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=rGM
Where:
v is the orbital velocity
G is the gravitational constant
M is the mass of the central body
r 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=21mv2−rGMm
Where:
E is the total energy
K is the kinetic energy
U is the potential energy
m 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=ma
Rearrange to solve for acceleration:
a=mF
Substitute values:
a=1000 kg1.0×10−5 N=1.0×10−8 m/s2
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