A climate-monitoring satellite in low Earth orbit (LEO) circles the planet under gravity — Kepler's third law fixes how fast. Its onboard radiometer scans a swath directly below (nadir), and because the orbit is inclined near-polar while Earth spins underneath, each pass covers a strip slightly west of the last one, painting the whole globe within about a day. This is exactly how NASA's Terra/Aqua (MODIS) and NOAA/NASA's Suomi-NPP (VIIRS) missions build their daily global climate and cloud maps.
T = 2π·√(a³/μ) orbital period, a = R⊕ + h
v = √(μ/a) circular orbital speed
W ≈ 2h·tan(θ_FOV) nadir swath width (flat-Earth approx.)
μ = 398,600.4 km³/s², R⊕ = 6,371 km
- Altitude h — higher orbits move slower (Kepler) but their sensor sees a wider patch of Earth per swath, trading resolution for period.
- Inclination i — near 98° (retrograde, just past polar) makes the orbit sun-synchronous: the orbital plane precesses at exactly the same rate Earth orbits the Sun, so the satellite crosses every latitude at the same local solar time every day — essential for comparing climate imagery day to day. Drag it toward 0° to see a low-inclination orbit fail to ever reach the poles.
- Sensor half-FOV — the scan half-angle of the radiometer off nadir; a wider FOV images a broader swath per orbit but with more distortion at the swath edges (omitted here for clarity).
- Earth coverage — the area-weighted (cos·latitude) fraction of a 5°×5° global grid that has fallen inside the swath at least once since the last reset; watch how a low inclination leaves the poles permanently uncovered.
Real-world relevance: this swath-sweep geometry is literally how satellite climate monitoring works — sea-surface temperature, cloud cover, vegetation greenness (NDVI), ice extent and aerosol/CO₂ column data are all built up from nadir-scanning sun-synchronous passes like this one.