2) Orbital Mechanics & Orbit Types

I. Kepler's Laws
• First law — orbits are ellipses with Earth at one focus.
• Second law — equal areas in equal times.
• Third law — T² ∝ a³.

II. The Six Keplerian Elements
• a — semi-major axis.
• e — eccentricity.
• i — inclination.
• Ω — RAAN.
• ω — argument of perigee.
• ν — true anomaly.

III. Orbit Regimes
• LEO 160–2000 km — 90 min period.
• MEO 2000–20000 km — 6–12 h period.
• GEO 35786 km — 24 h period.
• HEO — elliptical, slow near apogee.

IV. Special Orbits
• Geostationary — equatorial, circular, 24 h.
• Sun-synchronous — near-polar, constant solar illumination.
• Molniya — 12 h HEO, high-latitude coverage.
• Polar — 90° inclination.

V. Orbital Perturbations
• Earth's oblateness (J2) — nodal regression.
• Solar and lunar gravity.
• Atmospheric drag — significant in LEO.
• Solar radiation pressure.

VI. Coverage Geometry
• Elevation angle — must be above ~5–10°.
• Slant range — varies with elevation.
• Footprint — the area visible to the satellite.
• Eclipse period — satellite in Earth's shadow.