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Orbital Mechanics Basics: GEO, LEO and MEO For students.

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Orbital mechanics is the physics of how satellites stay in space: they perpetually fall toward Earth while moving sideways so fast they keep missing it. Three orbit families organize the industry — LEO (low), MEO (medium) and GEO (geostationary) — each trading altitude against coverage, latency and launch cost.

Every space application — GPS, satellite TV, weather forecasts, Starlink — is an orbit choice with consequences. Altitude sets the period through Kepler's laws, deciding whether a satellite hangs fixed over one spot or circles the planet sixteen times a day.

Key Concepts

  • Kepler's laws: (1) orbits are ellipses with Earth at one focus; (2) equal areas in equal times (faster near perigee); (3) T² ∝ a³.
  • Orbital velocity: v = √(μ/r), μ = 398,600 km³/s² (Earth's gravitational parameter), r from Earth's centre.
  • Period: T = 2π√(r³/μ) — Kepler's third law, quantified.
  • LEO (160–2,000 km): ~90–127 min periods; low latency, small footprints — constellations need hundreds (ISS ~420 km, Starlink ~550 km).
  • MEO (8,000–20,000 km): the navigation belt — GPS at 20,200 km, ~12-hour period, two revolutions daily.
  • GEO (35,786 km altitude): period = one sidereal day (23 h 56 m 4 s), equatorial — the satellite appears frozen in the sky.

Formulas

With μ = 398,600 km³/s² and r in km: v = √(μ/r) km/s, T = 2π√(r³/μ) seconds, r = 6,378 + altitude. Anchors: surface orbit v ≈ 7.9 km/s (first cosmic velocity); the Moon's T ≈ 27.3 days. Higher orbits are slower (v ∝ 1/√r) — the classic surprise. Escape velocity at any r is √2 × circular velocity there.

Worked Example

Derive the GEO slot from its required period. Step 1: invert the period formula → r = (μ(T/2π)²)^(1/3). Step 2: T = 86,164 s (sidereal day). T/2π = 13,713 s; squared = 1.8806×10⁸; × μ = 7.496×10¹³. Step 3: cube root → r ≈ 42,164 km from Earth's centre. Step 4: altitude = 42,164 − 6,378 = 35,786 km. Step 5: v = √(398,600/42,164) ≈ 3.07 km/s — far slower than LEO's ~7.8 km/s. Parked here with zero inclination and eccentricity, a satellite never moves in the sky — why dish antennas need no tracking.

Common Misconceptions

  • "There's no gravity in space." At ISS altitude gravity is ~90% of surface value. Satellites stay up through sideways velocity — continuous free fall curving around the planet.
  • "Higher orbits are faster." v = √(μ/r) decreases with altitude: GEO crawls at 3.07 km/s, LEO races at ~7.8 km/s.
  • "One GEO satellite sees all Earth." It covers ~one-third of the globe and nothing above ~81° latitude — poles need LEO or Molniya orbits.

Real-World Applications

  • GPS/GNSS (MEO): ~24 satellites at 20,200 km give global positioning.
  • Broadcast/weather (GEO): INSAT, GOES and TV satellites stare at fixed regions.
  • Earth observation (LEO): sun-synchronous orbits image the planet in consistent light.
  • Broadband (LEO): Starlink/OneWeb trade hundreds of satellites for ~25 ms latency.

Orbital mechanics is one insight — forward speed balances gravity's pull — quantified by v = √(μ/r) and T = 2π√(r³/μ). LEO is fast and close, MEO hosts navigation, and GEO's 35,786 km perch turns a speeding satellite into a fixed point in the sky.

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