Satellite Orbits

Learning Objectives

By the end of this study guide, the student should be able to:

1. Explain the fundamental principles governing satellite orbital motion, including Kepler's laws and Newton's law of gravitation.
2. Classify satellite orbits by altitude and eccentricity into Low Earth Orbit (LEO), Medium Earth Orbit (MEO), Geostationary Earth Orbit (GEO), and Highly Elliptical Orbit (HEO).
3. Compute orbital period, orbital velocity, and coverage characteristics for each orbit class using Kepler's third law.
4. Describe the advantages, disadvantages, and representative applications of LEO, MEO, GEO, and HEO satellite systems.
5. Compare the four orbit classes with respect to altitude, period, latency, coverage, launch energy, and typical missions.
6. Select an appropriate orbit class for a given satellite mission and justify the selection.

Introduction

A satellite orbit is the trajectory followed by a satellite as it revolves around the Earth under the influence of gravity. The choice of orbit is one of the most fundamental decisions in satellite system design, because it determines almost everything about the mission: coverage area, revisit time, link budget, launch cost, orbital lifetime, radiation environment, and latency for communication systems.

Orbits are commonly classified along two dimensions:

• By altitude (circular or near-circular orbits): LEO (Low Earth Orbit), MEO (Medium Earth Orbit), and GEO (Geostationary Earth Orbit).
• By eccentricity (elliptical orbits): HEO (Highly Elliptical Orbit) — a class in which the altitude varies dramatically between perigee (closest point) and apogee (farthest point).

Orbital Mechanics Fundamentals

1. Newton's Law of Universal Gravitation

2. Kepler's Laws of Planetary Motion (applied to satellites)

• First Law: Every satellite orbit is an ellipse with the centre of the Earth at one focus. A circle is the special case of zero eccentricity.
• Second Law: The line joining the satellite and the Earth's centre sweeps out equal areas in equal times (hence a satellite moves faster at perigee than at apogee).
• Third Law: The square of the orbital period is proportional to the cube of the semi-major axis.

3. Circular Orbital Velocity (Vis-Viva for e = 0)

4. Orbital Elements

Six classical orbital elements fully define an orbit: semi-major axis (a), eccentricity (e), inclination (i), right ascension of the ascending node (Ω), argument of perigee (ω), and true anomaly (ν). For this guide, altitude h = a − R_e and eccentricity e are the most relevant.

LEO: Low Earth Orbit

1. Definition and Key Parameters

LEO is the region of space from about 160 km up to 2,000 km above the Earth's surface. LEO is by far the most densely populated orbital regime, hosting the ISS, imaging satellites, and the new mega-constellations.

2. Characteristics

• Very short propagation delay and low path loss — attractive for communications and low-power terminals.
• A single satellite sees only a small ground swath; global coverage requires a constellation (e.g., Iridium uses 66 satellites in 6 planes).
• At low altitudes (below ~400 km) residual atmospheric drag causes orbital decay; station-keeping propellant is needed.
• High spatial resolution for Earth observation and remote sensing (higher than MEO/GEO).
• Sits below the inner Van Allen radiation belt, so radiation doses are comparatively low, permitting cheaper electronics and shorter design life.
• Low launch energy required: reaching LEO needs a delta-V of ~9.3–10 km/s from the surface.

3. Representative Systems

MEO: Medium Earth Orbit

1. Definition and Key Parameters

MEO occupies the altitude band between LEO and GEO, conventionally from about 2,000 km up to 35,786 km (below geostationary altitude). Its defining use today is satellite navigation.

2. Characteristics

• Navigation sweet spot: GPS uses six orbital planes at 20,200 km altitude with a period of 11 h 58 min (≈ half a sidereal day), so satellite geometry repeats daily; 24 satellites give continuous global coverage.
• Compromise between LEO and GEO: fewer satellites than LEO for global coverage, lower latency than GEO.
• Crosses the Van Allen radiation belts — satellites need radiation-hardened electronics.
• Coverage footprint is large (each GPS satellite sees ~42% of Earth's surface).
• Orbital perturbations (Earth's oblateness J2) must be actively corrected to maintain precise ground tracks.

3. Representative Systems

GEO: Geostationary Earth Orbit

1. Definition and Key Parameters

A satellite in GEO orbits at an altitude of exactly 35,786 km above the equator, in the equatorial plane (inclination = 0°), travelling west-to-east, with a period equal to the sidereal day (23 h 56 min 4 s). It therefore appears stationary over one point on the equator.

2. Characteristics

• Geostationary property: Fixed antennas on the ground can point at the satellite without tracking — ideal for broadcasting and fixed services.
• Coverage geometry: From GEO, a satellite covers about 42.5% of Earth's surface; in principle only 3 satellites spaced 120° apart provide near-global coverage (excluding polar regions above ~81° latitude).
• Link budget penalty: The 35,786 km slant range causes ~186 dB free-space path loss at 6 GHz (uplink) — large antennas and high power are needed.
• Latency: One-hop round trip is ~250–280 ms, noticeable in interactive voice/data and prohibitive for some real-time applications.
• Eclipse and station-keeping: Near equinoxes the satellite passes through Earth's shadow (eclipse seasons); orbit and inclination drift require periodic north-south/east-west station-keeping, consuming propellant and limiting life (~15 years).
• Launch to GEO requires ~2.5 km/s extra velocity (geostationary transfer orbit + apogee burn).

3. Representative Systems

HEO: Highly Elliptical Orbit

1. Definition and Key Parameters

HEO refers to orbits with large eccentricity (typically e > 0.5), so that the satellite's altitude varies greatly between perigee (low) and apogee (high, often above GEO). Although the satellite spends most time near apogee (by Kepler's second law), when high it can dwell over a specific hemisphere for hours.

2. The Molniya Orbit

The classic HEO is the Molniya orbit, developed by the USSR: inclination 63.4° (the "critical inclination" at which Earth's oblateness does not rotate the line of apsides), period 11 h 58 min, perigee ~1,000 km over the southern hemisphere, apogee ~39,700 km over the northern hemisphere. The satellite spends ~8 of every 12 hours near apogee over the northern hemisphere. Three satellites give continuous coverage of high northern latitudes (Russia, Scandinavia, Canada) where GEO links are poor or impossible.

• Why 63.4°: at this inclination the J2 apsidal precession rate is zero, keeping apogee permanently over the same hemisphere with minimal station-keeping.
• Tundra orbit (used by Sirius XM radio, some proposed comsats): 24 h period, e ≈ 0.27, i ≈ 63.4°, apogee over North America — 2 satellites provide continuous coverage.

3. Representative Systems

Comparison of Orbit Classes

Orbit Selection Decision Guide

• Low-latency broadband or high-resolution imaging? → LEO constellation.
• Precise global positioning/timing with modest constellation size? → MEO.
• Continuous fixed coverage of a region with simple ground terminals? → GEO.
• Service to polar/high-latitude regions? → HEO (or LEO polar constellation).

Summary of Key Points

1. Orbit selection is mission-driven; the four principal classes are LEO, MEO, GEO, and HEO.
2. LEO (160–2,000 km): cheap to reach, low latency and loss, high resolution — but needs constellations and suffers drag/debris.
3. MEO (2,000–35,786 km): the navigation regime — ~24 satellites (GPS at 20,200 km, T = 11 h 58 min) give continuous global coverage with moderate latency.
4. GEO (35,786 km, i = 0°, T = sidereal day): appears stationary; 3 satellites cover the globe except poles; high path loss and ~250 ms latency.
5. HEO (e > 0.5; Molniya: i = 63.4°, T = 11 h 58 min): long apogee dwell over high latitudes, serving regions GEO cannot reach; only 3 satellites needed for continuous coverage.
6. Kepler's third law (T = 2π√(a³/μ)) and the circular velocity (v = √(μ/r)) are the working tools for all orbit-class calculations.
7. Trade-offs: altitude ↑ → coverage ↑, ground-terminal simplicity ↑, but latency, path loss, launch energy ↑ and imaging resolution ↓.

Review Questions

References and Further Reading

• Richharia, M. (2014). Satellite Communication Systems. McGraw-Hill.
• Pratt, T., Bostian, C., & Allnutt, J. (2003). Satellite Communications (2nd ed.). Wiley.
• Maral, G., & Bousquet, M. (2009). Satellite Communications Systems: Systems, Techniques and Technology (5th ed.). Wiley.
• Curtis, H. D. (2020). Orbital Mechanics for Engineering Students (4th ed.). Butterworth-Heinemann.
• Wertz, J. R., & Larson, W. J. (1999). Space Mission Analysis and Design (3rd ed.). Microcosm Press.
• EEEN 567 Course Lecture Notes, Department of Electrical and Electronic Engineering, Egerton University.