Orbital Speed Calculator

Calculate circular or elliptical orbital speeds, period, escape speed and energy, or solve circular orbit size or central mass. Select a preset or custom central body. Optional transfer estimates use an ideal coplanar Hohmann model.

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Orbital Speed Formula

For an ideal circular orbit with negligible satellite gravity, speed depends on the central body’s GM and center-to-center radius. Earth values below are examples; the calculator also supports other preset bodies and custom mass.

v = √(GM/r) = √(μ/r)

Where:

• v = orbital speed
• G = universal gravitational constant
• M = mass of Earth
• μ = Earth’s standard gravitational parameter
• r = orbital radius, measured from Earth’s center to the orbiting object

If you know the object’s altitude above Earth’s surface rather than its orbital radius, convert altitude to radius first:

r = mean body radius + altitude

For Earth-based calculations, these reference values are commonly used:

Earth μ ≈3.986004418 ×10^14 m³/s²

Earth mean radius ≈6.371 ×10^6 m

Why the Formula Works

In a circular orbit, gravity supplies exactly the inward force needed to keep the object moving around Earth. Set gravitational force equal to centripetal force:

m v²/r = G M m/r²

After canceling the satellite mass m and solving for v, you get the circular-orbit speed formula. That is why, for ordinary satellite calculations, a heavier satellite does not need a different orbital speed at the same radius.

How to Use the Orbital Speed Calculator

1. Select the solve mode and central body. For a custom body, enter mass and a mean radius when altitude input is used.
2. Choose altitude above the modeled mean surface or radius from the center. The calculator adds mean body radius for altitude inputs; the central-mass solve always uses center radius.
3. Distance inputs accept meters, kilometers, miles or astronomical units. Enter speed or period in the units selected beside that field.
4. Select Calculate for labeled results. Optional satellite mass adds energy; a circular target distance adds transfer burns and time, while an elliptical sample distance must lie between periapsis and apoapsis.

The circular modes assume circular motion; the ellipse mode uses vis-viva and reports periapsis and apoapsis speeds. All modes neglect satellite gravity, atmospheric drag, thrust and perturbations. Below-mean-surface orbits and reversed ellipse endpoints are rejected. An accepted radius does not establish atmospheric or terrain clearance.

Quick Reference for Common Earth Orbits

Example at 400 km Altitude

Suppose a satellite is orbiting 400 km above Earth’s surface. First convert altitude to orbital radius:

r =6,371,000 +400,000 =6,771,000 m

Now apply the circular orbital speed formula:

v =√(3.986004418 ×10^14 /6,771,000) ≈7,672.60 m/s

That is about 7.67 km/s, which is roughly 27,621 km/h. This is why low Earth orbit spacecraft move around Earth so quickly even though they are still “falling” under gravity.

Related Equations

Once orbital speed is known, you can connect it to other orbital quantities.

Circular-orbit period:

T =2πr/v =2π√(r³/μ)

Escape velocity at the same radius:

escape speed =√(2μ/r) =√2 × circular speed

General speed equation for an elliptical orbit:

vis-viva speed =√[μ(2/r −1/a)]

In the last equation, a is the semi-major axis of the ellipse. For a circular orbit, a = r, which reduces back to the simpler orbital speed formula used by this calculator.

Important Interpretation Notes

• Higher orbit means lower speed. A satellite farther from Earth moves more slowly in a circular orbit.
• Higher orbit also means longer period. Even though speed is lower, the path is much larger, so orbital periods increase substantially.
• Radius is not the same as altitude. Radius is measured from Earth’s center; altitude is measured from the surface.
• Mass cancels out. For a small satellite around Earth, orbital speed does not depend on the satellite’s mass.
• Real orbits are not perfectly ideal. Drag, orbit eccentricity, and maneuvers can change the actual speed at a given point.

Common Mistakes

• Entering altitude directly when the formula requires orbital radius.
• Mixing kilometers and meters without converting units consistently.
• Using the circular-orbit formula for a strongly elliptical orbit.
• Confusing orbital speed with escape speed.
• Assuming a slower orbital speed means a shorter trip around Earth; in reality, higher orbits usually take much longer to complete.

FAQ

Does orbital speed depend on the mass of the satellite?

The modeled speed neglects satellite gravity and assumes its mass is small compared with the central body. Optional satellite mass affects total energy only. Comparable-mass systems require a different two-body treatment.

Why do low satellites move faster than high satellites?

Gravity is stronger closer to Earth, so a larger inward acceleration is available. To maintain a stable circular path at that smaller radius, the object must move faster.

Can I use this calculator for any planet?

Select a preset or custom central body; its GM and mean radius determine the result. Presets use approximate single-body constants, not a mission ephemeris. A geosynchronous period alone does not establish a geostationary orbit, which must also be circular, equatorial and prograde.

What is the difference between orbital speed and escape velocity?

Orbital speed is the speed required to stay in a closed orbit at a given radius. Escape velocity is the speed required to leave Earth’s gravity without further propulsion. At the same radius, escape velocity is √2 times the circular orbital speed.

Why is the orbital radius measured from Earth’s center?

Newtonian gravity depends on the distance between the centers of mass of Earth and the orbiting object, so the correct radius in the formula is center-to-center distance, not height above the ground.