# -*- coding:utf-8 -*- # title :拉格朗日点模拟 # description :拉格朗日点模拟 # author :Python超人 # date :2023-02-11 # link :https://gitcode.net/pythoncr/ # python_version :3.8 # ============================================================================== from bodies import Body, Sun, Earth, Moon from objs import Obj, Satellite, Satellite2 from common.consts import SECONDS_PER_HOUR, SECONDS_PER_DAY, SECONDS_PER_WEEK, SECONDS_PER_MONTH from sim_scenes.func import ursina_run, camera_look_at 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 import math bodies = [ Earth(init_position=[0, 0, 0], texture="earth_hd.jpg", init_velocity=[0, 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=[-1.054152222, 0, 0], size_scale=1e1) # 月球放大 10 倍,距离保持不变 ] earth = bodies[0] moon = bodies[1] def get_lagrangian_points(m1, m2, r): """ @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 # 计算地月拉格朗日点 L1_p, L2_p, L3_p, L4_p, L5_p = get_lagrangian_points(earth.mass, moon.mass, 363104) def create_satellite(name, init_position, init_velocity): """ 在 L1, L2, L3, L4, L5 创建卫星 @param name: @param init_position: @param init_velocity: @return: """ satellite = Satellite(name=name, mass=1.4e10, size_scale=4e3, color=(255, 200, 0), init_position=init_position, init_velocity=init_velocity, gravity_only_for=[earth, moon]) return satellite # L1:point=[0,0,308536.70059015526] velocity=[-0.890136271716, 0, 0] satelliteL1 = create_satellite(name=f'卫星L1', init_position=L1_p, init_velocity=[-0.890136271716, 0, 0]) bodies.append(satelliteL1) # L2:point=[0,0, 423338.5083198447] velocity=[-1.24, 0, 0] satelliteL2 = create_satellite(name=f'卫星L2', init_position=L2_p, init_velocity=[-1.24, 0, 0]) bodies.append(satelliteL2) vel_L345 = 1.048 # L3:point=[0,0, -364941.3043941873] velocity=[1.039 , 0, 0] satelliteL3 = create_satellite(name=f'卫星L3', init_position=L3_p, init_velocity=[vel_L345, 0, 0]) bodies.append(satelliteL3) # L4:point=[0,0, 177142.46945395062] velocity=[1.039 , 0, 0] satelliteL4 = create_satellite(name=f'卫星L4', init_position=L4_p, init_velocity=[-math.sin(math.pi * 30 / 180) * vel_L345, 0, math.cos(math.pi * 30 / 180) * vel_L345]) bodies.append(satelliteL4) # L5:point=[0,0, 177142.46945395062] velocity=[1.039 , 0, 0] satelliteL5 = create_satellite(name=f'卫星L5', init_position=L5_p, init_velocity=[-math.sin(math.pi * 30 / 180) * vel_L345, 0, -math.cos(math.pi * 30 / 180) * vel_L345]) bodies.append(satelliteL5) def create_connecting_lines(satellites_list): """ 创建连接线(将卫星列表用线条连接起来) @param satellites_list: @return: """ lines = [] for satellites in satellites_list: line = create_line(from_pos=satellites[0].planet.position, to_pos=satellites[1].planet.position, alpha=0.3) lines.append(line) return lines if __name__ == '__main__': def on_ready(): # 运行前触发 # 摄像机看向地球 camera_look_at(earth) def on_timer_changed(time_data: TimeData): # 删除和创建连接线 from ursina import destroy if hasattr(earth, "lines"): for line in earth.lines: destroy(line) earth.lines = create_connecting_lines([ [satelliteL2, satelliteL3], [satelliteL4, satelliteL1], [satelliteL5, satelliteL1], [satelliteL4, satelliteL2], [satelliteL5, satelliteL2], [satelliteL4, satelliteL3], [satelliteL5, satelliteL3], ]) # 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 * 5, # position=(-300000, 1500000, -100), position=(0, 1500000, 0), show_timer=True, # show_trail=True )