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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.

更新日 検証済みの例：8

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Orbital speed
m/s
Orbital speed: 7,672.62 m/s
有効桁数：6；最も近い値へ、等距離ならゼロから遠い値へ
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
計算方法 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}

Orbital velocity and gravity calculatorについて

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.

計算例

ISS-like orbit at 400 km

Calculate
Circular orbit
身体
Earth
Given
Altitude → speed and period
Altitude above the surface
400 km
結果の単位
km, m/s, N
Orbital speed
7,672.62 m/s
Orbital period
1.54023 h

照合元：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
結果の単位
km, m/s, N
Altitude above the surface
35,793.2 km
Orbital speed
3,074.67 m/s

照合元：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
結果の単位
km, m/s, N
Orbital speed
7,909.81 m/s

照合元：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
結果の単位
km, m/s, N
Escape velocity from that altitude
11,186.2 m/s

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

よくある質問

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」の精度はどのくらいですか？

精度は入力値と計算方法の前提に依存します。十進演算には有効数字50桁を使いますが、推定、数値計算手法、元データの精度はそれより低い場合があります。表示の丸め処理でこれらの制約がなくなるわけではありません。 独立した出典の解答と照合した計算例：8。 例えば、「ISS-like orbit at 400 km」は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と照合しています。

この計算方法の出典は何ですか？

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).

この計算機について

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}

出典

  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)

出典と照合済み

この計算機には、独立した出典の解答を使った計算例が 8 件あります。テストに組み込まれており、ここでも実行できます。

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