Orbital Velocity Calculator

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At the surface of the central body

How to Use the Orbital Velocity Calculator

1. 1. Choose the central body. Pick the Sun, a planet or the Moon to fill in its mass and radius from NASA's Planetary Fact Sheet, or type your own. Every box has a unit menu, and scientific notation such as 5.97e24 works. The Start from an example menu loads a space station, a geostationary satellite, a GPS satellite and others.
2. 2. Describe the orbit. Give the radius from the body's centre, the altitude above its surface, the speed, or the period. Switching between them carries the current orbit across, so you can start with an altitude and then read off the equivalent period.
3. 3. Read the result. Orbital speed, period, escape speed at that radius, the radius and altitude, and the gravitational acceleration at that height. If you gave the body's radius, the speeds needed at its surface are shown too.
4. 4. Check the working. The equations appear with your numbers substituted in SI units, along with the Kepler's-third-law constant for the central mass.

The Equations Behind a Circular Orbit

v = √(G M / r)

T = 2π r / v = 2π √(r³ / G M)

v_esc = √(2 G M / r) = √2 × v

A satellite in a circular orbit is in constant free fall, and gravity is exactly the centripetal force that keeps it turning: G M m / r² = m v² / r. Cancelling the satellite's mass m gives the speed above. It means every object at the same radius travels at the same speed, whatever its mass. A larger orbit is slower, not faster: lower orbits have to move quicker because gravity is stronger there.

Substituting v into the period gives Kepler's third law, T² = (4π² / G M) r³. The square of the period is proportional to the cube of the orbital radius, with a constant set only by the central mass. That is why the calculator shows the same 4π²/GM value whichever orbit you choose, and why the Moon, a space station and a GPS satellite all sit on one curve. OpenStax University Physics covers orbits in section 13.4.

Worked Examples

Each row is a preset in the Start from an example menu, rounded to four significant figures. A space station needs about 7.7 km/s, nearly 28,000 km/h, to stay up, and at that altitude gravity is still 8.674 m/s², 88% of its surface value. The geostationary period is one sidereal day (86,164 s, not 86,400 s), because Earth turns once relative to the stars in 23 h 56 min 4 s. The Moon's computed 27 d 10 h 50 min runs a little over the true sidereal month of 27.32 days, because the formula ignores the Moon's own mass.

Escape Velocity

Escape speed is the speed at which an object's kinetic energy equals the gravitational binding energy, so that it just reaches infinity with no speed to spare: ½mv² = G M m / r. At any radius it is √2 ≈ 1.414 times the circular orbital speed there. From Earth's surface it is 11.19 km/s, from the Moon's 2.376 km/s and from the Sun's visible surface 617.7 km/s. Air resistance is ignored, and the direction does not matter provided the path is clear.

Assumptions and Limits

• Circular orbits only. An elliptical orbit's speed varies with distance (the vis-viva equation); a circle is the special case.
• Spherical central body, negligible satellite. The satellite's own mass is ignored: exact enough for spacecraft, only roughly right for the Earth–Moon pair.
• Gravity only. Atmospheric drag, Earth's equatorial bulge and the Moon's pull change real satellite orbits, and very low orbits decay quickly because of drag.
• Gas giants. The radius used is the 1-bar level, and NASA's own escape speed for Jupiter uses its equatorial radius, so you may see 60.2 km/s here against 59.5 km/s in the fact sheet.

Frequently Asked Questions

How do you calculate orbital velocity?

Use v = √(G M / r), where G = 6.6743 × 10⁻¹¹ N·m²/kg², M is the mass of the body being orbited in kilograms and r is the distance from its centre in metres. For an orbit 408 km above Earth, r = 6,371 km + 408 km = 6,779 km and v ≈ 7,668 m/s.

Does orbital speed depend on the satellite's mass?

No. The satellite's mass cancels out of the equation, so a 1 kg cubesat and a 400,000 kg space station at the same radius travel at the same speed. Only the central body's mass and the orbital radius matter.

What is escape velocity and how does it relate to orbital velocity?

Escape velocity is the minimum launch speed to leave a body's gravity for good without further propulsion. At any radius it equals √2 times the circular orbital speed there, which is why a spacecraft already in low Earth orbit needs only about 41% more speed to escape.

What is Kepler's third law?

It states that the square of an orbit's period is proportional to the cube of its semi-major axis: T² = (4π² / G M) a³. For orbits around the Sun, measuring the period in years and the distance in astronomical units makes the constant exactly 1, which is why Mars, at 1.524 AU, takes about 1.88 years.

Why do satellites in higher orbits move more slowly?

Gravity weakens with distance, so less inward pull means a lower speed is needed to keep curving around. Speed falls as 1/√r, while the path length grows with r, so the period increases even faster, as r^(3/2).

What is a geostationary orbit?

It is a circular orbit above the equator whose period matches Earth's rotation, 23 h 56 min 4 s. The satellite then stays over one point on the ground. Solving T = 86,164 s gives a radius of about 42,164 km from Earth's centre, with a speed of 3.075 km/s.