一篇文章教你用Python绘画一个太阳系

目录

• 日地月三体
• 日地火
• 太阳系

#后续代码主要更改这里的参数
m = [1.33e20,3.98e14,4.9e12]
x = np.array([0,1.5e11,1.5e11+3.8e8])
y = np.array([0,0,0])
u = np.array([0,0,0])
v = np.array([0,2.88e4,1.02e3])

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import animation
m = [1.33e20,3.98e14,4.9e12]
x = np.array([0,1.5e11,1.5e11+3.8e8])
y = np.array([0.0,0,0])
u = np.array([0.0,0,0])
v = np.array([0,2.88e4,2.88e4+1.02e3])
fig = plt.figure(figsize=(12,12))
ax = fig.add_subplot(xlim=(-2e11,2e11),ylim=(-2e11,2e11))
ax.grid()
trace0, = ax.plot([],[],"-", lw=0.5)
trace1, = ax.plot([],[],"-", lw=0.5)
trace2, = ax.plot([],[],"-", lw=0.5)
pt0, = ax.plot([x[0]],[y[0]] ,marker="o")
pt1, = ax.plot([x[0]],[y[0]] ,marker="o")
pt2, = ax.plot([x[0]],[y[0]] ,marker="o")
k_text = ax.text(0.05,0.85,"",transform=ax.transAxes)
textTemplate = "t = %.3f days
"
N = 1000
dt = 36000
ts =  np.arange(0,N*dt,dt)/3600/24
xs,ys = [],[]
for _ in ts:
    x_ij = (x-x.reshape(3,1))
    y_ij = (y-y.reshape(3,1))
    r_ij = np.sqrt(x_ij**2+y_ij**2)
    for i in range(3):
        for j in range(3):
            if i!=j :
                u[i] += (m[j]*x_ij[i,j]*dt/r_ij[i,j]**3)
                v[i] += (m[j]*y_ij[i,j]*dt/r_ij[i,j]**3)
    x += u*dt
    y += v*dt
    xs.append(x.tolist())
    ys.append(y.tolist())
xs = np.array(xs)
ys = np.array(ys)
def animate(n):
    trace0.set_data(xs[:n,0],ys[:n,0])
    trace1.set_data(xs[:n,1],ys[:n,1])
    #绘图时的地月距离扩大100倍，否则看不清
    tempX2S = xs[:n,1]+100*(xs[:n,2]-xs[:n,1])
    tempY2S = ys[:n,1]+100*(ys[:n,2]-ys[:n,1])
    trace2.set_data(tempX2S,tempY2S)
    pt0.set_data([xs[n,0]],[ys[n,0]])
    pt1.set_data([xs[n,1]],[ys[n,1]])
    tempX = xs[n,1]+100*(xs[n,2]-xs[n,1])
    tempY = ys[n,1]+100*(ys[n,2]-ys[n,1])
    pt2.set_data([tempX],[tempY])
    k_text.set_text(textTemplate % ts[n])
    return trace0, trace1, trace2, pt0, pt1, pt2, k_text
ani = animation.FuncAnimation(fig, animate, 
    range(N), interval=10, blit=True)
plt.show()
ani.save("3.gif")

m = [1.33e20,3.98e14,4.28e13]
x = np.array([0,1.5e11,2.28e11])
y = np.array([0.0,0,0])
u = np.array([0.0,0,0])
v = np.array([0,2.88e4,2.4e4])
### 由于火星离地球很远，所以不必再改变尺度
def animate(n):
    trace0.set_data(xs[:n,0],ys[:n,0])
    trace1.set_data(xs[:n,1],ys[:n,1])
    trace2.set_data(xs[:n,2],ys[:n,2])
    pt0.set_data([xs[n,0]],[ys[n,0]])
    pt1.set_data([xs[n,1]],[ys[n,1]])
    pt2.set_data([xs[n,2]],[ys[n,2]])
    k_text.set_text(textTemplate % ts[n])
    return trace0, trace1, trace2, pt0, pt1, pt2, k_text

au,G,RE,ME = 1.48e11,6.67e-11,1.48e11,5.965e24
m = np.array([3.32e5,0.055,0.815,1,
              0.107,317.8,95.16,14.54,17.14])*ME*6.67e-11
r = np.array([0,0.387,0.723,1,1.524,5.203,
              9.537,19.19,30.7])*RE
theta = np.random.rand(9)*np.pi*2
x = r*np.cos(theta)
y = r*np.sin(theta)
v = np.array([0,47.89,35.03,29.79,
              24.13,13.06,9.64,6.81,5.43])*1000
u = -v*np.sin(theta)
v = v*np.cos(theta)
name = "solar.gif"
fig = plt.figure(figsize=(10,10))
ax = fig.add_subplot(xlim=(-31*RE,31*RE),ylim=(-31*RE,31*RE))
ax.grid()
traces = [ax.plot([],[],"-", lw=0.5)[0] for _ in range(9)]
pts = [ax.plot([],[],marker="o")[0] for _ in range(9)]
k_text = ax.text(0.05,0.85,"",transform=ax.transAxes)
textTemplate = "t = %.3f days
"
N = 500
dt = 3600*50
ts =  np.arange(0,N*dt,dt)
xs,ys = [],[]
for _ in ts:
    x_ij = (x-x.reshape(len(m),1))
    y_ij = (y-y.reshape(len(m),1))
    r_ij = np.sqrt(x_ij**2+y_ij**2)
    for i in range(len(m)):
        for j in range(len(m)):
            if i!=j :
                u[i] += (m[j]*x_ij[i,j]*dt/r_ij[i,j]**3)
                v[i] += (m[j]*y_ij[i,j]*dt/r_ij[i,j]**3)
    x += u*dt
    y += v*dt
    xs.append(x.tolist())
    ys.append(y.tolist())
xs = np.array(xs)
ys = np.array(ys)
def animate(n):
    for i in range(9):
        traces[i].set_data(xs[:n,i],ys[:n,i])
        pts[i].set_data(xs[n,i],ys[n,i])
    k_text.set_text(textTemplate % (ts[n]/3600/24))
    return traces+pts+[k_text]
ani = animation.FuncAnimation(fig, animate, 
    range(N), interval=10, blit=True)
plt.show()
ani.save(name)