Gravity & Orbit Calculator
Work out the gravitational pull between two masses, the surface gravity of Earth, the Moon, Mars or the Sun, and the speed and period of a circular orbit from its altitude, or the altitude from its period.
How to Use
- Pick a mode: Newton’s law for the pull between two masses, Surface gravity for a planet or moon, or Orbit for a satellite.
- In Newton’s law mode choose what to find (the force, the distance or the second mass) and enter the other three with their units.
- In Surface and Orbit modes pick Earth, the Moon, Mars or the Sun, or choose Custom and enter a mass and radius. Add your own mass to see your weight there.
- For an orbit, enter the altitude above the surface to get the period, or switch to finding the altitude from a period, such as one sidereal day for a geostationary orbit.
- Read the answer in the highlighted field and the readouts; the table and Show Work give every value and step.
Worked Example
The International Space Station. Earth’s GM = 6.6743 × 10⁻¹¹ × 5.972 × 10²⁴ = 3.9859 × 10¹⁴ m³/s². At 420 km up, the orbit radius is r = 6,371 + 420 = 6,791 km. T = 2π√(r³ ÷ GM) = 2π√((6.791 × 10⁶)³ ÷ (3.9859 × 10¹⁴)) = 5,569.5 s, 92.83 min, and v = √(GM ÷ r) = 7.661 km/s.
A geostationary orbit. Run Kepler’s third law backwards for one sidereal day, T = 86,164.09 s: r = ∛(GM × T² ÷ 4π²) = 42,164 km from the centre of the Earth, moving at 3.075 km/s.
The common mistake: using the altitude as r. Every formula here measures r from the centre of the planet. Putting the ISS’s 420 km in as r gives T = 85.7 s, an orbit that would lie deep inside the Earth. Add the planet’s radius first: r = 6,371 + 420 = 6,791 km gives the real 92.83 min.
Show Work
Formulas
Kepler, Newton and Cavendish
Johannes Kepler found the rule behind orbital periods in 1619, in Harmonices Mundi: the square of a planet’s period is proportional to the cube of its distance from the Sun. Isaac Newton explained it in the Principia of 1687 with one law, F = Gm₁m₂/r², the same pull that makes an apple fall and keeps the Moon in orbit.
Newton could not measure G itself. In 1798 Henry Cavendish hung lead balls from a torsion balance in his house and measured the tiny attraction between them, which gave the density, and so the mass, of the Earth; the value of G follows from his result. The body data here are from the NASA planetary fact sheets: Earth 5.972 × 10²⁴ kg and 6,371 km, the Moon 7.346 × 10²² kg and 1,737.4 km, Mars 6.417 × 10²³ kg and 3,389.5 km, the Sun 1.989 × 10³⁰ kg and 695,700 km (mean radii).
About This Tool
This calculator brings Newton’s gravity together in one place: the attraction between any two masses solved for the force, the distance or a mass; the surface gravity, escape velocity and weight on Earth, the Moon, Mars, the Sun or a body you define; and circular orbits from an altitude or from a period. Every value takes its own unit, from milligrams to astronomical units, and the working shows each step. The drawing puts the body and the orbit on the same scale, so a low orbit hugs the planet and a geostationary one stands well clear.
Everything runs in your browser; nothing you enter is sent anywhere.
Related tools: Circular Motion Calculator, Pendulum Calculator, and Physics Playground.
Frequently Asked Questions
What is Newton’s law of universal gravitation?
Every two masses attract with a force F = G × m₁ × m₂ ÷ r², where r is the distance between their centres and G = 6.6743 × 10⁻¹¹ N·m²/kg². Two 70 kg people standing 1 m apart pull on each other with only 3.27 × 10⁻⁷ N, about the weight of 0.03 mg.
How strong is gravity on the Moon?
Surface gravity is g = GM ÷ R². With the Moon’s mass (7.346 × 10²² kg) and mean radius (1,737.4 km) that gives 1.62 m/s², about a sixth of Earth’s. A 70 kg person there weighs 113.7 N, what 11.59 kg weighs on Earth.
How long does the ISS take to orbit the Earth?
At an altitude of about 420 km the orbit radius is 6,371 + 420 = 6,791 km, so T = 2π√(r³ ÷ GM) = 5,570 s, about 92.8 minutes, at 7.66 km/s. That is 15.5 orbits a day. Gravity up there is still 88% of its surface value; the crew float because they are falling around the Earth.
How high is a geostationary orbit?
It is the orbit whose period matches one turn of the Earth relative to the stars, 23 h 56 min 4 s (86,164 s). Kepler’s third law gives r = ∛(GM × T² ÷ 4π²) = 42,164 km from Earth’s centre, about 35,786 km above the equator, where satellites move at 3.07 km/s.
What is escape velocity?
The launch speed needed to coast away for good without further thrust: v = √(2GM ÷ r), which is √2 times the circular orbit speed at the same distance. From Earth’s surface it is 11.19 km/s, from the Moon 2.38 km/s and from Mars 5.03 km/s (ignoring air resistance).
How do I use the Gravity & Orbit Calculator?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Do I need to install or sign up for anything?
Not at all — it runs in the browser with nothing to install and no account. After it loads once, it even works without an internet connection.
Is my information private?
Yes. Everything happens in your browser. Nothing you type is sent to a server or saved anywhere.
Common Use Cases
Satellite orbits
A satellite 420 km up completes an orbit every 92.83 min at 7.661 km/s; one at 42,164 km from the centre keeps pace with the turning Earth.
Weight on other worlds
A 70 kg person weighs 260.95 N on Mars (what 26.6 kg weighs on Earth) and 113.7 N on the Moon.
Physics homework
Two 1,000 kg masses attract with 1 µN when they are 8.17 m apart, and the Earth and Moon with 1.98 × 10²⁰ N at 384,400 km.
Space mission sketches
Lunar orbit at 100 km altitude takes 117.8 min at 1.634 km/s, and leaving the Moon’s surface takes 2.38 km/s.
Astronomy
The Sun pulls on the Earth with 3.54 × 10²² N at 1 au, and its surface gravity is 274.3 m/s², nearly 28 times Earth’s standard g.
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