👩🏼‍🚀Intro to Aerospace Engineering Unit 8 – Spacecraft and Orbital Mechanics Basics

Key Concepts and Terminology

• Orbital mechanics involves the study of the motion of artificial satellites and space vehicles in orbit around Earth and other celestial bodies
• Kepler's laws of planetary motion describe the motion of planets around the sun and can be applied to satellites orbiting Earth
  • First law states that planets move in elliptical orbits with the sun at one focus
  • Second law states that a line segment joining a planet and the sun sweeps out equal areas during equal intervals of time
  • Third law relates the orbital period and semi-major axis of an orbit
• Newton's laws of motion and universal gravitation form the foundation of orbital mechanics
• Apogee represents the point in an orbit farthest from Earth, while perigee is the point closest to Earth
• Inclination measures the angle between the orbital plane and the equatorial plane of the central body (Earth)
• Eccentricity describes the shape of an orbit, with 0 being circular and values between 0 and 1 indicating elliptical orbits
• Orbital elements, such as semi-major axis, eccentricity, inclination, argument of perigee, and true anomaly, fully define an orbit

Orbital Mechanics Fundamentals

• Orbital velocity is the speed required for a spacecraft to maintain a stable orbit around a celestial body
  • Depends on the altitude of the orbit and the mass of the central body
  • For a circular orbit around Earth, orbital velocity decreases with increasing altitude
• Escape velocity is the minimum speed needed for an object to break free from a celestial body's gravitational influence
  • For Earth, escape velocity is approximately 11.2 km/s
• Orbital period is the time taken for a spacecraft to complete one full orbit around a celestial body
  • Determined by the semi-major axis of the orbit and the mass of the central body
  • Increases with increasing orbital altitude
• Orbital energy is the sum of a spacecraft's kinetic and potential energy in an orbit
  • Determines the shape and size of the orbit
  • Negative orbital energy results in closed, elliptical orbits, while positive energy leads to open, hyperbolic trajectories
• Orbital perturbations are forces that cause deviations from ideal Keplerian orbits
  • Include effects of Earth's non-spherical shape, atmospheric drag, solar radiation pressure, and gravitational influences of other celestial bodies
• Hohmann transfer orbits are elliptical orbits used to transfer a spacecraft between two circular orbits of different altitudes with minimal energy expenditure

Types of Orbits and Their Applications

• Low Earth Orbit (LEO) is an orbit below an altitude of 2,000 km
  • Characterized by short orbital periods (approximately 90-120 minutes) and low communication latency
  • Used for Earth observation, weather satellites, and human spaceflight (International Space Station)
• Medium Earth Orbit (MEO) lies between LEO and Geostationary Earth Orbit (GEO), typically at altitudes of 2,000-35,786 km
  • Commonly used for navigation satellite constellations (Global Positioning System)
• Geostationary Earth Orbit (GEO) is a circular orbit at an altitude of 35,786 km above Earth's equator
  • Spacecraft in GEO have an orbital period equal to Earth's rotational period, appearing stationary from the ground
  • Used for communication satellites and weather monitoring
• Polar orbits have an inclination of approximately 90 degrees, passing over Earth's poles
  • Sun-synchronous orbits are a special case of polar orbits that maintain a constant orientation relative to the sun
  • Used for Earth observation, spy satellites, and mapping applications
• Molniya orbits are highly elliptical orbits with an inclination of approximately 63.4 degrees and a period of half a sidereal day
  • Provide extended coverage over high-latitude regions (Russia) due to the orbit's apogee being positioned above these areas
• Lagrange points are positions in space where the gravitational forces of two large bodies (Earth and the sun) and the centrifugal force balance
  • L1, L2, and L3 are unstable equilibrium points, while L4 and L5 are stable
  • Used for space observatories (James Webb Space Telescope at L2) and potential future space colonies

Spacecraft Components and Systems

• Attitude Determination and Control System (ADCS) maintains a spacecraft's orientation in space
  • Uses sensors (star trackers, sun sensors, gyroscopes) to determine the spacecraft's attitude
  • Employs actuators (reaction wheels, thrusters, magnetorquers) to control and adjust the attitude
• Electrical Power System (EPS) generates, stores, and distributes electrical power to spacecraft subsystems
  • Solar panels convert sunlight into electricity, which is then regulated and distributed
  • Batteries store excess energy for use during eclipses or periods of high demand
• Thermal Control System (TCS) maintains the spacecraft's temperature within acceptable limits
  • Uses passive methods (insulation, coatings, heat pipes) and active methods (heaters, coolers) to regulate temperature
• Propulsion system provides thrust for orbital maneuvers, station-keeping, and attitude control
  • Chemical propulsion systems use the combustion of propellants (liquid or solid) to generate thrust
  • Electric propulsion systems, such as ion thrusters, use electric power to accelerate propellant, providing high specific impulse but low thrust
• Communication system enables the transmission and reception of data between the spacecraft and ground stations
  • Consists of antennas, transmitters, receivers, and associated electronics
  • Utilizes various frequency bands (S-band, X-band, Ka-band) depending on the mission requirements
• Command and Data Handling (C&DH) system manages the spacecraft's onboard computer, data storage, and processing
  • Receives, interprets, and executes commands from the ground
  • Collects, processes, and stores data from various subsystems and payloads

Rocket Propulsion Basics

• Rockets generate thrust by expelling propellant at high velocity in the opposite direction of motion
  • Thrust is the force produced by the rocket engine, enabling the spacecraft to overcome gravity and atmospheric drag
• Specific impulse (Isp) is a measure of the efficiency of a rocket engine
  • Represents the amount of thrust generated per unit weight of propellant consumed per second
  • Higher specific impulse indicates better propellant efficiency and potentially higher payload capacity
• Rocket equation, also known as Tsiolkovsky's equation, relates the change in velocity (delta-v) of a spacecraft to the specific impulse and the initial and final mass of the spacecraft
  • Determines the amount of propellant required for a given mission or maneuver
• Staging involves the use of multiple rocket stages to improve the overall efficiency of the launch vehicle
  • Each stage contains its own engines and propellant, which are discarded when depleted
  • Allows for a more efficient use of propellant by reducing the mass of the vehicle as it ascends
• Liquid propellant rockets use liquid fuel (kerosene, liquid hydrogen) and oxidizer (liquid oxygen) stored in separate tanks
  • Propellants are pumped into the combustion chamber, where they react to produce hot exhaust gases
  • Offer high specific impulse and the ability to throttle and restart engines
• Solid propellant rockets contain a solid mixture of fuel and oxidizer cast into a solid grain
  • Once ignited, solid rockets cannot be throttled or shut down until all the propellant is consumed
  • Provide high thrust-to-weight ratios and are often used for initial launch stages and military applications

Launch and Orbital Insertion

• Launch vehicles are designed to overcome Earth's gravity and atmospheric drag to place payloads into orbit
  • Consist of multiple stages, each with its own engines and propellant
  • Examples include Falcon 9 (SpaceX), Atlas V (United Launch Alliance), and Ariane 5 (Arianespace)
• Launch sites are chosen based on various factors, such as proximity to the equator, range safety, and infrastructure
  • Launching from sites closer to the equator (Kennedy Space Center, Guiana Space Centre) provides a velocity boost due to Earth's rotation
• Launch windows are specific time periods during which a spacecraft must be launched to reach its intended orbit
  • Determined by the desired orbital parameters and the relative positions of the launch site and the target orbit
• Ascent trajectory is the path followed by the launch vehicle from liftoff to orbital insertion
  • Designed to minimize aerodynamic stress, optimize propellant usage, and ensure range safety
  • May include pitch and yaw maneuvers to steer the vehicle and adjust its heading
• Orbital insertion is the process of placing a spacecraft into its desired orbit
  • Typically involves a final burn of the upper stage engine to circularize the orbit
  • Requires precise timing and control to achieve the correct orbital parameters
• Payload fairing is the protective cover that encapsulates the spacecraft during launch and ascent
  • Shields the payload from aerodynamic forces, heating, and contamination
  • Separates from the launch vehicle once it reaches a certain altitude, exposing the spacecraft

Orbital Maneuvers and Transfers

• Orbital maneuvers are changes in a spacecraft's orbit achieved by firing its thrusters or engines
  • Used to adjust the orbital parameters, such as altitude, inclination, or phasing
  • Examples include in-plane maneuvers (altitude changes) and out-of-plane maneuvers (inclination changes)
• Hohmann transfer is a two-impulse maneuver used to transfer a spacecraft between two coplanar circular orbits
  • Consists of an initial thrust to move the spacecraft into an elliptical transfer orbit tangent to both the initial and final orbits
  • A second thrust is applied at the apogee or perigee of the transfer orbit to circularize the orbit at the desired altitude
• Bi-elliptic transfer is a three-impulse maneuver used to transfer between two coplanar orbits with a large difference in radii
  • Involves an initial thrust to move the spacecraft into an elliptical orbit with an apogee much higher than the final orbit
  • A second thrust is applied at the apogee to move the spacecraft into a second elliptical orbit with a perigee at the desired final altitude
  • A third thrust is applied at the perigee to circularize the orbit
• Plane change maneuvers alter the inclination of a spacecraft's orbit
  • Require a significant amount of delta-v, especially for large changes in inclination
  • Often combined with other maneuvers, such as apogee or perigee burns, to minimize the total delta-v required
• Rendezvous and docking are the processes of bringing two spacecraft together and physically connecting them in orbit
  • Requires precise control of the relative position, velocity, and attitude of the spacecraft
  • Used for crew transfers, resupply missions, and the assembly of large structures in space (International Space Station)
• Deorbit and re-entry maneuvers are used to bring a spacecraft back to Earth's surface
  • Involves a retrograde burn to lower the spacecraft's perigee into the upper atmosphere
  • Atmospheric drag slows the spacecraft, causing it to descend and heat up due to friction
  • Spacecraft designed for re-entry, such as capsules and space shuttles, have heat shields to protect against the high temperatures experienced during descent

Space Environment and Its Effects

• Vacuum of space presents challenges for spacecraft design and operation
  • Lack of atmospheric pressure can cause outgassing of materials and cold welding of moving parts
  • Spacecraft must be designed to withstand the extreme temperature variations experienced in space
• Microgravity environment affects various physical processes and human physiology
  • Fluids and gases behave differently in microgravity, requiring special handling and storage techniques
  • Prolonged exposure to microgravity can lead to bone density loss, muscle atrophy, and cardiovascular changes in astronauts
• Space debris, consisting of defunct satellites, spent rocket stages, and fragments from collisions, poses a significant threat to spacecraft
  • High-velocity impacts can cause damage to spacecraft components and generate additional debris
  • Mitigation strategies include debris tracking, collision avoidance maneuvers, and the implementation of debris removal technologies
• Solar radiation and cosmic rays can damage spacecraft electronics and pose health risks to astronauts
  • Spacecraft are equipped with radiation-hardened components and shielding to mitigate the effects of radiation
  • Astronauts are monitored for radiation exposure and must adhere to strict exposure limits
• Spacecraft charging occurs when a spacecraft accumulates electric charge due to interactions with the space plasma environment
  • Can lead to electrostatic discharges, causing damage to spacecraft components and interfering with electronic systems
  • Mitigation techniques include the use of conductive materials, grounding, and active charge control devices
• Atmospheric drag affects spacecraft in low Earth orbits, causing orbital decay and eventual re-entry
  • Drag force depends on the spacecraft's velocity, cross-sectional area, and the density of the upper atmosphere
  • Spacecraft in LEO must perform periodic orbit-raising maneuvers to compensate for the effects of atmospheric drag
• Thermal control is crucial for maintaining spacecraft components within their acceptable temperature ranges
  • Spacecraft are exposed to extreme temperature variations, with the sun-facing side heating up and the shadow side cooling down
  • Thermal control systems use insulation, reflective coatings, heat pipes, and active heating and cooling devices to regulate spacecraft temperature