Low Earth and Geostationary Orbits

Expert reviewed 22 November 2024 9 minute read


Introduction to Satellites

Satellites play a crucial role in our modern world, providing essential services such as communication, weather forecasting, and Earth observation. Two primary types of orbits used for satellites are Low Earth Orbits (LEO) and Geostationary Orbits (GEO).

Orbital Motion Fundamentals

Before delving into specific orbit types, it’s important to understand the basic principles governing orbital motion.

What are the Factors Affecting Orbital Motion?

  • Velocity of the orbiting object
  • Mass of the central body (e.g., Earth)
  • Radius of the orbit

The relationship between these factors is described by Newton’s law of universal gravitation and the equations of circular motion.

Orbital Velocity

The velocity required for an object to maintain a stable orbit depends on the orbit’s radius and the mass of the central body. This relationship is given by the equation:

v=GMrv = \sqrt{\frac{GM}{r}}

Where:

  • vv is the orbital velocity
  • GG is the gravitational constant
  • MM is the mass of the central body
  • rr is the radius of the orbit

From this equation, we can deduce that:

  • Smaller orbits require greater orbital velocities
  • Orbits around more massive bodies require greater velocities

Orbital Energy

The total energy of an orbiting body is the sum of its kinetic and potential energy:

E=K+U=12mv2GMmrE = K + U \\= \frac{1}{2}mv^2 - \frac{GMm}{r}

Where:

  • EE is the total energy
  • KK is the kinetic energy
  • UU is the potential energy
  • mm is the mass of the orbiting body

Low Earth Orbits (LEO)

What are the Characteristics of a LEO?

  • Altitude: Typically between 160 km to 2,000 km above Earth’s surface
  • Velocity: Approximately 7.8 km/s
  • Orbital Period: About 90 minutes
  • Energy: Lower total energy compared to higher orbits

Advantages of LEO

  • Closer proximity to Earth’s surface
  • Higher resolution for Earth observation and imaging
  • Lower latency for communications
  • Lower energy requirements for satellite placement

Challenges in LEO: Orbital Decay

LEO satellites face significant orbital decay due to several factors:

  • Atmospheric Drag: Even at high altitudes, trace amounts of atmosphere create friction, slowing the satellite and reducing its altitude.
  • Gravitational Perturbations: Irregularities in Earth’s gravitational field can affect the satellite’s orbit.
  • Solar Radiation Pressure: Photons from the Sun exert a small but constant force on the satellite.

Practice Question 1

A LEO satellite initially at an altitude of 300 km experiences a drag force of $1.0 × 10^{-5}N$. If the satellite’s mass is 1000 kg, calculate its deceleration due to drag.

Use Newton’s Second Law:

F=maF = ma

Rearrange to solve for acceleration:

a=Fma = \frac{F}{m}

Substitute values:

a=1.0×105 N1000 kg=1.0×108 m/s2a = \frac{1.0 \times 10^{-5} \text{ N}}{1000 \text{ kg}} \\= 1.0 \times 10^{-8} \text{ m/s}^2

This small deceleration accumulates over time, leading to orbital decay.

What are the Applications of LEO Satellites?

  • Earth observation and remote sensing
  • Weather monitoring
  • Communications (e.g., Starlink)
  • Scientific research
  • Military and reconnaissance

Geostationary Orbits (GEO)

What are the Characteristics of a GEO?

  • Altitude: Approximately 35,786 km above Earth’s equator
  • Velocity: About 3.07 km/s
  • Orbital Period: 24 hours (synchronous with Earth’s rotation)
  • Energy: Higher total energy compared to LEO

Advantages of GEO

  • Appears stationary relative to Earth’s surface
  • Continuous coverage of a large area
  • Fewer satellites needed for global coverage
  • Minimal station-keeping required

Challenges in GEO

  • Higher latency due to greater distance from Earth
  • More energy required for satellite placement
  • Limited visibility of polar regions
  • Potential for signal interference and space debris

Applications of GEO Satellites

  • Television and radio broadcasting
  • Long-distance communications
  • Weather monitoring
  • Some navigation systems

Comparison of LEO and GEO

CharacteristicLow Earth Orbit (LEO)Geostationary Orbit (GEO)
Altitude160 - 2,000 km35,786 km
Orbital Period~90 minutes24 hours
Velocity~7.8 km/s~3.07 km/s
Coverage AreaSmaller, movingLarge, fixed
LatencyLowHigher
Number of Satellites for Global CoverageManyFew
Launch CostsLowerHigher
LifespanShorter due to orbital decayLonger

Return to Module 5: Advanced Mechanics