Python超人-宇宙模拟器

common/consts.py

@@ -27,7 +27,8 @@ AU: float = 149597870.700
 """
 万有引力常数
 """
-G: float = 6.67e-11
+# G: float = 6.67e-11
+G: float = 6.67408e-11
 
 """
 一分钟多少秒

common/func.py

@@ -7,7 +7,7 @@
 # python_version  :3.8
 # ==============================================================================
 from PIL import Image
-from common.consts import AU
+from common.consts import AU, G
 import numpy as np
 import random
 import os
@@ -108,8 +108,6 @@ def calculate_distance(pos1, pos2=[0, 0, 0]):
             pow(np.array(pos1[2]) - np.array(pos2[2]), 2), 1 / 2)
     return d
 
-G = 6.67408e-11
-# AU = 149597870700.0
 
 def calculate_velocity(mass, semimajor_axis, eccentricity):
     """
@@ -138,6 +136,101 @@ def calculate_velocity(mass, semimajor_axis, eccentricity):
     return v * math.sqrt(1 + (2 * mass) / (v ** 2 * AU)) * math.sin(psi)
 
 
+def get_lagrange_points(m1, m2, r, R, omega):
+    """
+    函数需要5个输入参数：
+
+    m1: 大质点的质量（单位：kg）
+    m2: 小质点的质量（单位：kg）
+    r: 小质点到拉格朗日点的距离（单位：km）
+    R: 大质点到拉格朗日点的距离（单位：km）
+    omega: 两个星体之间的夹角（单位：rad）
+    函数返回一个元组，其中包括五个元素（Tuple），每个元素又是由七个数据（Tuple）组成：
+
+    @param m1:
+    @param m2:
+    @param r:
+    @param R:
+    @param omega:
+    @return:
+    x: 拉格朗日点的x坐标（单位：km）
+    y: 拉格朗日点的y坐标（单位：km）
+    z: 拉格朗日点的z坐标（单位：km）
+    vx: 拉格朗日点物体的x方向速度（单位：km/s）
+    vy: 拉格朗日点物体的y方向速度（单位：km/s）
+    vz: 拉格朗日点物体的z方向速度（单位：km/s）
+    """
+    G = 6.673e-20  # gravitational constant in km^3/kg*s^2
+    M = m1 + m2
+
+    # Calculate mass ratio
+    mu = m2 / M
+
+    # Calculate distance between primary and secondary bodies
+    d = np.sqrt((R * mu) ** 2 + r ** 2 - 2 * R * r * mu * np.cos(omega))
+
+    # Calculate L1 point
+    a = (d - R) / (2 - mu)
+    x1 = R - a
+    y1 = 0
+    z1 = 0
+    v1 = np.sqrt(G * m2 * a / d) * (1 - mu)
+    vx1 = 0
+    vy1 = v1 * (R - x1) / d
+    vz1 = v1 * y1 / d
+
+    # Calculate L2 point
+    a = (d - R) / (2 - mu)
+    x2 = R + a
+    y2 = 0
+    z2 = 0
+    v2 = np.sqrt(G * m2 * a / d) * (1 - mu)
+    vx2 = 0
+    vy2 = v1 * (R - x2) / d
+    vz2 = v1 * y2 / d
+
+    # Calculate L3 point
+    a = (d + R) / (2 + mu)
+    x3 = -a
+    y3 = 0
+    z3 = 0
+    v3 = np.sqrt(G * m1 * a / d) * (1 + mu)
+    vx3 = 0
+    vy3 = v3 * (R - x3) / d
+    vz3 = v3 * -y3 / d
+
+    # Calculate L4 and L5 points
+    x4, y4, z4, v4, vx4, vy4, vz4 = get_l4_l5_points(m1, m2, R, omega, 1)
+    x5, y5, z5, v5, vx5, vy5, vz5 = get_l4_l5_points(m1, m2, R, omega, -1)
+
+    return ((x1, y1, z1, vx1, vy1, vz1),
+            (x2, y2, z2, vx2, vy2, vz2),
+            (x3, y3, z3, vx3, vy3, vz3),
+            (x4, y4, z4, vx4, vy4, vz4),
+            (x5, y5, z5, vx5, vy5, vz5))
+
+
+def get_l4_l5_points(m1, m2, R, omega, sign):
+    # G = 6.673e-20  # gravitational constant in km^3/kg*s^2
+    M = m1 + m2
+
+    # Calculate mass ratio
+    mu = m2 / M
+
+    # Calculate position of L4 or L5 point
+    x = R * np.cos(omega + sign * 60 * np.pi / 180)
+    y = R * np.sin(omega + sign * 60 * np.pi / 180)
+    z = 0
+
+    # Calculate velocity of L4 or L5 point
+    v = np.sqrt(G * M / (3 * R))
+    vx = -v * y / R
+    vy = v * x / R
+    vz = 0
+
+    return x, y, z, v, vx, vy, vz
+
+
 if __name__ == '__main__':
     # print(calculate_distance([6, 8, 0], [3, 4, 0]))
     # print(find_file("common/func.py"))
@@ -150,3 +243,7 @@ if __name__ == '__main__':
     velocity_earth = calculate_velocity(mass_earth, semimajor_axis_earth, eccentricity_earth)
 
     print("地球在轨道上的速度是：{:.2f} km/s".format(velocity_earth / 1000))
+
+"""
+你现在是一位资深的天体学家、请使用python完成一个获取拉格朗日点的函数，获取拉格朗日点的坐标(px,py 单位：km)同时，也要返回拉格朗日点物体的速度（vx,vy 单位：km/s）,需要返回L1-L5所有的点和速度。返回的L1、L2、L3、L4、L5 格式为：(x1, y1, vx1, vy1),(x2, y2, vx2, vy2), (x3, y3, vx3, vy3), (x4, y4, vx4, vy4) (x5, y5, vx5, vy5)，并针对太阳、地球拉格朗日点以及 地球、月球拉格朗日点举例。并使用matlibplot画图，并写上详细的注释。
+"""

sim_scenes/science/earth_seasons.py

@@ -42,6 +42,8 @@ if __name__ == '__main__':
                   text_color=[255, 255, 255], rotation_speed=0.5,  # 为演示效果，自转角速度取0.5度/小时，实际为15度/小时
                   init_position=[-1 * AU, 0, 0], init_velocity=[0, 0, -29.79])
 
+    earth.rotate_axis_color = (255, 255, 162)
+
     bodies = [
         sun, earth,
         earth_1, earth_2, earth_3, earth_4,

simulators/ursina/entities/planet.py

@@ -16,7 +16,7 @@ from simulators.ursina.ursina_event import UrsinaEvent
 from common.color_utils import adjust_brightness, conv_to_vec4_color, get_inverse_color
 from common.func import find_file
 from simulators.views.body_view import BodyView
-from simulators.ursina.ursina_mesh import create_sphere, create_torus, create_arrow_line
+from simulators.ursina.ursina_mesh import create_sphere, create_torus, create_arrow_line, create_line
 import math
 
 
@@ -101,13 +101,14 @@ class Planet(Entity):
         if hasattr(self.body, "rotate_angle"):
             if self.body.rotate_angle != 0:
                 # 为了给天体增加一个倾斜角，增加了一个Entity
-                self.rotate_angle = self.body.rotate_angle
-                self.main_entity = Entity()
-                self.main_entity.rotation_x = self.rotate_angle
-                self.main_entity.body_view = self.body_view
-                self.main_entity.body = self.body
-                self.parent = self.main_entity
-                self.position = [0, 0, 0]
+                self.create_rotate_entity()
+                # self.rotate_angle = self.body.rotate_angle
+                # self.main_entity = Entity()
+                # self.main_entity.rotation_x = self.rotate_angle
+                # self.main_entity.body_view = self.body_view
+                # self.main_entity.body = self.body
+                # self.parent = self.main_entity
+                # self.position = [0, 0, 0]
             else:
                 self.rotate_angle = 0
                 self.main_entity = self
@@ -115,6 +116,14 @@ class Planet(Entity):
             self.rotate_angle = 0
             self.main_entity = self
 
+        # Rotation axis color
+        if hasattr(self.body, "rotate_axis_color"):
+            if self.body.rotate_axis_color is not None:
+                axis_color = self.body.rotate_axis_color
+                axis_color = (axis_color[0] / 255, axis_color[1] / 255, axis_color[2] / 255, 1.0)
+                axis_color = color.rgba(*axis_color)
+                self.create_rotate_line(axis_color)
+
         if hasattr(self.body, "torus_stars"):
             # 星环小天体群（主要模拟小行星群，非一个天体）
             self.set_light_off()
@@ -143,6 +152,38 @@ class Planet(Entity):
                 # 创建行星环（目前只有土星环）
                 create_rings(self)
 
+    def create_rotate_entity(self):
+        """
+
+        @return:
+        """
+        self.rotate_angle = self.body.rotate_angle
+        self.main_entity = Entity()
+        self.main_entity.rotation_x = self.rotate_angle
+        self.main_entity.body_view = self.body_view
+        self.main_entity.body = self.body
+        self.parent = self.main_entity
+        self.position = [0, 0, 0]
+
+    def create_rotate_line(self, line_color):
+
+        from_pos = Vec3(0, 1, 0)
+        to_pos = Vec3(0, -1, 0)
+
+        # UrsinaConfig.SCALE_FACTOR * 10000000 = 5
+        # UrsinaConfig.auto_scale_factor = 1
+        # UrsinaConfig.body_size_factor = 1
+        if self.main_entity is self:
+            # 没有偏转角度
+            line_scale = math.pow(self.main_entity.scale_x, 1 / 10) / 1.5
+        else:
+            # 有偏转角度
+            # line_scale = math.pow(self.main_entity.scale_x, 1 / 10)
+            line_scale = self.scale_x
+        # camera.scale_x
+        create_line(from_pos, to_pos, parent=self.main_entity,
+                    len_scale=line_scale, color=line_color, thickness=2)
+
     def change_body_scale(self):
         if hasattr(self.body, "torus_stars"):
             # 星环小天体群（主要模拟小行星群，非一个天体）不受 body_size_factor 影响