Orbit of Earth: Plotting Trajectory

[Graham87]

Homework Statement

Write a program to calculate the orbit of the Earth using leapfrog and plot it

Relevant Equations

-GM r/r^3

I am attempting this homework exercise but my plot does not show the whole trajectory. I don't know if it is something wrong with my equations or if it is a plotting matter.

Cheers!This is my code:

import matplotlib.pyplot as plt
import numpy as np
import scipy.integrate as spi

G = 6.6738*10**-11
M = 1.9891*10**30
h = 3600
y = 1.4710*10**11
vx = 3.0287*20**4

def LeapFrog(f, t_start, t_stop, z0, h):

    t_vec = np.arange(t_start, t_stop, h)
    n = len(t_vec)
    d = len(z0) 
    z_vec = np.zeros((n, d))
    z_vec[0,:] = z0
    z_half_step=z_vec[0 , :] + (1/2)*h*f(z0,t_vec[0])    for i in range(0, n - 1):
        z_vec[i+1,:]=z_vec[i,:] + h*f(z_half_step, t_vec[i])
        z_half_step += h*f(z_vec[i+1,:], t_vec[i])   

    return t_vec, z_vec,def f(z,t):   

    x=z[0]
    y=z[1]
    vx=z[2]
    vy=z[3]
    r=np.sqrt(x**2+y**2)

    dz=np.zeros(4)

    dz[0]=vx
    dz[1]=vy
    dz[2]=-G*M*x/r**3
    dz[3]=-G*M*y/r**3

    return dz

t_start = 0
t_stop = 24*365*5
z0 = np.array([0,y,vx,0])
t_vec, z_vec = LeapFrog(f, t_start, t_stop, z0, h)

plt.plot(z_vec[:,0],z_vec[:,1], 'g', markersize=1, label='Earth trajectory')
plt.plot(0,0,'yo', label = 'Sun positon') 
plt.show()

 

[malawi_glenn]

vx = 3.0287*20**4

 

[Graham87]

vx = 3.0287*20**4

Ah!

Should be vx=3.0287*10**4 and
t_stop = 24 * 365 * 0.99 * h

Now it's correct.

Thanks!

 

[malawi_glenn]

Now it's correct.

Plot works now?

 

[Graham87]

Plot works now?

Works neatly !

 

[malawi_glenn]

Great job!

Could you fix the plot so that the non-cicrular shape is manifest?
Perhaps also you can plot a circular orbit centered around the sun with the Earth's average orbital distance as well

 

[Graham87]

Great job!

Could you fix the plot so that the non-cicrular shape is manifest?
Perhaps also you can plot a circular orbit centered around the sun with the Earth's average orbital distance as well

Great idea.
This is much clearer.