Orbital Speed Calculator
Calculate circular or elliptical orbital speed around Earth, the Moon, Mars or a custom body. Inspect the orbit geometry, speed at each position, period and energy with input-linked explanations.
Calculation inputs
Define the path before reading its speed
- 1Choose the geometry
Circular mode uses one altitude. Elliptical mode uses periapsis, apoapsis and a selected angle.
- 2Keep all distances consistent
Use kilometres or miles; conversion occurs before the equations. Earth-scaled custom bodies remain available.
- 3Read the selected position
The point on the calculated geometry and the speed curve both follow the same inputs.
Constants and methods are linked below. Illustrations show the setting; calculated plots carry the actual geometry and data.
Speed across the selected orbit model
Speed across the selected orbit model
Your calculated orbital geometry
Calculation results
Step-by-step solution
Build the orbit from center distances
Find the shape
Locate the spacecraft
True anomaly is measured from periapsis. Equal angle increments are not equal time intervals on an ellipse.
Apply vis-viva and Kepler’s period law
Read the orbit from its nearest and farthest points.
- 1Choose the geometry
Circular: periapsis and apoapsis are equal.
- 2Locate the selected angle
ν = 0° gives center distance 6,771.008 km.
- 3Keep time and angle distinct
A complete orbit takes 1.54 h. Uniform angle steps do not represent uniform elapsed time on an ellipse.
Isolated, spherical, non-rotating central body; negligible spacecraft mass. Atmosphere, terrain, other gravitating bodies and finite burns are excluded.
Speed is relative to the central body in an ideal inertial two-body model. Period is one full orbit, not a launch, landing or ground-repeat time. An ellipse’s speed changes with position. Rounded displays retain full calculation precision.
Measurements & calculation details
| Quantity | Value |
|---|---|
| Central body | Earth |
| Gravitational parameter μ | 398600.435507 km³/s² |
| Spherical reference radius R | 6371.0084 km |
| Periapsis center distance | 6771.0084 km |
| Apoapsis center distance | 6771.0084 km |
| Semi-major axis | 6771.0084 km |
| True anomaly | 0 degrees |
| Instantaneous center distance | 6771.0084 km |
| Orbital speed | 7.6725938285682 km/s |
| Period | 5544.8654580493 s |
| Specific orbital energy | -29.434348029091 MJ/kg |
Try a worked example
Choose an example to load its measurements into the calculator. Each result uses the same calculation engine as your own inputs. Back to your calculation
Inspect the nearest, selected and farthest points
| Position on this orbit | Altitude (km) | Speed (km/s) |
|---|---|---|
| Periapsis · 0° | 400 | 7.6726 |
| Selected · 0° | 400 | 7.6726 |
| Apoapsis · 180° | 400 | 7.6726 |
For this bound orbit, specific energy is -29.434348 MJ/kg. Local circular speed at the selected radius is 7.6726 km/s. Speed stays constant around this circle.
Understand the calculation
Concept & meaning
Orbital speed is the magnitude of velocity relative to the central body. A circular orbit has constant radius and speed; an ellipse varies both. Specifying the two endpoint altitudes fixes the size and eccentricity of the model ellipse, and true anomaly locates a point measured from periapsis. The body is at one focus, not generally at the ellipse’s geometric center.
Formula & special cases
Convert endpoint heights to center distances before finding a = (rₚ + rₐ)/2 and e = (rₐ − rₚ)/(rₐ + rₚ). Position follows r = a(1 − e²)/(1 + e cos ν), and vis-viva gives v = √[μ(2/r − 1/a)]. When the endpoints are equal, e is zero and this reduces to √(μ/r). The full-orbit period depends on a: T = 2π√(a³/μ), not on the currently selected true anomaly.
Scope & limitations
Low periapsis can introduce drag, terrain intersection and instability that a Keplerian model cannot evaluate. Zero altitude is only a mathematical boundary. A period near one sidereal day does not by itself establish a geostationary orbit; inclination, direction and eccentricity also matter. Body rotation, oblateness, other bodies and spacecraft thrust are excluded. For accurate operational states, use an appropriate ephemeris and orbit model rather than these scenarios.
Result from your current inputs
Circular orbital speed: 7.6726 km/s
Circular motion is a special case of an ellipse
| Calculation | Formula | Interpretation |
|---|---|---|
| Orbit endpoints | rₚ = R + hₚ; rₐ = R + hₐ | Always measured from the center |
| Orbit size and shape | a = (rₚ + rₐ)/2; e = (rₐ − rₚ)/(rₐ + rₚ) | The circular case has e = 0 |
| Selected position | r = a(1 − e²)/(1 + e cos ν) | True anomaly measured from periapsis |
| Instantaneous speed | √[μ(2/r − 1/a)] | Vis-viva |
| Period and energy | 2π√(a³/μ); −μ/(2a) | Full orbit time and specific energy |
Sources & References
NASA/JPL · astrodynamic constantsEarth/Moon μ, vacuum light speed, AU and Julian yearRead the referenceNASA/JPL · physical parametersAdopted planetary mean radiiRead the reference
NASA · Moon fact sheetMean lunar radius: 1,737.4 kmRead the referenceNASA/JPL · satellite parametersMars central-body μ, rather than the combined Mars-system valueRead the referenceNASA NTRS · orbit equationsSpace tether handbook: orbit equations and vis-vivaRead the referenceNASA · orbital mechanicsAcceleration and Kepler’s lawsRead the referenceReferences document the methods and their limitations; links and logos do not imply institutional endorsement or expert review.
