Calculator Inputs
This tool estimates the sub‑satellite point speed across Earth’s surface. It uses orbital elements, Earth rotation, and a short time step for accurate results.
Example Data Table
| Scenario | Altitude (km) | Inclination (deg) | Period (min) | Ground speed (km/h) | Orbital speed (km/s) |
|---|---|---|---|---|---|
| ISS-like LEO | 408 | 51.6 | 92.72 | 24,926.3 | 7.66404 |
| Polar LEO | 800 | 98.0 | 100.87 | 24,126.8 | 7.45183 |
| Sun-synchronous LEO | 700 | 98.2 | 98.77 | 24,638.3 | 7.50429 |
| Medium Earth Orbit | 20,200 | 55.0 | 718.70 | 2,751.5 | 3.87264 |
| Geostationary (near) | 35,786 | 0.0 | 1,436.07 | 0.0 | 3.07466 |
Values are computed with the same physics model used by the calculator. Real missions may differ due to Earth oblateness, drag, maneuvers, and attitude.
Formula Used
The calculator uses classical two‑body orbital mechanics and a rotating Earth frame:
- Mean motion: n = √(μ / a³)
- Orbital radius: r = a(1 − e²) / (1 + e cosν)
- Speed magnitude: v = √( μ(2/r − 1/a) ) (vis‑viva)
- Ground speed: sub‑satellite points are computed at t and t+Δt, then arc distance s = R·Δσ gives vg = s/Δt
Ground speed here means the speed of the point directly under the satellite, not the spacecraft speed through space.
How to Use This Calculator
- Select an input method (circular, perigee/apogee, or elements).
- Enter the orbit orientation: inclination, RAAN, and argument of perigee.
- Set true anomaly to choose where you are in the orbit.
- Keep Δt near 1 second for responsive results.
- Click Calculate and review ground speed and period.
- Use Download CSV or Download PDF for reporting.
Ground Speed Notes and Data
1) Typical speed ranges by orbit class
Low Earth orbits commonly produce orbital speeds near 7.3–7.9 km/s (about 26,000–28,500 km/h). Medium Earth orbits are often around 3.8–4.7 km/s. Near geostationary altitude, orbital speed is about 3.07 km/s, while the ground track can be nearly stationary.
2) Earth rotation changes the ground track speed
Earth rotates at roughly 7.292115×10−5 rad/s, giving an equatorial surface speed near 465 m/s (≈1,670 km/h). A prograde pass reduces ground speed, while a retrograde pass increases it. This difference is most noticeable near the equator.
3) Inclination and latitude matter
The sub‑satellite point does not move at a constant rate across all latitudes. Earth’s eastward surface speed scales with cos(latitude), so the rotation effect fades toward the poles. Example: at the equator, a ~7.6 km/s LEO can look like ~25,600 km/h prograde or ~29,200 km/h retrograde.
4) Time step (Δt) controls smoothness
Δt is used to measure arc distance between two nearby subpoints. Values around 0.5–5 seconds work well for quick estimates. Very large steps can average over fast changes, especially in eccentric orbits or when the path curves sharply on the map.
5) Elliptical orbits: speed changes along the path
In an ellipse, the spacecraft is fastest near perigee and slowest near apogee. For a sample orbit with perigee 400 km and apogee 800 km, vis‑viva gives about 7.78 km/s at perigee versus 7.34 km/s at apogee. Ground speed follows the same trend.
6) Quick unit conversions used in reports
Conversions are applied after computing ground speed in km/s: 1 km/s = 3,600 km/h. 1 km/h ≈ 0.621371 mph. 1 km/h ≈ 0.539957 knots. Use CSV or PDF export when you need consistent units across a mission log.
7) How far the subpoint moves each minute
A handy planning view is distance per minute. If ground speed is 27,000 km/h, the subpoint moves about 450 km per minute. At 14,000 km/h, it moves about 233 km per minute. This helps estimate how quickly a target region will pass under the ground track.
8) Why real missions can differ
This calculator assumes a simple two‑body orbit and a spherical Earth radius model for surface distance. Real ground tracks can drift due to Earth’s oblateness (J2), drag in LEO, station‑keeping burns, and attitude effects. Treat outputs as high‑quality estimates, not precision navigation.
FAQs
1) What is the difference between orbital speed and ground speed?
Orbital speed is the spacecraft’s speed through space. Ground speed here is the speed of the point directly beneath the satellite on Earth’s surface. Earth’s rotation makes ground speed smaller or larger than orbital speed depending on direction.
2) Does inclination change the speed?
Inclination mostly changes how Earth’s rotation combines with the orbit. Prograde, low‑inclination orbits “share” Earth’s eastward motion and can show lower ground speed. High‑inclination or retrograde orbits can show higher ground speed, especially near equator crossings.
3) What Δt value should I use?
Use 1 second for a responsive, accurate estimate. If you see noisy results, try 2–5 seconds. For highly eccentric orbits, smaller steps capture the rapid perigee speed change better. Very large steps can hide local variations in the ground track.
4) Why does a geostationary satellite sometimes show non‑zero ground speed?
“Geostationary” requires near‑zero eccentricity and near‑zero inclination, matched to Earth’s rotation. If inclination, eccentricity, or the rotation angle setting is different, the subpoint can trace a small loop and produce non‑zero ground speed over short intervals.
5) Can I use this for elliptical orbits?
Yes. Choose the perigee/apogee option or enter a and e directly. Then set true anomaly to evaluate the speed at a specific point along the orbit. The results reflect the local speed, so compare several anomaly values for a full picture.
6) What assumptions are built into the calculation?
The model uses two‑body dynamics, a chosen Earth radius for surface distance, and Earth rotation at a fixed rate. It ignores drag, Earth flattening in latitude conversion, station‑keeping, and maneuvering. For mission design, validate with higher‑fidelity tools and tracking data.