n-body问题的Python实现

import math

def calculate_force(mass1, mass2, distance):
    G = 6.67430e-11  # 万有引力常数
    force = (G * mass1 * mass2) / math.pow(distance, 2)
    return force

def calculate_acceleration(force, mass):
    acceleration = force / mass
    return acceleration

def update_velocity(velocity, acceleration, time_step):
    new_velocity = velocity + acceleration * time_step
    return new_velocity

def update_position(position, velocity, time_step):
    new_position = position + velocity * time_step
    return new_position

def simulate_n_body(masses, positions, velocities, time_step, num_iterations):
    num_bodies = len(masses)
    
    for iteration in range(num_iterations):
        for i in range(num_bodies):
            acceleration = 0.0
            for j in range(num_bodies):
                if i != j:
                    distance = math.sqrt(math.pow(positions[j][0] - positions[i][0], 2) + math.pow(positions[j][1] - positions[i][1], 2))
                    force = calculate_force(masses[i], masses[j], distance)
                    acceleration += calculate_acceleration(force, masses[i])
            
            velocities[i] = update_velocity(velocities[i], acceleration, time_step)
            positions[i] = update_position(positions[i], velocities[i], time_step)

# 示例用法
masses = [1.0, 2.0, 3.0]  # 物体的质量
positions = [(0.0, 0.0), (1.0, 0.0), (0.0, 1.0)]  # 物体的初始位置
velocities = [(0.0, 0.0), (0.0, 0.0), (0.0, 0.0)]  # 物体的初始速度
time_step = 0.1  # 时间步长
num_iterations = 100  # 模拟迭代次数

simulate_n_body(masses, positions, velocities, time_step, num_iterations)