Example Data Table
| Case | Inputs | Mean motion (rev/day) | Period (minutes) |
|---|---|---|---|
| Low Earth orbit | μ = 398600.4418 km³/s², a = 7000 km | ≈ 14.82 | ≈ 97.1 |
| Geostationary | T = 23.9345 hours | ≈ 1.0027 | ≈ 1436.1 |
| Fast spinner | T = 90 minutes | 16.0 | 90.0 |
Formula Used
Mean motion is the average angular rate of an orbit.
- Keplerian form: n = √( μ / a³ ) where μ is the gravitational parameter and a is the semi-major axis.
- Period form: n = 2π / T where T is the orbital period.
- Period from mean motion: T = 2π / n.
The calculator converts all inputs to SI units internally (meters and seconds) and then reports n in your chosen unit.
How to Use This Calculator
- Select a calculation mode based on available data.
- Enter μ and a, or enter the orbital period T.
- Pick an output unit such as rev/day or deg/day.
- Press Calculate to view results above the form.
- Use the download buttons to export CSV or PDF.
Article: Understanding Mean Motion
What mean motion represents
Mean motion (n) is the average angular speed of an orbiting body. It shows how quickly an object cycles around its primary and is reported as rad/s, deg/day, or rev/day. Knowing n helps estimate steady orbital progress and compare orbits of different sizes.
Two common ways to compute it
If you know the standard gravitational parameter μ and semi‑major axis a, Kepler’s third law gives n = √(μ/a³). If you know the orbital period T, then n = 2π/T. Both are equivalent in a two‑body model.
Units and conversions you’ll see
Tracking work often uses rev/day or deg/day, while dynamics uses rad/s. Conversions use 1 rev = 2π rad = 360° and 1 day = 86,400 s. The calculator converts outputs and also reports the implied period as a cross‑check. Choose the unit that matches your ephemeris and tracking workflow. It helps avoid rounding errors when you copy values into other tools.
Typical reference values
Low Earth orbit periods are about 90–100 minutes, roughly 14–16 rev/day. A geostationary orbit has T ≈ 23 h 56 m, so n is about 1 rev/day. Earth’s solar mean motion is close to 0.9856°/day. For Earth satellites, μ is often taken near 398,600 km³/s² when using kilometers.
Why semi‑major axis matters
Because of the a³ term, small changes in a cause noticeable changes in n. Increasing a reduces mean motion and lengthens the period. Decreasing a raises mean motion and shortens the period. This sensitivity supports maneuver planning and revisit estimates.
Circular vs. elliptical nuance
Mean motion depends on a, not instantaneous distance. In an ideal ellipse, n stays constant even though the object speeds up near periapsis and slows near apoapsis. That’s why mean motion pairs naturally with mean anomaly in simplified propagation.
Using mean motion in practice
With an epoch and mean anomaly at epoch, you can propagate mean anomaly via M = M₀ + n·Δt. Operators also use mean motion to spot drift, compare satellites, and validate catalog entries. Many teams convert to rev/day for daily reporting. In real orbits, drag and Earth’s oblateness slightly change n over time, so recomputing from updated elements keeps predictions consistent.
Input quality and sanity checks
Keep units consistent: μ must match the distance unit used for a (km³/s² with km, or m³/s² with m). Period T must be positive and in the chosen time unit. If results look odd, verify decimals and that a is the semi‑major axis, not altitude.
FAQs
What is mean motion measured in?
Mean motion is an angular rate. Common units are radians per second, degrees per day, and revolutions per day. Convert using 1 rev = 360° = 2π rad and 1 day = 86,400 seconds.
Does mean motion equal instantaneous orbital speed?
No. Mean motion is an average angular rate tied to the semi‑major axis. Instantaneous speed varies along an elliptical orbit, fastest near periapsis and slowest near apoapsis.
Which inputs should I use: μ and a, or period T?
Use μ and a when you have orbital size and a consistent gravitational parameter. Use period T when it is known from tracking or mission requirements. Both methods should agree when units are consistent.
Why do my results look wrong after changing units?
Most issues come from mismatched units. If μ is in km³/s², then a must be in km. If you switch a to meters, switch μ to m³/s² or convert a back to kilometers.
Can I compute the orbital period from mean motion?
Yes. Period is T = 2π/n when n is in rad/s. If n is in rev/day, then T (days) = 1/n, and you can convert days to hours or seconds as needed.
Is mean motion constant in real satellite orbits?
It is approximately constant over short times, but perturbations like atmospheric drag, Earth’s oblateness, and maneuvers cause slow changes. Updated elements or tracking data produce the best operational mean motion.
What does the CSV/PDF export include?
Exports include your selected mode, inputs, chosen units, and the computed mean motion with related values like period and angular rate. The file reflects the latest successful calculation shown above the form.