Satellite Orbits

Satellites occupy different orbital regimes from LEO to GEO for various purposes.

Kepler's Laws of Orbital Motion

All satellite orbits obey Kepler's three laws, derived from Newtonian gravity:

• First Law (Law of Ellipses):A satellite's orbit is an ellipse with the Earth (or central body) at one focus. The orbit is defined by semi-major axis a, eccentricity e (0 = circle, 1 = parabola), and inclination i.
• Second Law (Equal Areas): A satellite sweeps out equal areas in equal time. At perigee (closest approach), the satellite moves fastest; at apogee, it moves slowest.dA/dt = h/2 = constant, where h is the specific angular momentum.
• Third Law (Harmonic Law): The square of the orbital period is proportional to the cube of the semi-major axis: T² = (4π²/μ) · a³, where μis Earth's gravitational parameter (3.986 × 10¹⁴ m³/s²). For a circular orbit at altitude h above Earth (R_E = 6,371 km): T = 2π√((R_E + h)³/μ).

Orbital Regimes

Satellites orbit at different altitudes depending on their purpose. Each orbit has distinct characteristics for latency, coverage, and launch requirements.

Low Earth Orbit (LEO) - 200 to 2,000 km

LEO offers the lowest latency (round-trip delay of 20-40 ms) but covers only a small area, requiring constellations for global service. Orbital velocity is approximately 7.8 km/s, and a typical LEO satellite completes one orbit in roughly 90 minutes.

• Velocity: ~7.8 km/s (28,000 km/h)
• Period: ~90-120 minutes
• Atmospheric drag: Significant - LEO satellites experience drag that gradually lowers their orbit, requiring station-keeping or resulting in orbital decay within years to decades
• Examples: ISS (408 km), Starlink (550 km), OneWeb (1,200 km), Iridium (780 km)
• Launch cost: Lower than GEO due to less Δv required

Medium Earth Orbit (MEO) - 2,000 to 35,786 km

MEO is home to navigation constellations like GPS, GLONASS, Galileo, and BeiDou. At this altitude, satellites have lower latency than GEO while requiring fewer satellites than LEO for global coverage. GPS satellites orbit at exactly 20,200 kmwith a period of 11 hours 58 minutes (half a sidereal day), ensuring the same constellation geometry repeats twice daily.

• GPS altitude: 20,200 km
• GPS velocity: ~3.87 km/s
• GPS period: 11h 58m 2s
• GLONASS altitude: 19,100 km
• Galileo altitude: 23,222 km

Geostationary Orbit (GEO) - 35,786 km

Satellites in GEO orbit at the exact same angular velocity as Earth's rotation, appearing stationary in the sky. A single satellite can cover approximately one-third of Earth's surface (excluding polar regions). GEO is ideal for communications, weather, and broadcasting satellites.

• Altitude: 35,786 km (22,236 miles) above Earth's equator
• Orbital velocity: 3.07 km/s (11,060 km/h)
• Period: 23 hours, 56 minutes, 4 seconds (one sidereal day)
• Round-trip latency: ~600 ms (240 ms up + 240 ms down + processing)
• Footprint: ~1/3 of Earth's surface
• Limitation: Cannot serve polar regions effectively; signal delay is noticeable for voice and interactive applications

Hohmann Transfer Orbit

The most fuel-efficient way to move between two circular orbits is the Hohmann transfer: an elliptical orbit that touches both the initial and final orbits. The spacecraft performs two engine burns - one to enter the transfer ellipse, and one to circularize at the destination.

• LEO to GEO Δv: approximately 3.9 km/s total (2.45 km/s first burn + 1.45 km/s second burn)
• Transfer time: ~5.26 hours for LEO to GEO
• Δv formula: Δv = √(μ/r₁) · (√(2r₂/(r₁+r₂)) - 1) for first burn, where r₁ and r₂ are the radii of the initial and target orbits
• Bi-elliptic transfer: Can be more efficient than Hohmann when the ratio of final to initial radius exceeds ~11.94, requiring three burns but less total Δv

Station-Keeping

GEO satellites must maintain their position precisely to avoid drifting into neighboring orbital slots. They require two types of station-keeping:

• North-South (N-S): ~50 m/s per year - counteracts gravitational perturbations from the Sun and Moon that pull the satellite out of the equatorial plane. This is the dominant fuel consumer.
• East-West (E-W): 2-5 m/s per year - maintains longitude against longitudinal drift caused by Earth's non-spherical gravity field (triaxiality)

Typical GEO satellites carry 1,500-2,000 kg of propellant for a 15-year mission. The N-S station-keeping Δv budget is the primary factor limiting GEO satellite operational lifetime. Ion propulsion systems can dramatically reduce propellant mass for station-keeping.

Disposal Orbit

At end of life, GEO satellites must be moved to a graveyard orbit to free the valuable GEO orbital slot. International guidelines (IADC) recommend raising the orbit by235 to 300 kmabove GEO, depending on the satellite's mass and the time of year. This ensures the derelict satellite will not interfere with active GEO satellites for at least 100 years. The disposal maneuver requires approximately 11 m/s of Δv.

Other Orbital Regimes

• Highly Elliptical Orbit (HEO): Molniya orbit (63.4° inclination, 12-hour period) provides persistent high-latitude coverage for Russia
• Sun-Synchronous Orbit (SSO): ~700-800 km, passes over the same spot at the same local solar time - ideal for Earth observation
• Lagrange Point Orbits: L1-L5 points provide stable locations for solar observatories (SOHO at L1) and space telescopes (JWST at L2)

LEO Constellation Economics

OneWeb needs 648 satellites, Starlink plans 42,000+ for global coverage. At $500,000 per satellite and $50 million per launch, building a LEO constellation requires billions in capital. Yet companies keep trying because the addressable market - global broadband - represents trillions in potential revenue.