🚀 逃逸速度计算器Escape Velocity Calculator

使用说明与常见问题How-to & FAQ

「逃逸速度计算器」是什么？What is the Escape Velocity Calculator tool?

按 v = √(2GM ÷ r) 计算从地球、月球、火星、木星、太阳或自定义天体表面（或某高度）逃逸所需的速度，同时给出该高度的圆轨道速度。Calculate the escape velocity v = √(2GM ÷ r) from the surface (or an altitude) of Earth, the Moon, Mars, Jupiter, the Sun or a custom body, with the circular orbit speed at that height.

如何使用「逃逸速度计算器」？How do I use the Escape Velocity Calculator tool?

在「逃逸速度计算器」中，填写「天体」、「离表面高度 km」、「自定义质量 kg」、「自定义半径 km」等参数，结果会随输入实时计算并显示在下方。In the Escape Velocity Calculator: Fill in "Body", "Altitude above surface km", "Custom mass kg", "Custom radius km"; results are recalculated instantly as you type.

用的是什么公式？What is the formula?

v = √(2GM ÷ r)，G = 6.6743 × 10⁻¹¹ m³/(kg·s²)（CODATA 2018），M 为天体质量，r 为到天体中心的距离。圆轨道速度为 √(GM ÷ r)，正好是逃逸速度的 1/√2。v = √(2GM ÷ r), with G = 6.6743 × 10⁻¹¹ m³/(kg·s²) (CODATA 2018), M the body's mass and r the distance from its centre. Circular orbit speed is √(GM ÷ r), exactly 1/√2 of escape speed.

内置天体用的什么数据？What data do the built-in bodies use?

使用 GM（引力参数）而非质量，精度更高：地球 3.986004418 × 10¹⁴、太阳 1.32712440018 × 10²⁰ m³/s²（IAU/IERS 常用值），半径取平均半径（地球 6371 km）。They use GM (the gravitational parameter), which is known more precisely than mass: Earth 3.986004418 × 10¹⁴ and the Sun 1.32712440018 × 10²⁰ m³/s² (IAU/IERS values), with mean radii (Earth 6371 km).

火箭真的要达到这个速度吗？Must a rocket reach this speed?

逃逸速度是在没有空气阻力、不再加推力时一次性需要的速度。火箭持续推进，可以更慢地爬升，但总能量需求相当。Escape velocity is the speed needed with no further thrust and no air drag. A rocket that keeps thrusting can climb more slowly, though the total energy needed is similar.

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

「逃逸速度计算器」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 Escape Velocity Calculator 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.

「逃逸速度计算器」免费吗？需要注册吗？Is the Escape Velocity Calculator free? Do I need an account?

「逃逸速度计算器」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 Escape Velocity Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.