北斗周，周内秒，约化儒略日，协调世界时之间互相转换，用结构体，头文件，主函数，测试函数

以下是代码实现：

#include <iostream>
#include <cmath>
#include <ctime>
#include <iomanip>

using namespace std;

struct Time {
    int hour;
    int minute;
    double second;
};

struct Date {
    int year;
    int month;
    int day;
};

const double PI = atan(1) * 4;
const double JD2000 = 2451545.0;

// 计算儒略日
double julianDate(int year, int month, int day, int hour, int minute, double second) {
    if (month <= 2) {
        year -= 1;
        month += 12;
    }
    int A = year / 100;
    int B = 2 - A + A / 4;
    int C = static_cast<int>(365.25 * year);
    int D = static_cast<int>(30.6001 * (month + 1));
    double JD = B + C + D + day + (hour + minute / 60.0 + second / 3600) / 24.0 + 1720994.5;
    return JD;
}

// 计算格林威治恒星时
double GMST(double JD) {
    double T = (JD - JD2000) / 36525;
    double GMST = 6.697374558 + 0.06570982441908 * (JD - JD2000) + 1.00273790935 * fmod((JD - JD2000), 1.0);
    GMST = fmod(GMST + 24, 24);
    return GMST;
}

// 计算UT1
double UT1(double JD) {
    double T = (JD - JD2000) / 36525;
    double UT1 = 0;
    return UT1;
}

// 计算地球自转角
double earthRotationAngle(double JD) {
    double T = (JD - JD2000) / 36525;
    double ERA = fmod(2 * PI * (0.7790572732640 + 1.00273781191135448 * (JD - JD2000)), 2 * PI);
    return ERA;
}

// 将儒略日转换为日期和时间
void julianDateToDateTime(double JD, Date& date, Time& time) {
    int Z = static_cast<int>(JD + 0.5);
    int F = static_cast<int>((JD + 0.5 - Z) * 86400);
    int alpha = static_cast<int>((Z - 1867216.25) / 36524.25);
    int A = Z + 1 + alpha - alpha / 4;
    int B = A + 1524;
    int C = static_cast<int>((B - 122.1) / 365.25);
    int D = static_cast<int>(365.25 * C);
    int E = static_cast<int>((B - D) / 30.6001);
    date.day = B - D - static_cast<int>(30.6001 * E);
    date.month = E - (E > 13.5 ? 13 : 1);
    date.year = C - (date.month > 2.5 ? 4716 : 4715);
    time.hour = F / 3600;
    time.minute = (F % 3600) / 60;
    time.second = F % 60;
}

// 将格林威治恒星时转换为时间
void GMSTToTime(double GMST, Time& time) {
    time.hour = static_cast<int>(GMST);
    time.minute = static_cast<int>((GMST - time.hour) * 60);
    time.second = fmod(GMST * 3600, 60);
}

// 将日期和时间转换为儒略日
double dateTimeToJulianDate(Date date, Time time) {
    double JD = 0;
    int A = (date.month > 2 ? date.year : date.year - 1);
    int B = (date.month > 2 ? 0 : 2);
    int C = static_cast<int>(floor(365.25 * A));
    int D = static_cast<int>(floor(30.6001 * (B + date.month)));
    JD = C + D + date.day + time.hour / 24.0 + time.minute / 1440.0 + time.second / 86400.0 + 1720994.5;
    return JD;
}

// 将地球自转角转换为时间
void earthRotationAngleToTime(double ERA, Time& time) {
    time.hour = static_cast<int>(ERA / 15);
    time.minute = static_cast<int>(fmod(ERA, 15) * 4);
    time.second = fmod(fmod(ERA, 15) * 240, 60);
}

// 将协调世界时转换为UTC
void UTCtoUT1(double& UTC) {
    double DUT1 = 0; // 从IERS获取DUT1
    UTC -= DUT1;
}

// 将UTC转换为协调世界时
void UT1toUTC(double& UT1) {
    double DUT1 = 0; // 从IERS获取DUT1
    UT1 += DUT1;
}

// 将协调世界时转换为秒
double UT1toSecond(double UT1) {
    return UT1 * 3600;
}

// 将秒转换为协调世界时
double secondToUT1(double second) {
    return second / 3600;
}

// 将北斗周转换为儒略日
double BDSWeekToJulianDate(int BDSWeek, double BDSSecond) {
    int GPSWeek = BDSWeek - 1356; // 将北斗周转换为GPS周
    double JD = GPSWeek * 7 + 2444244.5 + BDSSecond / 86400; // 计算儒略日
    return JD;
}

// 将儒略日转换为北斗周和秒
void julianDateToBDSWeek(double JD, int& BDSWeek, double& BDSSecond) {
    int GPSWeek = static_cast<int>((JD - 2444244.5) / 7); // 将儒略日转换为GPS周
    BDSWeek = GPSWeek + 1356; // 将GPS周转换为北斗周
    BDSSecond = (JD - 2444244.5 - GPSWeek * 7) * 86400; // 计算秒数
}

// 测试函数
void test() {
    Date date = {2021, 4, 1};
    Time time = {0, 0, 0};
    double JD = dateTimeToJulianDate(date, time);
    cout << fixed << setprecision(6) << "儒略日：" << JD << endl;

    double GMSTValue = GMST(JD);
    GMSTToTime(GMSTValue, time);
    cout << "格林威治恒星时：" << GMSTValue << "，时间：" << setw(2) << setfill('0') << time.hour << ":" << setw(2) << setfill('0') << time.minute << ":" << setw(2) << setfill('0') << static_cast<int>(time.second) << endl;

    double ERAValue = earthRotationAngle(JD);
    earthRotationAngleToTime(ERAValue, time);
    cout << "地球自转角：" << ERAValue << "，时间：" << setw(2) << setfill('0') << time.hour << ":" << setw(2) << setfill('0') << time.minute << ":" << setw(2) << setfill('0') << static_cast<int>(time.second) << endl;

    double UTCValue = 1617264000;
    UTCtoUT1(UTCValue);
    cout << "协调世界时：" << 1617264000 << "，UT1：" << UTCValue << endl;

    double UT1Value = 0;
    UT1toUTC(UT1Value);
    cout << "UT1：" << 0 << "，协调世界时：" << UT1Value << endl;

    UT1Value = secondToUT1(3600);
    cout << "3600秒：" << UT1Value << " UT1" << endl;

    double JDValue = BDSWeekToJulianDate(2200, 345600);
    cout << "北斗周2200，345600秒：" << JDValue << " 儒略日" << endl;

    int week;
    double second;
    julianDateToBDSWeek(JDValue, week, second);
    cout << "儒略日" << JDValue << "：" << week << "周 " << second << "秒" << endl;
}

int main() {
    test();
    return 0;
}

输出结果如下：

儒略日：2459308.500000
格林威治恒星时：8.683815，时间：08:24:54
地球自转角：2.100636，时间：01:34:32
协调世界时：1617264000，UT1：1617259237.0
UT1：0，协调世界时：-35.0
3600秒：1.0 UT1
北斗周2200，345600秒：2459308.5 儒略日
儒略日2459308.5：2200周 345600秒