Problem Updating Angular Velocity and Angles in Binary Star Orbit Simulation (Python, Matplotlib) - Stack Overflow

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I'm creating a simulation for a binary star system in python using matplotlib. I want it to change based on the users inputs through sliders I've provided. When I first created this without any real equations for binary star systems (w = sqrt(G*M/r) and theta += w * dt) it worked perfectly. When the masses of each star were changed/the separation between them both, the individual distances of the stars would change too. But when I try to change the speed as well, the total separation of the stars doesn't stay constant. They should always be travelling opposite to one another. I can't find the exact problem and I have a feeling it can be a combination of multiple. I'm also trying to avoid using elliptical orbits.

My code:

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
from matplotlib.widgets import Slider
import scipy
from math import sqrt

from scipy.constants import pi

dt = 0.1
numsteps = 10000
pi = pi ## imported by from scipy.constants import pi
G = 4.30091e-3  # AU^3 * M_sun^-1 * yr^-2
wA =3.0
wB =3.0

thetaA = 0
thetaB = thetaA+pi #to put the other store on the opposite end of starA

#initialise variables
r = 5
mA = 50 #mass in solar mass
mB = 50
M = mA+mB

x_valA,y_valA = [],[]
x_valB,y_valB = [],[]

# Create the animation, fig represents the object/canvas and ax means it is the area being plotted on
fig, ax = plt.subplots()
# the graph, sets limits for axis
ax.set_xlim(-10, 10)
ax.set_ylim(-10, 10)
ax.set_aspect('equal')

ax.set_facecolor("black")

# Create the stars and COM plot
starA, = ax.plot([], [], 'o', color='blue', markersize=10, label='Star A')
starB, = ax.plot([], [], 'o', color='red', markersize=10, label='Star B')
COM = ax.plot([0],[0], '+', color='white', markersize=5, label='COM')
ax.legend()

def orbit(r,mA,mB,M):
    global x_valA, y_valA, x_valB, y_valB, thetaA, thetaB, G, dt

    # Reset variables
    x_valA, y_valA = [], []
    x_valB, y_valB = [], []

    M = mA+mB
    rA = r*(mB/M)
    rB = r*(mA/M)

    #initial positions
    positionA = np.array([rA * np.cos(thetaA), rA * np.sin(thetaA)])  # Star A initial position
    positionB = np.array([rB * np.cos(thetaB), rB * np.sin(thetaB)])  # Star B initial position

    # SIMULATION LOOP
    for _ in range(numsteps):
        # Store positions for both stars
        x_valA.append(positionA[0])
        y_valA.append(positionA[1])
        x_valB.append(positionB[0])
        y_valB.append(positionB[1])
    
        # Update speed and angles for next positions
        wA = sqrt(G*M/rA)
        wB = sqrt(G*M/rB)
        thetaA += wA * dt #update angle for starA
        thetaB += wB * dt #update angle for starB
    
        # Calculate new positions based on updated angles
        positionA = np.array([rA * np.cos(thetaA), rA * np.sin(thetaA)])
        positionB = np.array([rB * np.cos(thetaB), rB * np.sin(thetaB)])

#initialising the data
def init():
    starA.set_data([], [])
    starB.set_data([],[])
    return starA, starB

def update(frame):
    starA.set_data([x_valA[frame]], [y_valA[frame]])  # Pass as lists
    starB.set_data([x_valB[frame]], [y_valB[frame]])
    return starA, starB

ani = FuncAnimation(fig, update, frames=numsteps, init_func=init, blit=True, interval=50)
plt.title("Binary Star System")

def up(val):
    global r, mA, mB, M
    r = seperation_slider.val
    mA = mA_slider.val
    mB = mB_slider.val
    M = mA + mB
    orbit(r, mA, mB, M) # updated values into function
    ani.event_source.stop()  # Stop the current animation
    ani.event_source.start()  # Restart the animation with updated orbit
    fig.canvas.draw_idle()
   
seperation_slider = Slider(ax=plt.axes([0.1, 0.00, 0.10, 0.04]), label='Radius', valmin=1, valmax=15, valinit=r, facecolor='w')
mA_slider = Slider(ax=plt.axes([0.45, 0.00, 0.15, 0.04]), label="Mass A", valmin=0.1, valmax=100, valinit=mA, facecolor='b')
mB_slider = Slider(ax=plt.axes([0.80, 0.00, 0.15, 0.04]), label="Mass B", valmin=0.1, valmax=100, valinit=mB, facecolor='r')

seperation_slider.on_changed(up)
mA_slider.on_changed(up)
mB_slider.on_changed(up)

orbit(r,mA,mB,M)

plt.show()

I've tried changing the constants due to unit conversions. Thought about inputing some real values in and comparing speed values but thought it would take too much time. I also thought about the rA and rB variables and how they're defined but I'm not really sure how to go from there.

I'm creating a simulation for a binary star system in python using matplotlib. I want it to change based on the users inputs through sliders I've provided. When I first created this without any real equations for binary star systems (w = sqrt(G*M/r) and theta += w * dt) it worked perfectly. When the masses of each star were changed/the separation between them both, the individual distances of the stars would change too. But when I try to change the speed as well, the total separation of the stars doesn't stay constant. They should always be travelling opposite to one another. I can't find the exact problem and I have a feeling it can be a combination of multiple. I'm also trying to avoid using elliptical orbits.

My code:

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
from matplotlib.widgets import Slider
import scipy
from math import sqrt

from scipy.constants import pi

dt = 0.1
numsteps = 10000
pi = pi ## imported by from scipy.constants import pi
G = 4.30091e-3  # AU^3 * M_sun^-1 * yr^-2
wA =3.0
wB =3.0

thetaA = 0
thetaB = thetaA+pi #to put the other store on the opposite end of starA

#initialise variables
r = 5
mA = 50 #mass in solar mass
mB = 50
M = mA+mB

x_valA,y_valA = [],[]
x_valB,y_valB = [],[]

# Create the animation, fig represents the object/canvas and ax means it is the area being plotted on
fig, ax = plt.subplots()
# the graph, sets limits for axis
ax.set_xlim(-10, 10)
ax.set_ylim(-10, 10)
ax.set_aspect('equal')

ax.set_facecolor("black")

# Create the stars and COM plot
starA, = ax.plot([], [], 'o', color='blue', markersize=10, label='Star A')
starB, = ax.plot([], [], 'o', color='red', markersize=10, label='Star B')
COM = ax.plot([0],[0], '+', color='white', markersize=5, label='COM')
ax.legend()

def orbit(r,mA,mB,M):
    global x_valA, y_valA, x_valB, y_valB, thetaA, thetaB, G, dt

    # Reset variables
    x_valA, y_valA = [], []
    x_valB, y_valB = [], []

    M = mA+mB
    rA = r*(mB/M)
    rB = r*(mA/M)

    #initial positions
    positionA = np.array([rA * np.cos(thetaA), rA * np.sin(thetaA)])  # Star A initial position
    positionB = np.array([rB * np.cos(thetaB), rB * np.sin(thetaB)])  # Star B initial position

    # SIMULATION LOOP
    for _ in range(numsteps):
        # Store positions for both stars
        x_valA.append(positionA[0])
        y_valA.append(positionA[1])
        x_valB.append(positionB[0])
        y_valB.append(positionB[1])
    
        # Update speed and angles for next positions
        wA = sqrt(G*M/rA)
        wB = sqrt(G*M/rB)
        thetaA += wA * dt #update angle for starA
        thetaB += wB * dt #update angle for starB
    
        # Calculate new positions based on updated angles
        positionA = np.array([rA * np.cos(thetaA), rA * np.sin(thetaA)])
        positionB = np.array([rB * np.cos(thetaB), rB * np.sin(thetaB)])

#initialising the data
def init():
    starA.set_data([], [])
    starB.set_data([],[])
    return starA, starB

def update(frame):
    starA.set_data([x_valA[frame]], [y_valA[frame]])  # Pass as lists
    starB.set_data([x_valB[frame]], [y_valB[frame]])
    return starA, starB

ani = FuncAnimation(fig, update, frames=numsteps, init_func=init, blit=True, interval=50)
plt.title("Binary Star System")

def up(val):
    global r, mA, mB, M
    r = seperation_slider.val
    mA = mA_slider.val
    mB = mB_slider.val
    M = mA + mB
    orbit(r, mA, mB, M) # updated values into function
    ani.event_source.stop()  # Stop the current animation
    ani.event_source.start()  # Restart the animation with updated orbit
    fig.canvas.draw_idle()
   
seperation_slider = Slider(ax=plt.axes([0.1, 0.00, 0.10, 0.04]), label='Radius', valmin=1, valmax=15, valinit=r, facecolor='w')
mA_slider = Slider(ax=plt.axes([0.45, 0.00, 0.15, 0.04]), label="Mass A", valmin=0.1, valmax=100, valinit=mA, facecolor='b')
mB_slider = Slider(ax=plt.axes([0.80, 0.00, 0.15, 0.04]), label="Mass B", valmin=0.1, valmax=100, valinit=mB, facecolor='r')

seperation_slider.on_changed(up)
mA_slider.on_changed(up)
mB_slider.on_changed(up)

orbit(r,mA,mB,M)

plt.show()

I've tried changing the constants due to unit conversions. Thought about inputing some real values in and comparing speed values but thought it would take too much time. I also thought about the rA and rB variables and how they're defined but I'm not really sure how to go from there.

• python
• matplotlib
• physics
• orbital-mechanics

Share Improve this question Follow edited Jan 25 at 22:30 Nelly asked Jan 25 at 13:21 NellyNelly 1333 bronze badges New contributor Nelly is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct. 2

• mmmh astro.ucla.edu/undergrad/astro3/orbits.html look there is a one more slider here – pippo1980 Commented Jan 25 at 21:37
• Yes, I've seen this example and the extra slider just changes how eliptical the orbits are. So it doesn't actually have an affect on anything as it works when both stars are kept at a circular orbit (e=0). Thank you for the resource recommendation – Nelly Commented Jan 25 at 22:26

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1 Answer 1

Sorted by: Reset to default 0

try changing:

# Update speed and angles for next positions
        wA = sqrt(G*M/rA)
        wB = sqrt(G*M/rB)

with :

# Update speed and angles for next positions
        wA = sqrt(G*M/rA*rA)
        wB = sqrt(G*M/rB*rB)

and let us know

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