalg.no solution.y$[$:$,$ same$\_$position$\_$index$])[10$:$12])$

# Save positions to text files

np$.$ savetxt$(\text{'}/$Volumes$/$SEAGATE EXP$/$Data$\_$theia$/$earth$\_$positions$2.$txt$\text{'},$

earth$\_$positions$)$

venus$\_$positions$)$

np$.$ savetxt$(\text{'}/$Vol theia$\_$positions$)$

# Plotting

plt$.$ figure $($figsize $=(8,8)$

plt$.$plot$($venus$\_$positions$[0],$ venus$\_$positions$[1],$ label$=$'venus orbit'$)$

plt$.$scatter$($earth$\_$positions$[0][-1],$ earth$\_$positions$[1][-1],$ color$=$'blue',

marker$=\text{'}$o$\text{'},$ label$=\text{'}$ Earth'$)$

plt$.$scatter $($venus$\_$positions $[0][-1],$ venus$\_$positions$[1][-1],$ color$=$'green',

marker$=\text{'}0\text{'},$ label$=$'venus'$)$ plt$.$scatter$($theia$\_$positions$[0][-1],$ theia$\_$positions$[1][-1],$ color$=$'red',

marker$=\text{'}$o$\text{'},$ label$=\text{'}$ 'Theia'$)$

plt$.$ scatter $(,,$ color$=$'yellow', label$=$'Sun', zorder$=5)$

plt$.$xlabel$(\text{'}$x $($m$)\text{'})$ plt$.$ylabel$(\text{'}$y $($m$)\text{'})$

plt$.$title$(\text{'}$orbits of Earth, Venus, and Theia around the Sun'$)$

plt$.$gca$().$set$\_$aspend$()$ plt$.$legend

# Specify the path to save the plot

plot$\_$save$\_$path $=\text{'}/$Volumes$/$SEAGATE EXP$/$Data$\_$theia$/$untitled folder$/$plot$.$png$\text{'}$

# Save the plot to an external file

atot$\_$save$\_$path$)$

# Print a message indicating where the plot is saved print$($f$"$Plot saved to: $\{$plot save path$\}")$

print$($f$"$Plot saved to: $\{$plot$\_$save$\_$path$\}")$

print$($f$"$Time when Earth and Theia have the same position:

$\{$same position$\_$time:$\mathrm{.}2$f$\}$ seconds"$)$

print$($f$"$Final acceleration of Theia at that time: $\{$final$\_$acceleration$\_$theia:$\mathrm{.}2$e $($:$\frac{m}{s^2{?}^{\text{'}\text{'}}}\}$

# Print final positions and velocities

print$("$Final positions:"$)$

print$($f$"$Theia: $\{$theia$\_$positio

print$("\text{'}$nfinat velocities:"$)$

print$($f$"$Theia: $\{$solution$.$y$[10$:$12,-1]\}")$