Orbital Mechanics: The Science Behind Satellite Movement and Control

Orbital mechanics, also known as astrodynamics, is the field of study that explains how objects move in space under the influence of gravitational forces. It forms the foundation for understanding how satellites are launched, maneuvered, and maintained in orbit. Mastering orbital mechanics is essential for successful satellite missions, as it allows precise control of satellite trajectories to ensure they remain in their designated orbits, whether for communication, weather monitoring, or scientific research.

This article explores the principles governing satellite motion, the forces involved, and how these concepts are applied to manage satellites in orbit.

What Is Orbital Mechanics?

Orbital mechanics refers to the science that deals with the motion of objects in space, primarily under the influence of gravity. In the context of satellites, it addresses how these man-made objects move around the Earth or other celestial bodies, guided by specific laws of physics such as Newton’s Law of Universal Gravitation and his Three Laws of Motion.

Newton's insights into how objects interact with gravitational forces are the foundation of orbital mechanics. Specifically, the force of attraction between two masses, like a satellite and the Earth, determines the satellite's trajectory and speed in orbit.

The Basics of Satellite Orbits

When a satellite is launched into space, it is propelled into a particular orbit depending on its speed and altitude. The key factors that define a satellite's orbit are:

• Altitude: The height of the satellite above Earth's surface, which determines the type of orbit it occupies (e.g., Low Earth Orbit, Geostationary Orbit).

• Velocity: The speed at which the satellite travels, which must balance gravitational pull to avoid falling back to Earth or escaping into space.

• Inclination: The angle between the satellite's orbital plane and Earth's equatorial plane, influencing the regions of the Earth the satellite will cover.

Once in orbit, satellites follow elliptical paths around the Earth, as described by Kepler's Laws of Planetary Motion, which apply to any orbiting body, including moons and planets.

Kepler’s Laws of Planetary Motion

Johannes Kepler developed three fundamental laws that describe the movement of objects in orbit:

1. The Law of Ellipses: Satellites move in elliptical orbits with the Earth (or other celestial bodies) at one focus. This elliptical nature means the satellite's distance from the Earth changes as it moves along its orbit.

2. The Law of Equal Areas: A line segment joining a satellite and Earth sweeps out equal areas in equal intervals of time. In other words, the satellite moves faster when it is closer to the Earth (at perigee) and slower when it is farther away (at apogee).

3. The Law of Harmonies: The square of the orbital period of a satellite is proportional to the cube of the semi-major axis of its orbit. This law helps in predicting how long a satellite will take to complete one orbit based on its distance from the Earth.

These laws are critical for calculating satellite orbits, predicting their position, and adjusting their paths for long-term missions.

Types of Satellite Orbits

Satellites can be placed in various orbits, depending on their purpose and mission objectives. The most common types include:

1. Low Earth Orbit (LEO): Satellites in LEO typically orbit between 160 to 2,000 km above Earth. These satellites are used for Earth observation, communication, and research. Their proximity to Earth allows for quick data transmission and high-resolution imaging.

2. Geostationary Orbit (GEO): Satellites in GEO orbit at an altitude of about 35,786 km, where they move in sync with Earth’s rotation. As a result, they appear stationary relative to a fixed point on Earth, making them ideal for communication, weather monitoring, and broadcasting.

3. Medium Earth Orbit (MEO): Situated between LEO and GEO, MEO satellites are often used for navigation systems like GPS. They orbit at altitudes of around 20,000 km.

4. Polar and Sun-Synchronous Orbits: Polar orbits allow satellites to pass over Earth’s poles, offering complete global coverage. Sun-synchronous orbits are a type of polar orbit where the satellite passes over the same part of the Earth at roughly the same local time, which is useful for Earth observation satellites.

Forces Influencing Satellite Motion

Satellites in orbit are subject to several forces, the most significant being gravity. In addition to gravity, the following forces affect a satellite’s motion:

• Gravitational Force: This force, primarily from Earth, keeps the satellite in orbit by pulling it toward the center of the Earth. The satellite's velocity balances this pull, preventing it from falling to the Earth.

• Centrifugal Force: As a satellite moves forward in its orbit, centrifugal force works outward, counteracting the inward pull of gravity and maintaining the satellite’s stable orbit.

• Drag: Satellites in lower orbits, especially in LEO, experience atmospheric drag, which gradually slows them down and can cause them to re-enter Earth's atmosphere if not corrected.

• Solar Radiation Pressure: While minimal, the force exerted by sunlight on a satellite can affect its motion, especially over long periods. Satellites with large surface areas, such as solar panels, are more susceptible to this force.

Orbital Maneuvering and Control

Controlling a satellite’s position and velocity in orbit is crucial for maintaining its functionality. To achieve this, satellites are equipped with thrusters or propulsion systems that allow for orbital adjustments. These maneuvers are necessary for various reasons, including:

• Orbit Insertion: After a satellite is launched, it may require precise positioning in its designated orbit. This is achieved through orbital insertion burns, where thrusters adjust the satellite’s velocity.

• Station-Keeping: Satellites in geostationary orbits need frequent adjustments to remain in their precise position relative to Earth. Even small forces, such as gravitational perturbations from the Moon and Sun or solar radiation pressure, can cause drifts.

• Collision Avoidance: With the growing number of satellites and space debris, collision avoidance is becoming a critical aspect of satellite operations. Satellites are maneuvered to avoid potential collisions using onboard thrusters.

• End-of-Life Decommissioning: At the end of their operational life, satellites in lower orbits may be deorbited to burn up in the Earth’s atmosphere, while those in higher orbits are often moved to a "graveyard orbit" to avoid contributing to space debris.

Conclusion

Orbital mechanics is a fundamental science that governs how satellites move and function in space. From the moment a satellite is launched to the end of its mission, understanding these principles ensures the satellite can be controlled, maneuvered, and maintained for optimal performance. The application of Newton’s Laws, Kepler’s Laws, and other principles of motion and gravity allows satellites to serve their essential roles in communication, navigation, Earth observation, and scientific discovery.

As satellite technology continues to advance, the precise knowledge of orbital mechanics remains at the heart of successful space missions, allowing us to explore the vastness of space while making life on Earth more connected and informed.

Recommended products for building a satellite

If you're planning to build a satellite at home, here are some top products you can purchase online to get started with a small satellite project, like a CubeSat:

1. Arduino Uno R3 Microcontroller Ideal for controlling various satellite components. Easy to program and widely used in DIY projects.

2. Raspberry Pi 4 Model B Perfect for running satellite operations and data management. Powerful and compact, used for space projects like Pi-Sat.

3. Adafruit Ultimate GPS Breakout – 66 channel A compact GPS module for real-time positioning and tracking. Great for satellite navigation and telemetry.

4. Sun Power Solar Cells Reliable small solar panels to power your satellite. Lightweight and efficient for CubeSat-sized projects.

5. XBee 3 RF Module Used for wireless communication between your satellite and ground station. Designed for long-range communication and low power consumption.

6. Tiny Circuits 9-Axis IMU (Inertial Measurement Unit) Essential for satellite orientation and stabilization. Measures acceleration, rotation, and magnetic field for accurate positioning.

7. Lipo Battery Pack 3.7V 10000mAh A reliable power source to store energy generated by solar panels. Lightweight and commonly used for small satellite projects.

8. CubeSat Structure Kit 3D-printed frame kits available for DIY satellite projects. A basic structure for housing your satellite's electronics.

9. TTGO LoRa SX1276 Module A radio communication module designed for long-range communication. Great for sending telemetry data from low Earth orbit.

10. MATLAB & Simulink Student Version Essential for simulating and testing your satellite’s functions, including orbit trajectories and control systems.

These products, along with open-source satellite kits, can give you a solid foundation to design and assemble a small satellite for educational or hobbyist purposes!

Building a fully functional satellite using the listed products is an exciting and complex project. Here's a step-by-step guide to help you assemble these components into a working satellite, such as a CubeSat:

Step 1: Define Your Satellite’s Mission

Before assembly, decide what your satellite will do. Whether it’s Earth observation, communication, or scientific experiments, defining the mission will help you choose the right sensors and equipment.

Step 2: Build the CubeSat Frame

1. Assemble the CubeSat Structure Kit Begin by constructing the physical frame of your CubeSat. These kits usually come with lightweight, durable materials such as 3D-printed parts or aluminum. Ensure the structure has enough space for components like the microcontroller, battery, and sensors.

Step 3: Design the Power System

1. Install the Solar Panels (Pololu High-Power Solar Cells) Mount the solar panels on the exterior of your CubeSat. These panels will provide continuous power to your satellite in orbit. Ensure that they are positioned to maximize exposure to sunlight when in space.

2. Connect the Battery Pack (Lipo Battery Pack 3.7V 10000mAh) Wire the solar panels to the LiPo battery to store energy. The battery will ensure your satellite has power even when it's in Earth's shadow.

Step 4: Set Up the Onboard Computer

1. Install the Raspberry Pi 4 Model B This serves as the “brain” of your satellite. It will process data and control operations. Connect the Raspberry Pi to the CubeSat’s power system via the battery pack. Add a microSD card with your pre-written code and data management software for the satellite's mission.

2. Integrate the Arduino Uno R3 Microcontroller Use Arduino to handle real-time tasks, like managing sensors or communication. It’s a complementary system to the Raspberry Pi, which handles the overall mission, while Arduino handles specific control tasks.

Step 5: Attach Sensors and Modules

1. Install the GPS Module (Adafruit Ultimate GPS Breakout) Attach the GPS module to track the satellite’s position in orbit. Program the GPS to report position data to the Raspberry Pi for logging and telemetry.

2. Mount the 9-Axis IMU (Tiny Circuits IMU) This module measures acceleration, rotation, and magnetic fields to stabilize your satellite. Connect it to the Arduino for real-time orientation and attitude control.

Step 6: Communication System

1. Install the XBee 3 RF Module This module handles communication between the satellite and your ground station. Attach the antenna to the exterior of the satellite frame for optimal signal reception.

2. Integrate the TTGO LoRa SX1276 Module LoRa offers long-range communication and is ideal for sending telemetry data. Connect the module to the Raspberry Pi and program it to transmit data to Earth.

Step 7: Write and Upload the Software

1. Create Control and Data Processing Software On the Raspberry Pi, write code that controls the satellite’s mission—whether it's capturing images, logging GPS data, or transmitting data back to Earth. Use Python, MATLAB, or Simulink to create algorithms that simulate orbital functions and process sensor data.

2. Upload the Control Code to Arduino Use the Arduino IDE to upload code that manages real-time control systems, such as adjusting the satellite’s orientation using the IMU data.

Step 8: Testing and Simulation

1. Simulate the Satellite’s Orbit and Functionality Before launch, test your satellite’s functionality using MATLAB & Simulink. Simulate its orbit, test communication ranges, and monitor the power system. Place the satellite in a vacuum chamber (if available) to test how it will function in space conditions.

2. Test Communication and Power Systems Ensure that your communication modules are working by setting up a ground station and testing data transmission. Test the solar panels and battery pack to confirm they are providing adequate power.

Step 9: Launch Preparation

1. Coordinate with a Launch Provider Once your CubeSat is fully assembled and tested, work with a launch provider such as SpaceX or Rocket Lab for a ride-share launch. Ensure your satellite meets their size, weight, and regulatory standards.

2. Obtain Regulatory Approvals Depending on your location, you may need licensing from local or international space authorities (such as the FCC in the U.S.) to launch and operate your satellite.

Step 10: Launch and Operate

1. Launch the Satellite Your satellite will be deployed into orbit by the launch provider.

2. Operate the Satellite from the Ground Use your ground station to communicate with your satellite, receive telemetry data, and monitor its mission progress.

Building a satellite at home is an ambitious yet achievable goal for hobbyists, engineers, and students. With these components, proper planning, and the right mission objectives, you can contribute to space research and innovation right from your home.