Average Orbital Speed Calculator

The Average Orbital Speed Calculator uses Newton's law of gravitation to compute the mean orbital speed for a circular orbit: v = √(GM / r).

Choose a preset (Earth, Moon, Sun, Mars, etc.) or enter your own central-body mass and orbital radius. The calculator returns the orbital speed in m/s, km/s, km/h and mph, plus the orbital period (one full circumference at that speed).

Average Orbital Speed is calculated from central-body mass M and orbital radius r: v = √(GM / r), with G = 6.674 × 10⁻¹¹ N·m²/kg². The Average Orbital Speed Calculator reports this in km/s, m/s, km/h.

Low Earth Orbit averages 7.7–7.8 km/s. Geostationary orbit averages 3.07 km/s. Mercury orbits the Sun at ~47.4 km/s; Pluto at 4.7 km/s.

Average Orbital Speed is a statistical / derived quantity rather than a measured distance ÷ time. It describes the average behaviour of a population — gas molecules, orbiting bodies, fluid parcels or rotating points — at equilibrium.

The Average Orbital Speed formula is v = √(GM / r), with G = 6.674 × 10⁻¹¹ N·m²/kg². Symbolically: v = √(GM / r).

The formula has these rearrangements that solve for any unknown:

1. v = √(GM / r) — solve for the average speed
2. Solve for the temperature / mass input — see the worked example below.

The output unit depends on the input units. SI inputs (kelvin, kg/mol or kg, m³/s, m²) produce km/s.

To calculate average orbital speed:

• Step 1: Identify the input variables: central-body mass M and orbital radius r.
• Step 2: Convert to SI units (kelvin, kg/mol, m, m²) before substituting.
• Step 3: Apply the formula: v = √(GM / r).

Worked example: ISS at r = 6 778 km (Earth M = 5.972 × 10²⁴ kg). v = √(6.674e−11 × 5.972e24 / 6.778e6) = 7660 m/s = 7.66 km/s.

Three steps:

• Step 1: Enter the inputs: central-body mass M and orbital radius r.
• Step 2: Pick the units from the dropdowns — the calculator converts internally to SI.
• Step 3: Read the result — the calculator updates as you type and shows km/s plus all conversions.

Enter central-body mass (or pick a preset: Sun, Earth, Mars) and orbital radius. The calculator returns mean orbital speed and orbital period via Kepler's third law.

Substitute the physical inputs directly into the formula. Unlike distance / time tools, Average Orbital Speed doesn't need a measured trip — it derives from a state variable (temperature, mass, radius).

Worked example: ISS at r = 6 778 km (Earth M = 5.972 × 10²⁴ kg). v = √(6.674e−11 × 5.972e24 / 6.778e6) = 7660 m/s = 7.66 km/s.

Switch input units freely; the calculator does the conversion before substituting.

Rearrange the formula to solve for any input given the output. The calculator inverts v = √(GM / r) for you.

Worked example: Solving for r given v: r = GM / v². To average 5 km/s around Earth, r = (6.674e−11 × 5.972e24) / (5000)² = 1.594 × 10⁷ m = 15 940 km.

This is useful for planning — e.g. finding the temperature required to reach a target average orbital speed, or the orbital radius for a target km/s speed.

For a tour of multiple targets, compute v at each radius and weight by transit time on each leg.

For example, comparing two different operating conditions side-by-side highlights the inverse-square / square-root scaling that governs orbital mechanics.

Orbital period T = 2π r / v. For ISS: T = 2π × 6.778e6 / 7660 = 5560 s ≈ 93 min.

Where a derived time (e.g. orbital period, mean-free-path) is requested, convert units in the calculator's results panel rather than in the input form.

Elliptical orbits change speed continuously — perihelion is fastest, aphelion slowest. Time-averaged speed equals 2π a / T where a is the semi-major axis.

Segment-by-segment analysis is most useful when the input variable changes — e.g. temperature ramp, orbital perihelion → aphelion, pipe diameter step-down.

Average Orbital Speed is normally reported in km/s. Common alternative units:

• 1. km/s — SI / scientific convention
• 2. m/s — alternative reporting unit
• 3. km/h — alternative reporting unit

The calculator handles all conversions automatically.

Average Orbital Speed is a scalar — magnitude only. Velocity is a vector that adds direction.

For a orbiting body in a thermal / isotropic situation, the average velocity is zero (directions cancel out) even though the average speed is large. Average Orbital Speed reflects the typical magnitude that matters for kinetic energy, mean free path or transport.

Average Orbital Speed is the population / time-averaged value. Instantaneous average orbital speed is the value at one moment for one orbiting body.

For gas molecules, instantaneous speeds follow the Maxwell–Boltzmann distribution; the average is the central tendency, not the value any individual molecule has.

Constant average orbital speed means the value doesn't change with time. Average Orbital Speed can equal that constant if conditions are steady (constant T, constant r, constant Q), but the moment one input drifts, the average drifts with it.

For practical purposes treat Average Orbital Speed as a snapshot of the system's current state — re-evaluate whenever an input changes.

For elliptical orbits, v(t) is sinusoidal-ish. Plot v vs anomaly to see speed peaks at perihelion. Mean v̄ ≈ √(GM / a).

The "graph" for a physics-style average average orbital speed is usually a distribution plot rather than a v(t) trace — the average corresponds to the area-weighted centroid of the distribution.

Velocity changes direction continuously in a circular orbit, so the velocity-time plot is a rotating vector of constant magnitude.

For isotropic systems, plotting one Cartesian component of velocity yields a Gaussian centred at zero whose width sets the magnitude of Average Orbital Speed.

There are several common mistakes when computing average orbital speed. Click each card below to expand the explanation.

Practice the following worked average orbital speed problems. Click "Show Solution" to reveal the step-by-step answer.