时间系统转换
2026/5/31小于 1 分钟
时间系统转换
概述
航天任务中常用六种时间系统：UTC、TAI、TT、TDB、UT1 和 GPS。它们之间的关系由常数偏移、闰秒累计和周期项决定：
TAI = UTC + ΔAT (闰秒累计, 2024年为37s)
TT = TAI + 32.184s (常数偏移)
TDB = TT + P(t) (周期项, 幅度约1.6ms)
GPS = TAI - 19s (常数偏移)
UT1 = UTC + DUT1 (地球自转修正, |DUT1|<0.9s)本例演示 TimePoint、JulianDate、DateTime 三种时间表示形式之间的转换，以及六种时间系统的相互转换。
使用示例
#include "ast/TimePoint.hpp"
#include "ast/TimeSystem.hpp"
#include "ast/JulianDate.hpp"
#include "ast/DateTime.hpp"
#include "ast/Duration.hpp"
#include <iostream>
#include <iomanip>
#include <clocale>
AST_USING_NAMESPACE
int main()
{
setlocale(LC_ALL, ".UTF-8");
// ============================================================
// 第一步: 从 UTC 日历日期创建 TimePoint
// 2024-01-01 00:00:00 UTC (闰秒累计 ΔAT = 37s)
// ============================================================
TimePoint tp = TimePoint::FromUTC(2024, 1, 1, 0, 0, 0.0);
std::cout << "===== TimePoint 基本信息 =====" << std::endl;
std::cout << " TimePoint 字符串: " << tp.toString() << std::endl;
std::cout << " integerPart: " << tp.integerPart() << std::endl;
std::cout << " fractionalPart: " << tp.fractionalPart() << std::endl;
// ============================================================
// 第二步: TimePoint → JulianDate (五种时间系统)
// ============================================================
JulianDate jdUTC, jdTAI, jdTT, jdTDB, jdUT1;
aTimePointToUTC(tp, jdUTC);
aTimePointToTAI(tp, jdTAI);
aTimePointToTT(tp, jdTT);
aTimePointToTDB(tp, jdTDB);
aTimePointToUT1(tp, jdUT1);
std::cout << "\n===== TimePoint → JulianDate (五种时间系统) =====" << std::endl;
std::cout << " UTC: day=" << jdUTC.day() << " sec=" << jdUTC.second() << std::endl;
std::cout << " TAI: day=" << jdTAI.day() << " sec=" << jdTAI.second() << std::endl;
std::cout << " TT: day=" << jdTT.day() << " sec=" << jdTT.second() << std::endl;
std::cout << " TDB: day=" << jdTDB.day() << " sec=" << jdTDB.second() << std::endl;
std::cout << " UT1: day=" << jdUT1.day() << " sec=" << jdUT1.second() << std::endl;
// ============================================================
// 第三步: 各时间系统之间的偏移量
// ============================================================
std::cout << "\n===== UTC 为基准的各系统偏移 =====" << std::endl;
double taiOff = (jdTAI - jdUTC).totalSecond();
double ttOff = (jdTT - jdUTC).totalSecond();
double tdbOff = (jdTDB - jdUTC).totalSecond();
double ut1Off = (jdUT1 - jdUTC).totalSecond();
std::cout << " TAI - UTC = " << taiOff << " s" << std::endl;
std::cout << " TT - UTC = " << ttOff << " s (= TAI-UTC + 32.184s)" << std::endl;
std::cout << " TDB - UTC = " << tdbOff << " s" << std::endl;
std::cout << " UT1 - UTC = " << ut1Off << " s (地球自转不均匀)" << std::endl;
// ============================================================
// 第四步: JulianDate 之间的直接转换 (使用 TimeSystem 函数)
// ============================================================
std::cout << "\n===== JulianDate 间直接转换 =====" << std::endl;
// UTC → TAI → TT → TDB
JulianDate jdTAI2, jdTT2, jdTDB2;
aUTCToTAI(jdUTC, jdTAI2);
aTAIToTT(jdTAI2, jdTT2);
aTTToTDB(jdTT2, jdTDB2);
std::cout << " UTC → TAI → TT → TDB:" << std::endl;
std::cout << " TAI: day=" << jdTAI2.day() << " sec=" << jdTAI2.second() << std::endl;
std::cout << " TT: day=" << jdTT2.day() << " sec=" << jdTT2.second() << std::endl;
std::cout << " TDB: day=" << jdTDB2.day() << " sec=" << jdTDB2.second() << std::endl;
// TT → TDB 差值 (周期项, ~1.6ms)
double tdbMinusTT = aTDBMinusTT(jdTT);
std::cout << " TDB - TT 周期项 = " << std::scientific << tdbMinusTT << " s (" << tdbMinusTT * 1e3 << " ms)" << std::endl;
// ============================================================
// 第五步: JulianDate → DateTime (日历表示)
// ============================================================
std::cout << "\n===== JulianDate → DateTime (日历表示) =====" << std::endl;
DateTime dttmUTC, dttmTAI, dttmTT;
aJDToDateTime(jdUTC, dttmUTC);
aJDToDateTime(jdTAI, dttmTAI);
aJDToDateTime(jdTT, dttmTT);
std::cout << " UTC: " << dttmUTC.toString() << std::endl;
std::cout << " TAI: " << dttmTAI.toString() << std::endl;
std::cout << " TT: " << dttmTT.toString() << std::endl;
// ============================================================
// 第六步: 不同时间系统的 DateTime 创建 TimePoint
// ============================================================
std::cout << "\n===== DateTime → TimePoint 往返 =====" << std::endl;
TimePoint tpFromUTC = TimePoint::FromUTC(dttmUTC);
TimePoint tpFromTAI = TimePoint::FromTAI(dttmTAI);
TimePoint tpFromTT = TimePoint::FromTT(dttmTT);
std::cout << " FromUTC: " << tpFromUTC.toString() << std::endl;
std::cout << " FromTAI: " << tpFromTAI.toString() << std::endl;
std::cout << " FromTT: " << tpFromTT.toString() << std::endl;
// ============================================================
// 第七步: 儒略世纪数 (天体力学常用)
// ============================================================
std::cout << "\n===== 儒略世纪数 (以 J2000.0 TT 为基准) =====" << std::endl;
double jcTT = jdTT.julianCenturyFromJ2000();
double jcTDB = jdTDB.julianCenturyFromJ2000();
double daysTT = jdTT.daysFromJ2000();
std::cout << " 距 J2000.0 (TT): " << daysTT << " days" << std::endl;
std::cout << " T_TT = " << std::fixed << std::setprecision(8) << jcTT << " centuries" << std::endl;
std::cout << " T_TDB = " << std::fixed << std::setprecision(8) << jcTDB << " centuries" << std::endl;
// ============================================================
// 第八步: TimePoint 算术运算
// ============================================================
std::cout << "\n===== TimePoint 算术运算 =====" << std::endl;
TimePoint tpNext = tp + 86400.0; // 一天后
std::cout << " 原始: " << tp.toString() << std::endl;
std::cout << " +1天: " << tpNext.toString() << std::endl;
JulianDate jdTT2_val;
aTimePointToTT(tpNext, jdTT2_val);
double diffDays = jdTT2_val.daysFromJ2000() - jdTT.daysFromJ2000();
std::cout << " 实际 TT 天数差: " << diffDays << " days" << std::endl;
// ============================================================
// 第九步: J2000.0 历元 (常用参考时刻)
// ============================================================
std::cout << "\n===== J2000.0 历元 =====" << std::endl;
TimePoint j2000 = TimePoint::J2000TT();
JulianDate j2000TT, j2000TAI, j2000UTC;
aTimePointToTT(j2000, j2000TT);
aTimePointToTAI(j2000, j2000TAI);
aTimePointToUTC(j2000, j2000UTC);
std::cout << " J2000 TT: day=" << j2000TT.day() << " sec=" << j2000TT.second() << std::endl;
std::cout << " J2000 TAI: day=" << j2000TAI.day() << " sec=" << j2000TAI.second() << std::endl;
std::cout << " J2000 UTC: day=" << j2000UTC.day() << " sec=" << j2000UTC.second() << std::endl;
// ============================================================
// 总结
// ============================================================
std::cout << "\n===== 时间系统对照表 (2024-01-01 00:00:00 UTC) =====" << std::endl;
std::cout << " [UTC] 协调世界时: " << dttmUTC.toString() << std::endl;
std::cout << " [TAI] 国际原子时: " << dttmTAI.toString() << " (UTC + " << taiOff << "s)" << std::endl;
std::cout << " [TT] 地球时: " << dttmTT.toString() << " (TAI + 32.184s)" << std::endl;
std::cout << " [TDB] 质心动力学时: TT + " << std::scientific << tdbMinusTT << "s (周期项)" << std::endl;
std::cout << " [UT1] 世界时: UTC + " << ut1Off << "s (地球自转修正)" << std::endl;
std::cout << " [GPS] GPS时: TAI - 19s = UTC + " << (taiOff - 19.0) << "s" << std::endl;
std::cout << "\n 时间系统关系:" << std::endl;
std::cout << " TAI = UTC + ΔAT (闰秒累计, 当前 " << taiOff << "s)" << std::endl;
std::cout << " TT = TAI + 32.184s" << std::endl;
std::cout << " TDB = TT + 周期项 (幅度 ~1.6ms)" << std::endl;
std::cout << " GPS = TAI - 19s" << std::endl;
std::cout << " UT1 = UTC + DUT1 (地球自转, |DUT1| < 0.9s)" << std::endl;
std::cout << "\nexample completed." << std::endl;
return 0;
}注意事项
- TimePoint 内部以 TAI 为基准存储，各系统转换通过偏移量实现
- UTC ↔ TAI 转换依赖闰秒表，库内置了截至 2016 年底的闰秒数据
- TDB ↔ TT 的周期项计算基于解析公式，幅度约 1.6ms
- JulianDate 用 (int day, double second) 保证精度，避免单 double 的舍入误差
- 长时间跨度建议用 TimePoint 而非 DateTime，精度更高