""" 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 """ # # AU = 1.496e8 # # # 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 = (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 # # 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 # # if barycenter is not None: # plt.plot(barycenter[0], barycenter[1], "gx", markersize=10, label=f"L{idx}") # # # 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 # # # 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)