Astronomy & Celestial Mechanics
the sky, computed
Concept

Walker constellation — where it appears

A satellite constellation with equal numbers of satellites in equally spaced circular orbital planes at a common inclination, phased by a single parameter. It is the standard family for navigation and communication constellations.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

A 5/5/1 constellation at one instant: where no satellite is above 0°. The points beneath the 5 satellites of a 5/5/1 Walker delta pattern at 43.5°, at 11,605 km, at one instant, with each satellite's 0° footprint — a circle 69.2° in radius at the Earth's centre — drawn round it, on an equirectangular map that swells the circles towards the poles. The shaded cells are ground with no satellite above the mask: none at this instant. Everywhere else is seen by between 1 and 3 at once. The largest empty circle at this instant is 67.6° in radius, computed exactly from the satellites' directions, inside the footprint, which is why there are none.

Five satellites and not four

No single orbit keeps a satellite above every point on the Earth. How many are needed is a question about the largest empty circle among their directions at the worst instant, and it has sharp answers. Four can never do it, five can from 11,605 kilometres up, and past that the arrangement of the orbits matters as much as their number.

spaceflight · Ground tracks Four satellites, and which four. Two sets of four navigation satellites seen on the sky from below, zenith at the centre and the horizon at the rim, with circles at 30° and 60° elevation. Left: one overhead and three low and spread around the horizon. Right: four bunched in one part of the sky. Each set fixes a position, and the error it leaves is the range error multiplied by the dilution of precision — 2.0 for the spread set, 62.0 for the bunched one. The same four range measurements, made with the same precision, give positions 31 times more uncertain when the satellites are bunched.

Four satellites in view, and which four

A satellite navigation receiver needs four satellites to fix its position, and a constellation is designed to keep at least four above every place. Four is the count, not the answer. The same four ranges, measured equally well, give a position thirty times worse when the satellites are bunched in one part of the sky than when they are spread around it, and the constellations carry their extra satellites to pay for the moments when the geometry, not the count, fails.

spaceflight · Ground tracks

Named alongside it

The objects these essays reach for when they reach for this one.

Elevation maskClock biasContinuous coverageCoverageCovering radiusDilution of precisionFootprintGeometry matrixGround trackGround tracksInclinationLeast-squares

All concepts