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Orbital velocity and gravity calculator

Orbital velocity and period, escape velocity, surface gravity, your weight on the Moon or Mars, and the gravitational force between two masses.

更新于 已验证的示例：8

试一试
Orbital speed
m/s
Orbital speed: 7,672.62 m/s
有效数字：6；取最近值，等距时远离零
Orbital period
1 h 32 min 24 s / 1.54023h
Altitude above the surface
400km
Orbit radius from the centre
6,771km
Escape velocity from that altitude
10,850.7m/s
Gravitational parameter GM
3.98603 × 10¹⁴m³/s²
G is known to about 2 parts in 100,000 (CODATA 2022), so the last one or two significant figures shown are uncertain.

A circular orbit 400 km above Earth needs 7.6726 km/s and takes 92.414 minutes per lap. Mass of the satellite doesn't matter.

Orbit around Earth to scale (km)

7.6726 km/sr = 6,771 km
计算方法 S

  1. Gravitational parameter

    GM=(6.67430×10−11)(5.9722×1024)=398,603,000,000,000 m3/s2GM = (6.67430\times10^{-11})(5.9722 \times 10^{24}) = 398{,}603{,}000{,}000{,}000\ \mathrm{m^3/s^2}

  2. Kepler's third law

    T=2πr3GM=2π(6,771,000)3398,603,000,000,000=5,544.84 s=1.54023 hT = 2\pi\sqrt{\frac{r^3}{GM}} = 2\pi\sqrt{\frac{(6{,}771{,}000)^3}{398{,}603{,}000{,}000{,}000}} = 5{,}544.84\ \mathrm{s} = 1.54023\ \mathrm{h}

  3. Circular orbit speed

    v=GMr=398,603,000,000,0006,771,000=7,672.62 m/sv = \sqrt{\frac{GM}{r}} = \sqrt{\frac{398{,}603{,}000{,}000{,}000}{6{,}771{,}000}} = 7{,}672.62\ \mathrm{m/s}

关于Orbital velocity and gravity calculator

Newton's law of gravitation, F = Gm₁m₂/r², gives the pull between two masses. For a body of mass M the same law sets the speed of a circular orbit, v = √(GM/r), its period from Kepler's third law, T = 2π√(r³/GM), the escape velocity √(2GM/r) and the surface gravity GM/R². Pick the Earth, Moon, Mars, Jupiter or the Sun, or enter any mass and radius.

The default, an orbit 400 km above Earth like the International Space Station's, gives 7.67 km/s (about 17,200 mph) and 92.4 minutes per lap. Entering one sidereal day, 23.934 hours, as the period returns the geostationary radius of 42,164 km.

Radii are volumetric means from NASA's fact sheets and rotation is ignored, so Earth's surface gravity comes out at 9.82 m/s², between the 9.78 m/s² measured at the equator and 9.83 m/s² at the poles. Orbits are circular and drag-free.

计算示例

ISS-like orbit at 400 km

Calculate
Circular orbit
身体
Earth
Given
Altitude → speed and period
Altitude above the surface
400 km
结果单位
km, m/s, N
Orbital speed
7,672.62 m/s
Orbital period
1.54023 h

核验来源：Python 3.8 decimal: GM = 6.6743e-11 × 5.9722e24, r = 6771 km, v = √(GM/r) = 7672.619, T = 2π√(r³/GM) = 1.5402335 h

Geostationary altitude from one sidereal day

Calculate
Circular orbit
身体
Earth
Given
Period → altitude
Orbital period
23.9344696 h
结果单位
km, m/s, N
Altitude above the surface
35,793.2 km
Orbital speed
3,074.67 m/s

核验来源：Python 3.8 decimal: r = (GM T²/4π²)^⅓ = 42164.2 km (the published GEO radius); minus the 6371 km mean radius (35,786 km is quoted above the 6378 km equatorial radius)

Orbit skimming the surface (altitude 0)

Calculate
Circular orbit
身体
Earth
Given
Altitude → speed and period
Altitude above the surface
0 km
结果单位
km, m/s, N
Orbital speed
7,909.81 m/s

核验来源：Python 3.8 decimal: √(GM/R) with R = 6371.0 km = 7909.813

Escape velocity from Earth's surface

Calculate
Escape velocity
身体
Earth
Altitude above the surface
0 km
结果单位
km, m/s, N
Escape velocity from that altitude
11,186.2 m/s

核验来源：Python 3.8 decimal: √(2GM/R) = 11186.165 m/s (NASA fact sheet lists 11.186 km/s)

常见问题

How fast does the International Space Station orbit Earth?

About 7.67 km/s at 400 km altitude, which is 27,600 km/h or roughly 17,200 mph, and one lap takes 92.4 minutes. The speed depends only on Earth's GM and the orbit radius (6,771 km here), not on the station's mass. Raising the orbit to 410 km slows it by 5.7 m/s and lengthens the lap by 12 seconds.

What is the escape velocity of Earth?

11.186 km/s from the surface, about 40,270 km/h, the figure on NASA's Earth fact sheet. It is the speed at which an unpowered object never falls back, ignoring air drag, and it is the same for a pebble and a rocket. The Moon's is 2.38 km/s, Mars's 5.03 km/s and Jupiter's about 60 km/s. From 400 km up it drops to 10.85 km/s.

Why is escape velocity √2 times orbital velocity?

Escaping takes twice the kinetic energy of a circular orbit at the same height. In a circular orbit the kinetic energy is GMm/2r; reaching infinity needs GMm/r, the full depth of the potential well. Doubling kinetic energy multiplies speed by √2 ≈ 1.414, so the 7.67 km/s orbital speed at 400 km above Earth becomes an escape speed of 10.85 km/s.

How high is a geostationary orbit?

35,786 km above the equator, a radius of 42,164 km from Earth's centre. At that radius Kepler's third law gives a period of one sidereal day, 23 h 56 min 4 s, so the satellite keeps pace with Earth's rotation. Entering that period here gives the same radius and an altitude of 35,793 km, because the calculator subtracts the 6,371 km mean radius rather than the 6,378 km equatorial radius.

How much would I weigh on the Moon or Mars?

About 16.6% of your Earth weight on the Moon and 38% on Mars. Surface gravity GM/R² is 1.62 m/s² on the Moon and 3.73 m/s² on Mars with NASA's mean radii, against the 9.80665 m/s² standard gravity defined for Earth. A 70 kg person weighs 113.7 N on the Moon, which a scale calibrated on Earth would show as 11.6 kg.

“Orbital velocity and gravity calculator”有多准确？

准确性取决于输入值和方法的假设。十进制运算使用50位有效数字，但估算、数值方法和源数据的精度可能较低；显示时的舍入并不能消除这些限制。 已按独立来源核验的计算示例：8。 例如，“ISS-like orbit at 400 km”根据Python 3.8 decimal: GM = 6.6743e-11 × 5.9722e24, r = 6771 km, v = √(GM/r) = 7672.619, T = 2π√(r³/GM) = 1.5402335 h进行核验。

这种方法出自哪里？

OpenStax University Physics Volume 1, ch. 13 Gravitation (§13.5 Satellite orbits, §13.3 Escape velocity); CODATA 2022 — Newtonian constant of gravitation G = 6.67430(15) × 10⁻¹¹ m³ kg⁻¹ s⁻²; NASA Planetary Fact Sheets (mass, volumetric mean radius).

关于此计算器

F=Gm1m2r2,v=GMr,T=2πr3GM,vesc=2GMr,g=GMR2F = \frac{Gm_1m_2}{r^2},\quad v = \sqrt{\frac{GM}{r}},\quad T = 2\pi\sqrt{\frac{r^3}{GM}},\quad v_{\text{esc}} = \sqrt{\frac{2GM}{r}},\quad g = \frac{GM}{R^2}

来源

  1. OpenStax University Physics Volume 1, ch. 13 Gravitation (§13.5 Satellite orbits, §13.3 Escape velocity)
  2. CODATA 2022 — Newtonian constant of gravitation G = 6.67430(15) × 10⁻¹¹ m³ kg⁻¹ s⁻²
  3. NASA Planetary Fact Sheets (mass, volumetric mean radius)

已对照来源验证

此计算器包含 8 个已解示例，答案来自独立来源。这些示例会在测试套件中运行，你也可以在此运行验证。

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