🛰️ 轨道周期计算器（开普勒第三定律，地球/太阳/月球等）Orbital Period Calculator (Kepler Third Law, Earth, Sun, Moon and More)

使用说明与常见问题How-to & FAQ

「轨道周期计算器（开普勒第三定律，地球/太阳/月球等）」是什么？What is the Orbital Period Calculator (Kepler Third Law, Earth, Sun, Moon and More) tool?

选择中心天体（地球、太阳、月球、火星、木星或自定义质量），输入轨道半长轴或离表面的高度，用开普勒第三定律 T = 2π√(a³/GM) 求轨道周期，并给出圆轨道速度；也可以反过来由周期求半长轴和高度（例如地球同步轨道）。本地处理。Choose the central body (Earth, Sun, Moon, Mars, Jupiter or a custom mass), enter the semi-major axis or the altitude above the surface, and get the period from Kepler third law T = 2π√(a³/GM) with the circular orbital speed, or work back from a period to the semi-major axis and altitude (such as geostationary orbit). Processed locally.

如何使用「轨道周期计算器（开普勒第三定律，地球/太阳/月球等）」？How do I use the Orbital Period Calculator (Kepler Third Law, Earth, Sun, Moon and More) tool?

在「轨道周期计算器（开普勒第三定律，地球/太阳/月球等）」中，填写「计算」、「中心天体」、「自定义质量（10²⁴ kg）」、「轨道输入」、「半长轴或高度（km）」等参数，结果会随输入实时计算并显示在下方。In the Orbital Period Calculator (Kepler Third Law, Earth, Sun, Moon and More): Fill in "Calculate", "Central body", "Custom mass (10²⁴ kg)", "Orbit given as", "Semi-major axis or altitude (km)"; results are recalculated instantly as you type.

公式是什么？What is the formula?

开普勒第三定律：T = 2π × √(a³ ÷ GM)，a 为半长轴（从天体中心量起），GM 为中心天体的引力参数。卫星质量远小于中心天体时可以忽略。Kepler third law: T = 2π × √(a³ / GM), with a the semi-major axis measured from the centre of the body and GM its gravitational parameter. The satellite mass can be ignored when it is tiny by comparison.

高度和半长轴有什么区别？How do altitude and semi-major axis differ?

高度从天体表面量起，半长轴从中心量起。圆轨道时半长轴 = 天体半径 + 高度，例如国际空间站高度约 400 km，半长轴约 6771 km，周期约 92 分钟。Altitude is measured from the surface and the semi-major axis from the centre. For a circular orbit a = radius + altitude: the ISS at about 400 km has a ≈ 6771 km and a period of about 92 minutes.

地球同步轨道多高？How high is geostationary orbit?

周期等于一个恒星日（23.9345 小时）时，半长轴约 42,164 km，离赤道地面约 35,786 km。选择“由周期求轨道”即可验证。With a period of one sidereal day (23.9345 h) the semi-major axis is about 42,164 km, about 35,786 km above the equator. Use orbit from period to check.

能举个计算实例吗？Can you show a worked example?

例如在「轨道周期计算器（开普勒第三定律，地球/太阳/月球等）」中填 计算 = 由轨道求周期，中心天体 = 地球，轨道输入 = 半长轴（从中心算），半长轴或高度（km） = 6700，周期单位 = 小时，结果区显示：轨道周期：1 时 30 分 57.9 秒；90.9645 分钟 = 1.51607 小时 = 0.06317 天；圆轨道速度：7.7131 km/s；离表面高度：329 kmFor example, entering Calculate = Period from orbit, Central body = Earth, Orbit given as = Semi-major axis (from centre), Semi-major axis or altitude (km) = 6700, Period unit = hours in the Orbital Period Calculator (Kepler Third Law, Earth, Sun, Moon and More) gives: Orbital period: 1h 30m 57.9s; 90.9645 min = 1.51607 h = 0.06317 days; Circular speed: 7.7131 km/s; Altitude: 329 km

哪些输入会被检查？Which inputs are validated?

「轨道周期计算器（开普勒第三定律，地球/太阳/月球等）」会检查这些输入——「自定义质量（10²⁴ kg）」、「半长轴或高度（km）」、「周期」：所选方式用到时必须填写，须大于 0；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Orbital Period Calculator (Kepler Third Law, Earth, Sun, Moon and More) checks its inputs — "Custom mass (10²⁴ kg)", "Semi-major axis or altitude (km)", "Period": required when the chosen option uses it, must be greater than 0; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.

有哪些选项可以调整？What options can I adjust?

「轨道周期计算器（开普勒第三定律，地球/太阳/月球等）」的设置：「计算」可选 由轨道求周期、由周期求轨道（默认 由轨道求周期）；「中心天体」可选 地球、太阳、月球、火星、木星、自定义质量（默认 地球）；「自定义质量（10²⁴ kg）」默认 5.972；「轨道输入」可选 半长轴（从中心算）、离表面高度（圆轨道）（默认 半长轴（从中心算））；「半长轴或高度（km）」默认 6700；「周期」默认 23.9345；「周期单位」可选 分钟、小时、天、年（默认 小时）。每次生成结果都按当前设置处理。Settings in the Orbital Period Calculator (Kepler Third Law, Earth, Sun, Moon and More) — "Calculate": Period from orbit, Orbit from period (default Period from orbit); "Central body": Earth, Sun, Moon, Mars, Jupiter, Custom mass (default Earth); "Custom mass (10²⁴ kg)" default 5.972; "Orbit given as": Semi-major axis (from centre), Altitude above surface (circular) (default Semi-major axis (from centre)); "Semi-major axis or altitude (km)" default 6700; "Period" default 23.9345; "Period unit": minutes, hours…

计算结果可以用于作业或工程吗？Can I use the results for homework or engineering?

「轨道周期计算器（开普勒第三定律，地球/太阳/月球等）」使用教科书标准公式（公式写在说明和常见问题中），适合学习和估算核对；涉及安全的工程设计请以规范和实测为准。The Orbital Period Calculator (Kepler Third Law, Earth, Sun, Moon and More) uses standard textbook formulas (given in the description and FAQ), which is good for learning and checking estimates; for safety-critical engineering follow codes and measured values.

「轨道周期计算器（开普勒第三定律，地球/太阳/月球等）」免费吗？需要注册吗？Is the Orbital Period Calculator (Kepler Third Law, Earth, Sun, Moon and More) free? Do I need an account?

「轨道周期计算器（开普勒第三定律，地球/太阳/月球等）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Orbital Period Calculator (Kepler Third Law, Earth, Sun, Moon and More) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.