Python超人-宇宙模拟器

docs/拉格朗日点计算公式.md

+### 拉格朗日点公式
+
+$$
+a = \frac{m2}{m1+m2}
+$$
+```
+a = m2 / (m1 + m2)
+```
+
+$$
+L1 = (R ⋅ (1 - \sqrt[3]{\frac{a}{3}} ) , 0)
+$$
+```
+l1 = (r * (1 - pow(a / 3, 1 / 3)), 0)
+```
+$$
+L2 = (R ⋅ (1 + \sqrt[3]{\frac{a}{3}} ) , 0)
+$$
+```
+l2 = (r * (1 + pow(a / 3, 1 / 3)), 0)
+```
+$$
+L3 = (-R ⋅ (1 + {\frac{5 ⋅ a}{12}} ) , 0)
+$$
+```
+l3 = (-r * (1 + (5 * a) / 12), 0)
+```
+$$
+L4 = (\frac{R}{2} ⋅ {\frac{m1-m2}{m1+m2}}  , \frac{\sqrt{3}}{2} ⋅R)
+$$
+```
+l4 = ((r / 2) * ((m1 - m2) / (m1 + m2)), pow(3, 1 / 2) / 2 * r)
+```
+$$
+L5 = (\frac{R}{2} ⋅ {\frac{m1-m2}{m1+m2}}  , -\frac{\sqrt{3}}{2} ⋅R)
+$$
+```
+l5 = ((r / 2) * ((m1 - m2) / (m1 + m2)), -pow(3, 1 / 2) / 2 * r)
+```
\ No newline at end of file

objs/obj.py

@@ -23,7 +23,7 @@ class Obj(metaclass=ABCMeta):
     def __init__(self, name, mass, init_position, init_velocity,
                  density=5e3, color=(125 / 255, 125 / 255, 125 / 255),
                  texture=None, size_scale=1.0, distance_scale=1.0,
-                 parent=None, ignore_mass=False,
+                 parent=None, ignore_mass=False, trail_scale_factor=1.0,
                  trail_color=None, show_name=False,
                  rotation=None,
                  gravity_only_for=[], model=None):
@@ -95,6 +95,7 @@ class Obj(metaclass=ABCMeta):
         self.light_disable = False
 
         self.__has_rings = False
+        self.trail_scale_factor = trail_scale_factor
 
     def find_model(self, model: str):
         if not model.endswith(".obj"):
@@ -317,7 +318,8 @@ class Obj(metaclass=ABCMeta):
 
     def __repr__(self):
         return '<%s(%s):%s(%s)> m=%.3e(kg), d=%.3e(kg/m³), p=[%.3e,%.3e,%.3e](km), v=%s(km/s), s=%.3e' % \
-               (self.name, self.__class__.__name__, os.path.basename(self.model), os.path.basename(self.texture), self.mass, self.density,
+               (self.name, self.__class__.__name__, os.path.basename(self.model), os.path.basename(self.texture),
+                self.mass, self.density,
                 self.position[0], self.position[1], self.position[2], self.velocity, self.size_scale)
 
     def ignore_gravity_with(self, body):

objs/satellite.py

@@ -20,7 +20,7 @@ class Satellite(Obj):
                  texture="satellite.png", size_scale=1.0, distance_scale=1.0,
                  ignore_mass=False, density=1e3, color=(7, 0, 162),
                  trail_color=(255, 255, 255), show_name=False,
-                 model="satellite.obj",
+                 trail_scale_factor=5.0, model="satellite.obj",
                  parent=None, gravity_only_for=[]):
         params = {
             "name": name,
@@ -34,6 +34,7 @@ class Satellite(Obj):
             "distance_scale": distance_scale,
             "ignore_mass": ignore_mass,
             "trail_color": trail_color,
+            "trail_scale_factor": trail_scale_factor,
             "show_name": show_name,
             "parent": parent,
             "gravity_only_for": gravity_only_for,

sim_lab/lagrangian_points.py

-# https://www.163.com/dy/article/G5F1016F053102ZV.html
-# https://www.sciencedirect.com/topics/physics-and-astronomy/lagrangian-points
-
-
-# 以下是太阳和地球的第一、二、三个拉格朗日点的真实坐标和速度数据：
+"""
+https://www.163.com/dy/article/G5F1016F053102ZV.html
+https://www.sciencedirect.com/topics/physics-and-astronomy/lagrangian-points
+以下是太阳和地球的第一、二、三个拉格朗日点的真实坐标和速度数据：
+L1点： 坐标： x = 0.010205 AU， y = 0 AU， z = 0 AU 速度： vx = 0 m/s， vy = 246.593 m/s， vz = 0 m/s
+L2点： 坐标： x = -0.010205 AU， y = 0 AU， z = 0 AU 速度： vx = 0 m/s， vy = -246.593 m/s， vz = 0 m/s
+L3点： 坐标： x = 0.990445 AU， y = 0 AU， z = 0 AU 速度： vx = 0 m/s， vy = 11.168 m/s， vz = 0 m/s
+L4点： 坐标： x = 0.500 AU， y = 0.866025 AU， z = 0 AU 速度： vx = -2446.292 m/s， vy = -1412.901 m/s， vz = 0 m/s
+L5点： 坐标： x = 0.500 AU， y = -0.866025 AU， z = 0 AU 速度： vx = -2446.292 m/s， vy = 1412.901 m/s， vz = 0 m/s
+https://baike.baidu.com/pic/%E6%8B%89%E6%A0%BC%E6%9C%97%E6%97%A5%E7%82%B9/731078/0/dbb44aed2e738bd4510fa07aa98b87d6277ff94b?fr=lemma&fromModule=lemma_content-image&ct=single#aid=0&pic=dbb44aed2e738bd4510fa07aa98b87d6277ff94b
+"""
 #
-# L1点： 坐标： x = 0.010205 AU， y = 0 AU， z = 0 AU 速度： vx = 0 m/s， vy = 246.593 m/s， vz = 0 m/s
+# AU = 1.496e8
 #
-# L2点： 坐标： x = -0.010205 AU， y = 0 AU， z = 0 AU 速度： vx = 0 m/s， vy = -246.593 m/s， vz = 0 m/s
 #
-# L3点： 坐标： x = 0.990445 AU， y = 0 AU， z = 0 AU 速度： vx = 0 m/s， vy = 11.168 m/s， vz = 0 m/s
+# def compute_barycenter(masses, positions):
+#     """
+#     Compute the barycenter position of celestial objects in 3D space
+#     masses: a list of masses of celestial objects
+#     positions: a list of positions of celestial objects, each position is a tuple (x, y, z)
+#     """
+#     m_sum = sum(masses)
+#     x_sum = 0
+#     y_sum = 0
+#     z_sum = 0
+#     for i in range(len(masses)):
+#         x_sum += masses[i] * positions[i][0] / m_sum
+#         y_sum += masses[i] * positions[i][1] / m_sum
+#         z_sum += masses[i] * positions[i][2] / m_sum
+#     return (x_sum, y_sum, z_sum)
 #
-# L4点： 坐标： x = 0.500 AU， y = 0.866025 AU， z = 0 AU 速度： vx = -2446.292 m/s， vy = -1412.901 m/s， vz = 0 m/s
 #
-# L5点： 坐标： x = 0.500 AU， y = -0.866025 AU， z = 0 AU 速度： vx = -2446.292 m/s， vy = 1412.901 m/s， vz = 0 m/s
+# def get_lagrangian_points(m1, m2, r):
+#     """
+#     https://baike.baidu.com/item/%E6%8B%89%E6%A0%BC%E6%9C%97%E6%97%A5%E7%82%B9/731078
 #
-# 其中，AU表示“天文单位”，即地球与太阳之间的平均距离，约为1.496 x 10^8公里。速度以m/s为单位。
-# 这些数据是基于2021年3月的真实数据，并经过了卫星组织、NASA和欧洲航天局等机构的验证。
-
-# AU = 1.496e8
-AU = 1
-
-import matplotlib.pyplot as plt
-
-points = [(0.010205 * AU, 0), (-0.010205 * AU, 0),
-          # (0.990445 * AU, 0),
-          (0.500 * AU, 0.866025 * AU),
-          (0.500 * AU, -0.866025 * AU)]
-
-# plt.plot(AU, 0, "r.")
-plt.plot(0, 0, "b.")
-for x,y in points:
-    plt.plot(x, y, "g.")
-# x = [1, 2, 3, 4]
-# y = [2, 4, 2, 6]
-# y1 = [e + 1 for e in y]
-# y2 = [e + 2 for e in y]
-# plt.plot(x, y, "b.")  # b：蓝色，.：点
-# plt.plot(x, y1, "ro")  # r：红色，o：圆圈
-# plt.plot(x, y2, "kx")  # k：黑色，x：x字符(小叉)
-plt.show()  # 在窗口显示该图片
-
+#     @param m1: 大质量
+#     @param m2: 小质量
+#     @param r: 半径
+#     @return:
+#     """
+#     a = m2 / (m1 + m2)
+#     l1 = (r * (1 - pow(a / 3, 1 / 3)), 0)
+#     l2 = (r * (1 + pow(a / 3, 1 / 3)), 0)
+#     l3 = (-r * (1 + (5 * a) / 12), 0)
+#     l4 = ((r / 2) * ((m1 - m2) / (m1 + m2)), pow(3, 1 / 2) / 2 * r)
+#     l5 = ((r / 2) * ((m1 - m2) / (m1 + m2)), -pow(3, 1 / 2) / 2 * r)
+#
+#     # print(l1[0]/AU, l2[0]/AU, l3[0]/AU, l4[0]/AU, l5[0]/AU)
+#     return l1, l2, l3, l4, l5
 #
+#
+# def show_figure(points, p1_name, p2_name, unit, barycenter=None):
 #     import matplotlib.pyplot as plt
 #
-# # Data from NASA
-# L1 = [1.5e6, 0]
-# L2 = [-1.5e6, 0]
-# L3 = [-1.5e6, 0]
-# L4 = [0.5e6, 0.87e6]
-# L5 = [0.5e6, -0.87e6]
-# sun = [0, 0]
-# earth = [0, -1.5e8]
+#     plt.figure(figsize=(16, 12))
+#     plt.plot(0, 0, "ro", markersize=20, label=p1_name)
+#     plt.text(-unit / 20, -unit / 10, p1_name, fontsize=30, color="r")
+#     plt.plot(unit, 0, "b.", markersize=4, label=p2_name)
+#     plt.text(unit - unit / 20, -unit / 20, p2_name, fontsize=20, color="b")
+#     idx = 1
+#
+#     for x, y in points:
+#         plt.plot(x, y, "gx", markersize=3, label=f"L{idx}")
+#         if idx == 1:
+#             x_offset = -unit / 22
+#         else:
+#             x_offset = unit / 300
+#         plt.text(x + x_offset, y + unit / 300, f"L{idx}", fontsize=18, color="g")
+#         idx += 1
 #
-# # Create plot and set axis limits
-# fig, ax = plt.subplots()
-# # ax.set_xlim(-2.5e8, 2.5e8)
-# # ax.set_ylim(-2.5e8, 2.5e8)
+#     if barycenter is not None:
+#         plt.plot(barycenter[0], barycenter[1], "gx", markersize=10, label=f"L{idx}")
 #
-# # Plot positions of Lagrange points, Sun and Earth
-# ax.plot(sun[0], sun[1], 'o', markersize=10, color='yellow')
-# # ax.plot(earth[0], earth[1], 'o', markersize=5, color='blue')
-# ax.plot(L1[0], L1[1], 'x', markersize=10, color='red')
-# ax.plot(L2[0], L2[1], 'x', markersize=10, color='green')
-# ax.plot(L3[0], L3[1], 'x', markersize=10, color='purple')
-# ax.plot(L4[0], L4[1], '+', markersize=10, color='red')
-# ax.plot(L5[0], L5[1], '+', markersize=10, color='green')
+#     # plt.plot(x, y, "b.")  # b：蓝色，.：点
+#     # plt.plot(x, y1, "ro")  # r：红色，o：圆圈
+#     # plt.plot(x, y2, "kx")  # k：黑色，x：x字符(小叉)
+#     plt.show()  # 在窗口显示该图片
 #
-# # Plot labels for Lagrange points, Sun and Earth
-# # ax.annotate('Sun', (sun[0]+2e7, sun[1]+2e7))
-# # ax.annotate('Earth', (earth[0]+2e7, earth[1]+2e7))
-# ax.annotate('L1', (L1[0]+2e7, L1[1]+2e7))
-# ax.annotate('L2', (L2[0]+2e7, L2[1]+2e7))
-# ax.annotate('L3', (L3[0]+2e7, L3[1]+2e7))
-# ax.annotate('L4', (L4[0]+2e7, L4[1]+2e7))
-# ax.annotate('L5', (L5[0]+2e7, L5[1]+2e7))
 #
-# # Set title and show plot
-# plt.title('Positions of Lagrange Points L1 to L5, Sun and Earth')
-# plt.show()
\ No newline at end of file
+# barycenter = compute_barycenter([5.97237e24, 7.342e22], [[0, 0, 0], [363104, 0, 0]])
+# print(barycenter)
+# # show_figure(get_lagrangian_points(1.9891e30, 5.97237e24, AU), "Sun", "Earth", AU)
+# show_figure(get_lagrangian_points(5.97237e24, 7.342e22, 363104), "Earth", "Moon", 363104, barycenter)
+
+# **************************************************************************************************************
+# **************************************************************************************************************
+
+# -*- coding:utf-8 -*-
+# title           :地月场景模拟
+# description     :地月场景模拟
+# author          :Python超人
+# date            :2023-02-11
+# link            :https://gitcode.net/pythoncr/
+# python_version  :3.8
+# ==============================================================================
+from bodies import Sun, Earth, Moon
+from objs import Satellite, Satellite2
+from common.consts import SECONDS_PER_HOUR, SECONDS_PER_HALF_DAY, SECONDS_PER_DAY, SECONDS_PER_WEEK, SECONDS_PER_MONTH
+from sim_scenes.func import ursina_run, camera_look_at
+from bodies.body import AU
+from simulators.ursina.entities.body_timer import TimeData
+from simulators.ursina.entities.entity_utils import create_directional_light
+from simulators.ursina.ursina_event import UrsinaEvent
+from simulators.ursina.ursina_mesh import create_line
+
+
+def compute_barycenter(masses, positions):
+    """
+    Compute the barycenter position of celestial objects in 3D space
+    masses: a list of masses of celestial objects
+    positions: a list of positions of celestial objects, each position is a tuple (x, y, z)
+    """
+    m_sum = sum(masses)
+    x_sum = 0
+    y_sum = 0
+    z_sum = 0
+    for i in range(len(masses)):
+        x_sum += masses[i] * positions[i][0] / m_sum
+        y_sum += masses[i] * positions[i][1] / m_sum
+        z_sum += masses[i] * positions[i][2] / m_sum
+    return (x_sum, y_sum, z_sum)
+
+
+def get_lagrangian_points(m1, m2, r):
+    """
+    https://baike.baidu.com/item/%E6%8B%89%E6%A0%BC%E6%9C%97%E6%97%A5%E7%82%B9/731078
+
+    @param m1: 大质量
+    @param m2: 小质量
+    @param r: 半径
+    @return:
+    """
+    a = m2 / (m1 + m2)
+    l1 = (0, 0, r * (1 - pow(a / 3, 1 / 3)))
+    l2 = (0, 0, r * (1 + pow(a / 3, 1 / 3)))
+    l3 = (0, 0, -r * (1 + (5 * a) / 12))
+    l4 = (pow(3, 1 / 2) / 2 * r, 0, (r / 2) * ((m1 - m2) / (m1 + m2)))
+    l5 = (-pow(3, 1 / 2) / 2 * r, 0, (r / 2) * ((m1 - m2) / (m1 + m2)))
+
+    return l1, l2, l3, l4, l5
+
+
+if __name__ == '__main__':
+    """
+    地球、月球
+    """
+    OFFSETTING = 0
+    # TODO: 可以抵消月球带动地球的力，保持地球在原地
+    # OFFSETTING = 0.01265
+    bodies = [
+        Earth(init_position=[0, 0, 0], texture="earth_hd.jpg",
+              init_velocity=[OFFSETTING, 0, 0], size_scale=0.5e1),  # 地球放大 5 倍，距离保持不变
+        Moon(init_position=[0, 0, 363104],  # 距地距离约: 363104 至 405696 km
+             init_velocity=[-1.03, 0, 0], size_scale=1e1)  # 月球放大 10 倍，距离保持不变
+    ]
+    earth = bodies[0]
+    moon = bodies[1]
+
+    points = get_lagrangian_points(earth.mass, moon.mass, 363104)
+    offset_points = [
+        [0, 0, 21590],  # 调整加速度为0
+        [0, 0, 0],
+        [0, 0, 0],
+        [0, 0, 0],
+        [0, 0, 0],
+    ]
+    velocities = [
+        [-0.7, -0.1, 0],  # [-0.859, 0, 0],
+        [-1.265, 0, 0],
+        [1.03, 0, 0],
+        [0, 0, 0],
+        [0, 0, 0],
+    ]
+    for i, point in enumerate(points):
+        satellite = Satellite(name=f'卫星{i + 1}', mass=1.4e10, size_scale=1e3, color=(255, 200, 0),
+                              init_position=[point[0] + offset_points[i][0],
+                                             point[1] + offset_points[i][1],
+                                             point[2] + offset_points[i][2]],
+                              init_velocity=velocities[i])
+        bodies.append(satellite)
+
+
+    def on_ready():
+        # 运行前触发
+        # 运行开始前，将摄像机指向地球
+
+        # 摄像机看向地球
+        camera_look_at(moon)
+
+
+    def on_timer_changed(time_data: TimeData):
+        from ursina import destroy
+        if hasattr(earth, "line"):
+            destroy(earth.line)
+        earth.line = create_line(from_pos=earth.planet.position, to_pos=moon.planet.main_entity.position)
+
+
+    # 订阅事件后，上面的函数功能才会起作用
+    # 运行前会触发 on_ready
+    UrsinaEvent.on_ready_subscription(on_ready)
+    # 运行中，每时每刻都会触发 on_timer_changed
+    UrsinaEvent.on_timer_changed_subscription(on_timer_changed)
+
+    # 使用 ursina 查看的运行效果
+    # 常用快捷键： P：运行和暂停  O：重新开始  I：显示天体轨迹
+    # position = 左-右+、上+下-、前+后-
+    ursina_run(bodies, SECONDS_PER_HOUR,
+               position=(-300000, 1500000, -100),
+               show_timer=True,
+               show_trail=True)

simulators/ursina/entities/entity_utils.py

@@ -57,6 +57,14 @@ def trail_init(parent, scale):
     trail_color = conv_to_vec4_color(parent.body_view.body.trail_color)
     trail_color = adjust_brightness(trail_color, 0.4)
     parent.trail_color = color.rgba(trail_color[0], trail_color[1], trail_color[2], 0.6)
+
+    if hasattr(parent.body, "trail_scale_factor"):
+        if parent.body.trail_scale_factor is not None:
+            parent.trail_scale = parent.body.trail_scale_factor * scale
+        else:
+            # 拖尾球体的大小为该天体的 1/5
+            parent.trail_scale = scale / 5
+    else:
         # 拖尾球体的大小为该天体的 1/5
         parent.trail_scale = scale / 5
     if parent.trail_scale < 1: