What it is
The resonant orbit calculator helps you deploy a constellation of several satellites evenly spaced on one circular orbit with a single launch. The carrier goes into a resonant orbit — an ellipse whose period relates to the period of the target circular orbit as (n + 1)/n (or (n − 1)/n in "Dive orbit" mode). Each time it passes the point where it touches the target orbit, the carrier releases a satellite, which circularises into place. While the carrier makes one revolution, the satellite moves exactly 1/n of a circle ahead — so the next one ends up at the right distance.
The calculator works for Kerbal Space Program bodies (KSP Stock, Outer Planets Mod and others) and for the real Solar System (Real Solar System).
How it is calculated
- Target orbit period — from Kepler's third law:
T = 2π·√(a3 / GM), where a is the orbit radius (body radius + altitude). - Carrier period = T·(n + 1)/n: periapsis at the target altitude, apoapsis higher. If the apoapsis leaves the sphere of influence or "Dive orbit" is on, T·(n − 1)/n is used: apoapsis at the target altitude, periapsis lower.
- Injection Δv — the burn each satellite needs to go from the carrier's speed at release to a circular orbit.
- Distance between neighbouring satellites — the chord
2·r·sin(180°/n). - Minimum LOS orbit — the lowest altitude at which neighbours see each other above the horizon (Line-of-Sight):
r·cos(180°/n) ≥ R. Occlusion modifiers account for the signal not passing through the atmosphere or part of the body. - Sync orbit — the synchronous (for Earth, geostationary) altitude where the period equals the body's day.
Example
Three relay satellites around Kerbin (radius 600 km) at 776 km:
| Parameter | Normal | Dive orbit |
|---|---|---|
| Target orbit period | 1 h 29 min 56.6 s | 1 h 29 min 56.6 s |
| Carrier period | ×4/3 = 1 h 59 min 55.5 s | ×2/3 = 0 h 59 min 57.7 s |
| Apoapsis / periapsis | 1,357,811 m / 776,000 m | 776,000 m / 124,169 m |
| Injection Δv | 134.17 m/s | 271.65 m/s |
| Distance between satellites | 2,383,302 m | 2,383,302 m |
Distance: 2·(600,000 + 776,000)·sin 60° = √3·1,376,000 ≈ 2,383,302 m. The minimum LOS altitude for three satellites is r·cos 60° ≥ R, i.e. r ≥ 2R: an altitude of 600 km.
Good to know
- Red highlighting warns that the carrier's periapsis is inside the atmosphere (it will slow down and burn up) or below the surface.
- Three satellites need an altitude of at least the body's radius to see each other; four or more can be lower.
- "Dive orbit" keeps the apoapsis low but needs more Δv to circularise and is risky around bodies with an atmosphere.
- Real orbits are perturbed (non-spherical bodies, other bodies), so periods are trimmed precisely — to fractions of a second — with small thrusters.
Where it is used
- Kerbal Space Program — relay networks (RemoteTech, CommNet) around Kerbin, the Mun, Duna, Jool.
- Real spaceflight — communication and navigation constellations: 3 geostationary satellites cover almost all of Earth (except the poles), GPS/GLONASS satellites fly at about 20,000 km.
- Studying — a visual way to learn Kepler's laws, orbit transfers and Δv calculations.
How to use
- Choose the system and body, the number of satellites and the orbit altitude in metres.
- The ⌾ buttons next to Sync orbit and Minimum LOS orbit put those altitudes into the Altitude field.
- Checkboxes show the line-of-sight (LOS) lines and enable occlusion modifiers for the atmosphere (atm) and the body (vac).
- The "Resonant orbit" block shows the carrier's period, apoapsis, periapsis, the injection Δv and the distance between satellites; the orbit diagram is on the right.
- The buttons in the "Examples" block fill the form with ready-made cases, "Reset" clears it.