A satellite in low Earth orbit is not hanging in space. It is falling — continuously, all the way around the planet — and the only reason it never hits the ground is that it moves sideways fast enough to keep missing. Get the speed slightly wrong and the orbit decays into the atmosphere or stretches out into a long ellipse. Orbital velocity is the precise speed that turns a fall into a stable circle.
This article explains where orbital velocity comes from, walks through the speed and period of a real low-orbit satellite, and points out the mistakes that trip up students and engineers when they first run the numbers.
Why this calculation matters
Orbital velocity is the starting point for almost every space mission calculation. Before you can plan a launch, size a propulsion system, or schedule a ground-station pass, you need to know how fast the spacecraft will be moving and how long one lap takes. The orbit's speed sets the energy a launch vehicle must deliver, the Doppler shift a radio link will see, and the window during which a camera can see a target on the ground.
It also explains some counterintuitive behavior. A satellite in a lower orbit moves faster than one in a higher orbit, not slower — closer to the planet, gravity is stronger, and a faster sideways speed is needed to balance it. That single fact governs why the International Space Station laps the Earth roughly every 90 minutes while a GPS satellite takes about 12 hours, and why a geostationary satellite, matched to the 24-hour rotation of the Earth, has to sit far out at about 36,000 km altitude.
The core formula
For a circular orbit, the physics is a balance between two effects. Gravity pulls the satellite toward the center of the planet. The satellite's own motion along a curved path requires a centripetal acceleration directed at that same center. Set the gravitational pull equal to the mass times the centripetal acceleration, and the satellite's mass cancels out completely:
G*M*m / r^2 = m * v^2 / r
Solving for the speed gives the circular orbital velocity:
v = sqrt(G*M / r)
Here G*M is the gravitational parameter of the central body — for Earth, G*M = 3.986e14 m^3/s^2 — and r is the orbital radius measured from the center of the planet, not from its surface. That distinction matters: r is the planet's radius plus the orbital altitude.
The orbital period, the time for one full lap, follows from dividing the circumference by the speed:
T = 2*pi*r / v
Two features are worth fixing in your mind. First, the satellite's mass never appears — a bolt and a space station at the same altitude orbit at the same speed. Second, speed falls as r grows: v scales with 1/sqrt(r). Double the orbital radius and the speed drops by a factor of about 1.41, while the period grows even faster. That last relationship, taken further, is Kepler's third law.
A worked example
Consider a satellite in a circular low Earth orbit at an altitude of 400 km — close to the altitude band where the International Space Station operates.
Step 1 — find the orbital radius. Orbital velocity depends on the distance from Earth's center, so add the planet's mean radius to the altitude:
r = R_earth + h = 6371 + 400 = 6771 km = 6.771e6 m
Step 2 — compute the circular speed. Substitute r and Earth's gravitational parameter into the velocity formula:
v = sqrt(G*M / r)
v = sqrt(3.986e14 / 6.771e6)
v = sqrt(5.887e7)
v = 7673 m/s
So the satellite must travel at about 7.67 km/s — roughly 27,600 km/h — just to maintain that orbit.
Step 3 — compute the orbital period. Divide the circumference of the orbit by the speed:
T = 2*pi*r / v
T = 2*pi*6.771e6 / 7673
T = 5545 s
That works out to about 92 minutes per lap. A satellite at this altitude completes more than fifteen orbits of the Earth every day. The number lines up with the familiar fact that the ISS sees a sunrise roughly every hour and a half.
Common mistakes
Using altitude instead of orbital radius. The most common slip. The r in the formula is measured from the center of the Earth. Plugging in 400 km instead of 6771 km inflates the predicted speed by a factor of about four and produces a meaningless answer.
Mixing up kilometers and meters. The gravitational parameter G*M = 3.986e14 is expressed in cubic meters per second squared. If r is left in kilometers, the result is wrong by orders of magnitude. Convert everything to SI before substituting.
Assuming higher orbits are faster. Intuition from cars and planes says more energy means more speed. In orbit it is the reverse: raising the orbit raises the total energy but lowers the orbital speed. The extra energy goes into potential energy, not kinetic.
Applying the circular formula to an elliptical orbit. v = sqrt(G*M/r) holds only when the orbit is a circle. On an ellipse the speed changes continuously, fastest at periapsis and slowest at apoapsis. For those cases you need the vis-viva equation, which uses both the current radius and the semi-major axis.
Forgetting that low orbits are not truly stable. Below roughly 600 km there is still enough residual atmosphere to produce drag. A real satellite at 400 km slowly loses altitude and needs periodic reboosts. The circular-orbit speed is the ideal, not a permanent state.
Try the interactive NovaSolver calculator
Running the square root once is straightforward, but seeing how the orbit changes as you adjust altitude and shape is far more instructive. The Orbital Mechanics — Kepler Orbit Visualizer on NovaSolver lets you set the central body, semi-major axis, and eccentricity, then returns the orbital period, periapsis and apoapsis altitudes, the speeds at those two points, and the specific orbital energy, with a live animation of the satellite tracing its path. Preset buttons for LEO, the ISS, GEO, the Moon, and Mars make it easy to compare regimes side by side.
Related calculators
- Orbital Mechanics Simulator — for exploring how multiple bodies and initial conditions shape a trajectory over time.
- Orbital Transfer Calculator — to find the delta-v needed to move between two orbits, the next question after you know the speed of each.
- Rocket Equation Calculator — to size the propellant a launch vehicle needs to reach orbital velocity in the first place.
You can browse the full set in the space and orbital mechanics tools hub.
Closing note
Orbital velocity is one of the cleanest results in physics: a single square root that captures the balance between gravity and motion. The takeaways are easy to keep: measure the radius from the planet's center, work in SI units, and remember that lower orbits are faster, not slower. Once that circular case is solid, the elliptical orbits, transfer maneuvers, and rendezvous problems of real missions all build naturally on top of it. Run your own altitudes, check the period against what you know about real satellites, and let the simple circle be the foundation for everything that follows.
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