Satellites and Constellations

Draft

Earlier sections covered orbits, propulsion and the spacecraft itself. This section is about satellites as systems that deliver a service: how the orbit choice determines the business, how many satellites a coverage requirement implies, what the payloads can physically measure, and what happens on the ground and in the debris environment around them.

How the pages connect

Orbit regime selection comes first because everything else follows from it. The four application pages are independent of each other. Debris and ground segment apply to all of them.

The quantities this section turns on

Earth-central coverage angle

\lambda = 90° - \varepsilon - \eta, \qquad \sin\eta = \frac{R_\oplus}{r}\cos\varepsilon

How much of Earth one satellite sees. At a 25° elevation mask, a satellite at 550 km covers 0.54% of the globe, which sets a floor of 184 satellites for instantaneous global coverage. Real constellations need two to four times that.

Satellite capacity with frequency reuse

C = \frac{N_{\text{beams}}}{N_{\text{colours}}} \times B \times \eta_{\text{spectral}}

Why high-throughput satellites exist. A hundred spot beams in a four-colour reuse scheme deliver twenty-five times the capacity of a single wide beam from exactly the same spectrum allocation.

Rayleigh criterion

\text{GSD} = 1.22\,\frac{\lambda h}{D}

The hard bound on optical resolution. Sub-metre imaging requires a metre-class aperture at any budget, which is why high-resolution imaging satellites are large and why CubeSats cannot do it.

Pseudorange

\rho_i = \sqrt{(x_i-x)^2 + (y_i-y)^2 + (z_i-z)^2} + c\,\delta t + \epsilon_i

Four unknowns, four satellites. The receiver clock error is solved for rather than eliminated, which is why a GNSS receiver needs no accurate clock and why it is simultaneously a precision timing device.

Five things worth knowing

The orbit regime determines the business, not just the physics. GEO is a capital project with a fifteen-year payback and one satellite. LEO is a manufacturing operation: a 1584-satellite constellation with a five-year life must launch about six satellites a week forever just to stand still.

The CubeSat’s innovation was the interface, not the miniaturisation. Standardising the dispenser interface let launch providers certify once and accept any conforming payload, turning a multi-year bespoke negotiation into a catalogue purchase.

Capacity comes from reuse, not from spectrum. The move from wide-beam to spot-beam GEO raised satellite capacity by two orders of magnitude without any additional bandwidth allocation.

Better tracking data can raise the computed collision probability. Probability of collision peaks at intermediate uncertainty, so an operator whose risk number rises after a tracking update has become better informed, not more endangered.

Earth observation is bottlenecked on downlink, not on sensors. A high-resolution optical satellite generates about 10 Gbit/s while imaging and can downlink roughly 30 GB per pass. The gap is more than an order of magnitude, and it is why onboard processing is attractive.

Pages

01LEO, MEO and GEO

The three regimes compared across coverage geometry, latency, link budget, radiation and disposal, with the worked numbers behind each trade and how the choice determines the shape of the business.

02CubeSats and small satellites

What the standard actually specifies and why the interface was the innovation, size classes, what commercial parts buy, the early-failure problem and its causes, and the aperture and power limits that no budget removes.

03Constellation design

Walker Delta and Star patterns explained in full, streets of coverage, the plane count trade, deployment by J2 drift, and the replenishment arithmetic that makes a constellation a factory.

04Earth observation

The diffraction limit, the resolution-swath-revisit trilemma with worked data rates, how synthetic aperture radar defeats the aperture limit, spectral sensing, processing levels and the downlink bottleneck.

05GNSS and positioning

Pseudoranges and the four-unknown solution, why the constellations sit in MEO, the full error budget with worked ionospheric delay, dilution of precision, RTK and PPP, and the jamming and spoofing problem.

06Communications satellites

Frequency reuse as the source of capacity, GEO payload architecture, the LEO constellation and its gateway problem, direct-to-device link budgets, and the ITU filing process that gates everything.

07Space debris and traffic management

The population and where it came from, hypervelocity impact physics, the Kessler cascade as a threshold rather than a gradient, conjunction assessment, mitigation rules and why active removal remains unsolved.

08Ground segment

Antenna sizing and G/T, why polar stations are worth more than larger dishes, scheduling as a combinatorial problem, ground station as a service, operations, and the processing pipeline.