Calculator Inputs
The page stays single-column overall, while the form fields use a responsive three, two, and one-column layout.
Example Data Table
| Preset | μ (km³/s²) | Radius (km) | Rotation (hours) | Computed Radius (km) | Altitude (km) | Velocity (km/s) |
|---|---|---|---|---|---|---|
| Earth | 398600.4418 | 6378.137 | 23.9344696 | 42,164.170 | 35,786.033 | 3.074660 |
| Mars | 42828.375214 | 3396.190 | 24.6229 | 20,427.651 | 17,031.461 | 1.447960 |
| Saturn | 37931187.000 | 60268.000 | 10.656 | 112,238.893 | 51,970.893 | 18.383429 |
These sample values help verify that your installed calculator returns sensible synchronous orbit outputs.
Formula Used
ω = 2π / T
r = ( μ / ω² )1/3
h = r − R
v = √( μ / r )
C = 2πr
ε = − μ / (2r)
ρ = √( r² + R² − 2rR cos ψ )
ψ = arccos( cos φ · cos Δλ )
E = arctan( (cos ψ − R/r) / sin ψ )
t = π √( a³ / μ )
Here, μ is the gravitational parameter, T is the rotation period, R is planetary radius, φ is ground latitude, Δλ is longitude difference, and a is the transfer orbit semi-major axis.
How to Use This Calculator
- Select Earth for a true geostationary calculation, or choose another rotating body.
- Review or edit the gravitational parameter, equatorial radius, and rotation period.
- Enter the satellite mass to estimate orbital kinetic energy.
- Enter a parking orbit altitude to estimate two-burn transfer requirements.
- Set the satellite slot longitude and ground station coordinates.
- Press Calculate Orbit to display results above the form.
- Use the CSV or PDF buttons to export the computed outputs.
- Compare your results with the example data table for a quick check.
8 FAQs
1) What is a geostationary orbit?
It is a circular equatorial orbit around Earth whose period matches Earth’s sidereal rotation. The satellite appears fixed above one longitude, which makes communication coverage continuous.
2) Why does Earth use a sidereal day?
A geostationary satellite must match Earth’s rotation relative to the stars, not the Sun. That period is about 23.934 hours, which gives the standard geostationary radius.
3) Why is the altitude near 35,786 km?
That altitude makes the circular orbit period equal to Earth’s sidereal day. Smaller altitudes orbit too quickly, while larger altitudes orbit too slowly.
4) Does this tool work for Mars or Saturn?
Yes. It computes stationary synchronous orbits around any rotating body when you provide valid constants. Only Earth’s case is called geostationary.
5) What does the elevation angle mean?
Elevation angle shows how high the satellite appears above the local horizon. Higher elevation usually improves link quality and reduces obstruction risk.
6) Why is signal delay important?
Propagation delay affects voice, video, control loops, and network responsiveness. Geostationary links usually have noticeable latency because the path is very long.
7) What is the Hohmann transfer output for?
It estimates the two main burns needed to raise a circular parking orbit into the synchronous orbit. It is a useful first-pass mission design figure.
8) Are perturbations and station-keeping included?
No. This calculator gives ideal two-body results. Real missions also consider oblateness, solar and lunar perturbations, inclination control, and propellant margins.