问题
How can I put a sphere of radius 1737 at the location of (384400,0,0)?
This sphere would be the moon in my trajectory.
Everything else with the code is fine, I just don't know how to add a sphere in that location with that radius.
import numpy as np
from scipy.integrate import odeint
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
me = 5.974 * 10 ** (24) # mass of the earth
mm = 7.348 * 10 ** (22) # mass of the moon
G = 6.67259 * 10 ** (-20) # gravitational parameter
re = 6378.0 # radius of the earth in km
rm = 1737.0 # radius of the moon in km
r12 = 384400.0 # distance between the CoM of the earth and moon
M = me + mm
pi1 = me / M
pi2 = mm / M
mue = 398600.0 # gravitational parameter of earth km^3/sec^2
mum = G * mm # grav param of the moon
mu = mue + mum
omega = np.sqrt(mu / r12 ** 3)
nu = -129.21 * np.pi / 180 # true anomaly angle in radian
x = 327156.0 - 4671
# x location where the moon's SOI effects the spacecraft with the offset of the
# Earth not being at (0,0) in the Earth-Moon system
y = 33050.0 # y location
vbo = 10.85 # velocity at burnout
gamma = 0 * np.pi / 180 # angle in radians of the flight path
vx = vbo * (np.sin(gamma) * np.cos(nu) - np.cos(gamma) * np.sin(nu))
# velocity of the bo in the x direction
vy = vbo * (np.sin(gamma) * np.sin(nu) + np.cos(gamma) * np.cos(nu))
# velocity of the bo in the y direction
xrel = (re + 300.0) * np.cos(nu) - pi2 * r12
# spacecraft x location relative to the earth
yrel = (re + 300.0) * np.sin(nu)
# r0 = [xrel, yrel, 0]
# v0 = [vx, vy, 0]
u0 = [xrel, yrel, 0, vx, vy, 0]
def deriv(u, dt):
n1 = -((mue * (u[0] + pi2 * r12) / np.sqrt((u[0] + pi2 * r12) ** 2
+ u[1] ** 2) ** 3)
- (mum * (u[0] - pi1 * r12) / np.sqrt((u[0] - pi1 * r12) ** 2
+ u[1] ** 2) ** 3))
n2 = -((mue * u[1] / np.sqrt((u[0] + pi2 * r12) ** 2 + u[1] ** 2) ** 3)
- (mum * u[1] / np.sqrt((u[0] - pi1 * r12) ** 2 + u[1] ** 2) ** 3))
return [u[3], # dotu[0] = u[3]
u[4], # dotu[1] = u[4]
u[5], # dotu[2] = u[5]
2 * omega * u[5] + omega ** 2 * u[0] + n1, # dotu[3] = that
omega ** 2 * u[1] - 2 * omega * u[4] + n2, # dotu[4] = that
0] # dotu[5] = 0
dt = np.arange(0.0, 320000.0, 1) # 200000 secs to run the simulation
u = odeint(deriv, u0, dt)
x, y, z, x2, y2, z2 = u.T
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot(x, y, z)
plt.show()
回答1:
You can add the following code to draw the sphere, before the plt.show():
phi = np.linspace(0, 2 * np.pi, 100)
theta = np.linspace(0, np.pi, 100)
xm = rm * np.outer(np.cos(phi), np.sin(theta)) + r12
ym = rm * np.outer(np.sin(phi), np.sin(theta))
zm = rm * np.outer(np.ones(np.size(phi)), np.cos(theta))
ax.plot_surface(xm, ym, zm)
However, your moon will look all stretched out because the scale is not equal for all axes. In order to change the scales of the axes, you can add something like
ax.auto_scale_xyz([-50000, 400000], [0, 160000], [-130000, 130000])
before plt.show(). The result is still not completely right, but I leave it up to you to play around to get better results -- I just picked some numbers that make it look somewhat better.
回答2:
All the code for a sphere is here:
http://matplotlib.org/examples/mplot3d/surface3d_demo2.html
From there you just have to shift in whichever direction you want and change the 10 to whatever radius you desire.
来源：https://stackoverflow.com/questions/16158339/plotting-a-sphere-in-python-for-an-orbital-trajectory