Orbital Speed Calculator

Enter the orbital radius (distance from Earth’s center to the object) to calculate orbital speed. This calculator assumes an object orbiting Earth in a (nearly) circular orbit, and orbital speed does not depend on the satellite’s mass for this case. If you have altitude above Earth’s surface, add Earth’s mean radius (~6,371 km) to get orbital radius.

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Orbital Speed Formula

For a satellite or spacecraft in a nearly circular Earth orbit, the orbital speed depends on only two things: the strength of Earth’s gravity and the orbital radius measured from Earth’s center.

v = \sqrt{\frac{GM}{r}} = \sqrt{\frac{\mu}{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 = R_E + h

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

\mu_{\oplus} \approx 3.986004418\times10^{14}\ \text{m}^3/\text{s}^2

R_E \approx 6.371\times10^6\ \text{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:

\frac{mv^2}{r} = \frac{GMm}{r^2}

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. Enter the orbital radius if you already know the distance from Earth’s center.
2. If you only know altitude, add Earth’s radius to convert altitude into orbital radius.
3. Select the most convenient unit for your input, such as meters, kilometers, feet, or miles.
4. Click Calculate to get orbital speed in the output units you prefer, including m/s, km/h, ft/s, mph, or knots.

The calculator is most accurate for circular or nearly circular Earth orbits. It does not account for atmospheric drag, engine thrust, non-spherical gravity effects, or elliptical-orbit speed changes.

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\times10^6 + 4.00\times10^5 = 6.771\times10^6\ \text{m}

Now apply the circular orbital speed formula:

v = \sqrt{\frac{3.986004418\times10^{14}}{6.771\times10^6}} \approx 7.67\times10^3\ \text{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 = \frac{2\pi r}{v} = 2\pi\sqrt{\frac{r^3}{\mu}}

Escape velocity at the same radius:

v_{esc} = \sqrt{\frac{2\mu}{r}} = \sqrt{2}\,v

General speed equation for an elliptical orbit:

v = \sqrt{\mu\left(\frac{2}{r} - \frac{1}{a}\right)}

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?

No. In the circular-orbit derivation, the satellite mass cancels out, so speed is determined by Earth and the orbital radius.

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?

The structure of the formula is universal, but the value of μ or GM changes with the central body. This calculator is specifically framed for Earth orbit.

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.