用python写一段脚本，实现用真近点角和偏心率计算出平近点角，包含迭代次数和误差率

在Python中，我们可以编写一个函数来利用真近点角（True Anomaly, \( \nu \)）和偏心率（Eccentricity, \( e \)）来估算平近点角（Mean Anomaly, \( M \)）。由于这是一个数值计算过程，通常通过牛顿迭代法进行逼近。下面是一个简单的示例：

import math

def calculate_mean_anomaly(true_anomaly, eccentricity, max_iterations=100, tolerance=1e-6):
    def f(mean_anomaly):
        return mean_anomaly - ecc_to_mean_anomaly(true_anomaly, eccentricity, mean_anomaly)
    
    def df(mean_anomaly):
        return 1 - ecc_derivative(mean_anomaly, true_anomaly, eccentricity)

    mean_anomaly = true_anomaly
    for _ in range(max_iterations):
        next_mean_anomaly = mean_anomaly - f(mean_anomaly) / df(mean_anomaly)
        error = abs(next_mean_anomaly - mean_anomaly)
        if error < tolerance:
            break
        mean_anomaly = next_mean_anomaly
    
    return next_mean_anomaly, error, max_iterations

# 辅助函数
def ecc_to_mean_anomaly(true_anomaly, ecc, mean_anomaly):
    return (true_anomaly + ecc * math.sin(math.radians(true_anomaly))) % (2 * math.pi) - ecc * math.sin(math.radians(ecc * true_anomaly))

def ecc_derivative(mean_anomaly, true_anomaly, ecc):
    return math.cos(math.radians(mean_anomaly)) - ecc * math.cos(math.radians(ecc * true_anomaly))

# 示例输入
true_anomaly = math.radians(90)  # 真近点角（这里以90度为例）
eccentricity = 0.5  # 偏心率

mean_anomaly, error, iterations = calculate_mean_anomaly(true_anomaly, eccentricity)
print(f"平近点角: {math.degrees(mean_anomaly)}度, 迭代次数: {iterations}, 误差: {error:.6f}")

#