Constellation design

A constellation is a set of orbits chosen so that, collectively, satellites are always where they need to be. The design problem is to find the smallest such set, and it is unusually constrained: only a few families of solutions are practical, because deployment cost and long-term maintenance both punish irregularity severely.

Why regular patterns

In principle any set of orbits is a constellation. In practice nearly every operational system uses a highly symmetric pattern, for four reasons that compound.

Uniform coverage

A symmetric pattern gives similar performance everywhere within its latitude band, so the system has no accidental weak spots that appear only at certain longitudes.

Uniform perturbations

Satellites at the same altitude and inclination precess at the same J2 rate, so the pattern holds its shape without differential station keeping. An irregular constellation would distort continuously.

Deployment efficiency

Satellites in one plane can be launched together and separated by phasing within that plane, which is nearly free. Satellites in different planes require either separate launches or a slow drift.

Replenishment

Any spare is interchangeable with any failed satellite in its plane, which makes sparing arithmetic tractable and lets one on-orbit spare cover a whole plane.

The second reason is the strongest. From Orbital perturbations, the nodal regression rate depends on altitude and inclination:

Satellites sharing an altitude and inclination share $\dot{\Omega}$ exactly, so their relative geometry is preserved indefinitely at no propellant cost. A constellation mixing altitudes would shear apart, and holding it together would consume propellant continuously for the whole mission.

Walker constellations

The standard parameterisation, due to John Walker, describes a constellation with four numbers:

From these, everything else follows:

• Satellites per plane: $s = t/p$
• In-plane spacing: $360°/s$
• Right ascension spacing between planes: $360°/p$ for a Delta pattern
• Phase offset between adjacent planes: $f \times 360°/t$

The phasing parameter $f$ is the subtle one and is what distinguishes a good Walker constellation from a mediocre one. It sets how much satellites in one plane are offset in true anomaly from those in the neighbouring plane. Choosing $f$ well staggers the satellites so that coverage gaps in one plane are filled by the next; choosing it badly lines them up and leaves diamond-shaped holes between planes.

Delta and Star patterns

Two arrangements of the planes, suited to different coverage requirements.

Walker Delta, sometimes called a rosette, distributes the ascending nodes over a full 360° of right ascension. All satellites orbit in the same sense, and the pattern is uniform in longitude. This suits global or mid-latitude coverage and is what GPS, Galileo and the main Starlink shells use.

Walker Star distributes the ascending nodes over 180° instead, with all planes near-polar. Because the planes converge at the poles, coverage is dense at high latitudes and sparse at the equator, which is the opposite of a Delta. Iridium uses this, and it is why Iridium has genuine pole-to-pole coverage where a 53° Delta constellation has none above about 60° latitude.

The counter-rotating seam in a Star pattern deserves explanation because it is a real operational complication. Since the planes span only 180° of RAAN, satellites on one side of the pattern travel north while those on the other side travel south. Along the boundary between them, adjacent satellites approach each other at twice orbital velocity rather than drifting slowly. Inter-satellite links cannot be maintained across that seam, and collision geometry there needs care.

Streets of coverage

For near-polar constellations, the standard analysis treats each plane as projecting a continuous street of coverage onto the ground, of half-width $c$ given by

where $\lambda$ is the coverage half-angle of a single satellite and $s$ is the number of satellites per plane.

The logic is worth unpacking. Satellites within a plane are spaced $2\pi/s$ apart in true anomaly. Directly beneath the plane, coverage is continuous because consecutive footprints overlap. Moving sideways from the ground track, the overlap shrinks until at some cross-track distance the footprints separate and gaps appear between successive satellites. That distance is the street half-width, and it is always smaller than the single-satellite footprint radius.

Two design consequences follow immediately.

More satellites per plane widens the street, not just by adding footprints but by increasing the overlap so coverage is continuous further off-axis. This is why adding a satellite to an existing plane is often better value than adding a whole plane.

The street is narrower than the footprint, so intuitions based on footprint radius overestimate coverage. A designer sizing plane count from footprint radius alone will be short.

Continuous global coverage then requires enough planes that the streets overlap across all longitudes, which for a Star pattern means the streets must tile the 180° of RAAN the planes span.

The plane count trade

For a fixed total satellite count, the number of planes is a genuine optimisation with opposing pressures.

Real designs land across the range: GPS uses 6 planes of 4, Galileo 3 planes of 8, Iridium 6 planes of 11, OneWeb 12 planes of 49, and Starlink’s first shell 72 planes of 22. The Starlink figure reflects a system optimised for capacity density over the populated mid-latitudes rather than for minimum satellite count, and it is affordable only because the operator also owns the launch vehicle.

Deployment and phasing

Getting satellites into the right planes is a major cost driver, and there are two strategies.

Direct injection launches each plane separately, so the launcher places satellites at the correct right ascension. It is fast and expensive, requiring as many launches as there are planes at minimum.

Drift deployment exploits the $J_2$ nodal regression rate, which depends on altitude. Satellites launched into one plane are placed at slightly different altitudes, so they precess at slightly different rates and their planes separate over weeks to months. Once the desired separation is reached, each satellite circularises to the operational altitude and its plane is locked in.

This is free in propellant and expensive in time. A typical differential of a few tens of kilometres in altitude gives a fraction of a degree per day of relative nodal drift, so distributing satellites across many planes takes months. Both OneWeb and Starlink use variants of it, and it is the technique that makes a 72-plane constellation deployable at all.

The in-plane phasing at the end uses the same mechanism at a smaller scale. From Rendezvous and docking, a semi-major axis difference $\delta a$ produces an along-track drift of $3\pi\,\delta a$ per revolution, so a satellite can be walked to its slot within the plane and then circularised.

Replenishment

A constellation is never finished. With a design life $L$ and $t$ satellites, the steady-state replacement rate is

Three hundred and seventeen satellites per year is about six per week, sustained indefinitely. That is not a deployment campaign, it is a factory, and it must run for as long as the service exists.

This arithmetic is why constellation economics are inseparable from launch and manufacturing economics. It also explains why constellation operators integrate vertically: an operator buying launches on the open market at six satellites a week is exposed to launch price and availability in a way that no GEO operator ever was. See Launch and mission economics.

Sparing strategy follows the same logic. Options are on-orbit spares parked in each plane, ground spares held for launch on demand, or simply accepting degraded coverage until the next scheduled batch. Large LEO constellations generally take the third route, because with hundreds of satellites the loss of one is statistically absorbed, whereas a 66-satellite constellation must hold spares in every plane.

Verification

A constellation design is verified by simulation over a full repeat cycle, because coverage varies with the pattern’s phase relative to Earth’s rotation. The metrics are those in Ground tracks and coverage: maximum gap, mean revisit, and availability, each reported as a function of latitude rather than as a single global number.

The failure mode to guard against is optimising a summary statistic. A design with excellent mean revisit and one four-hour gap at a specific latitude has failed, and a global average conceals exactly that.

References

• Walker, J. G. “Satellite Constellations”, Journal of the British Interplanetary Society, 37:559, 1984.
• Wertz, J. R. Mission Geometry: Orbit and Constellation Design and Management, Microcosm Press, 2001. The definitive treatment of coverage analysis and streets of coverage.
• Adams, W. S. and Rider, L. “Circular polar constellations providing continuous single or multiple coverage above a specified latitude”, Journal of the Astronautical Sciences, 35:155, 1987.
• Lang, T. J. “Symmetric circular orbit satellite constellations for continuous global coverage”, AAS 87-499.
• Del Portillo, I., Cameron, B. G. and Crawley, E. F. “A technical comparison of three low earth orbit satellite constellation systems to provide global broadband”, Acta Astronautica, 159:123, 2019.