• VPhysics程式設計

行星公轉

• 講義

• 「地球繞太陽」的程式碼：

  Web VPython 3.2
  # 匯入視覺化套件
  from vpython import *
  
  scene = canvas(width=800, height=800, background=vector(0.5,0.5,0))
  scene.forward = vector(0, -1, 0)
  
  G=6.673E-11
  
  def G_force(mass, pos_vector):
                  return -G * sun.mass * mass / mag2(pos_vector) * norm(pos_vector)
  
  sun = sphere(radius = 2.1E10, color = color.orange, texture = textures.stucco)
  sun.mass = 1.989E30
  sun.pos = vector(0,0,0)
  
  earth = sphere(radius = 9.56E9, texture = textures.earth, make_trail = True)
  earth.mass = 5.972E24
  earth.distance = 1.495E11
  earth.v = vector(0,0,2.9783E4)
  earth.pos = vector(earth.distance, 0, 0)
  
  dt = 60*60
  while True:
      rate(6*24)
      earth.a = G_force(earth.mass, earth.pos) / earth.mass
      earth.v = earth.v + earth.a * dt
      earth.pos = earth.pos + earth.v * dt

  【作業1】

  • 增加一顆火星

  mars.radius = 4.9E9

  mars.mass = 6.42E23

  mars.distance = 2.279E11

  mars.v = vector(0, 0, 2.4077E4)

  • 參考解答

  Web VPython 3.2
  # 匯入視覺化套件
  from vpython import *
  
  scene = canvas(width=800, height=800, background=vector(0.5,0.5,0))
  scene.forward = vector(0, -1, 0)
  
  G=6.673E-11
  
  def G_force(mass, pos_vector):
                  return -G * sun.mass * mass / mag2(pos_vector) * norm(pos_vector)
  
  sun = sphere(radius = 2.1E10, color = color.orange, texture = textures.stucco)
  sun.mass = 1.989E30
  sun.pos = vector(0,0,0)
  
  earth = sphere(radius = 9.56E9, texture = textures.earth, make_trail = True)
  earth.mass = 5.972E24
  earth.distance = 1.495E11
  earth.v = vector(0,0,2.9783E4)
  earth.pos = vector(earth.distance, 0, 0)
  
  mars = sphere(radius = 4.9E9, texture = textures.stucco, make_trail = True)
  mars.mass = 6.42E23
  mars.distance = 2.279E11
  mars.v = vector(0, 0, 2.4077E4)
  mars.pos = vector(mars.distance, 0, 0)
  
  dt = 60*60
  while True:
      rate(6*24)
      earth.a = G_force(earth.mass, earth.pos) / earth.mass
      earth.v = earth.v + earth.a * dt
      earth.pos = earth.pos + earth.v * dt
      
      mars.a = G_force(mars.mass, mars.pos) / mars.mass
      mars.v = mars.v + mars.a * dt
      mars.pos = mars.pos + mars.v * dt

  【作業2】

  • 增加一顆哈雷慧星

  halley.radius = 1.0E10

  halley.mass = 2.2E14

  halley.distance = 8.7665E10

  halley.v = vector(0, 0, 54563.3)

  • 參考解答

  Web VPython 3.2
  # 匯入視覺化套件
  from vpython import *
  
  scene = canvas(width=800, height=800, background=vector(0.5,0.5,0))
  scene.forward = vector(0, -1, 0)
  
  G=6.673E-11
  
  def G_force(mass, pos_vector):
                  return -G * sun.mass * mass / mag2(pos_vector) * norm(pos_vector)
  
  sun = sphere(radius = 2.1E10, color = color.orange, texture = textures.stucco)
  sun.mass = 1.989E30
  sun.pos = vector(0,0,0)
  
  earth = sphere(radius = 9.56E9, texture = textures.earth, make_trail = True)
  earth.mass = 5.972E24
  earth.distance = 1.495E11
  earth.v = vector(0,0,2.9783E4)
  earth.pos = vector(earth.distance, 0, 0)
  
  mars = sphere(radius = 4.9E9, texture = textures.stucco, make_trail = True)
  mars.mass = 6.42E23
  mars.distance = 2.279E11
  mars.v = vector(0, 0, 2.4077E4)
  mars.pos = vector(mars.distance, 0, 0)
  
  halley = sphere(radius = 1.0E10, texture = textures.stucco, make_trail = True)
  halley.mass = 2.2E14
  halley.distance = 8.7665E10
  halley.v = vector(0, 0, 54563.3)
  halley.pos = vector(halley.distance, 0, 0)
  
  dt = 60*60
  while True:
      rate(1000*24)
      earth.a = G_force(earth.mass, earth.pos) / earth.mass
      earth.v = earth.v + earth.a * dt
      earth.pos = earth.pos + earth.v * dt
      
      mars.a = G_force(mars.mass, mars.pos) / mars.mass
      mars.v = mars.v + mars.a * dt
      mars.pos = mars.pos + mars.v * dt
      
      halley.a = G_force(halley.mass, halley.pos) / halley.mass
      halley.v = halley.v + halley.a * dt
      halley.pos = halley.pos + halley.v * dt