Orbital Mechanics: Principles and Applications
A description of the physical laws governing the motion of objects in curved paths around a central body due to gravity. This encompasses natural satellites, planets, artificial satellites, and other celestial bodies. Understanding these principles is fundamental to astrodynamics, space mission design, and celestial navigation.
Fundamental Principles
- Newton's Law of Universal Gravitation: The force of attraction between two objects with mass, directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
- Kepler's Laws of Planetary Motion:
- First Law (Law of Ellipses): Planets move in elliptical paths with the star at one focus.
- Second Law (Law of Equal Areas): A line segment joining a planet and the star sweeps out equal areas during equal intervals of time.
- Third Law (Law of Harmonies): The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.
- Conservation of Energy and Angular Momentum: These principles dictate the relationships between orbital parameters and velocities.
Orbital Elements
A set of parameters that uniquely define an orbit in space.
- Semi-major axis (a): Defines the size of the orbit; half the longest diameter of the ellipse.
- Eccentricity (e): Defines the shape of the orbit, ranging from 0 (circular) to nearly 1 (highly elliptical).
- Inclination (i): Angle between the orbital plane and a reference plane (e.g., the ecliptic for solar orbits, the equator for Earth orbits).
- Longitude of the ascending node (Ω): Angle between a reference direction (e.g., the vernal equinox) and the point where the orbit crosses the reference plane from south to north.
- Argument of periapsis (ω): Angle between the ascending node and the point of closest approach (periapsis) to the central body.
- True anomaly (ν): Angle between the periapsis and the current position of the orbiting object, measured in the orbital plane.
Orbital Maneuvers
Changes to an orbit accomplished through the application of thrust. Delta-v (Δv) represents the change in velocity required for a maneuver.
- Hohmann Transfer: An efficient two-burn transfer between two circular orbits.
- Bi-elliptic Transfer: A potentially more efficient transfer (in terms of Δv) than the Hohmann transfer in certain situations, involving two burns to reach a higher orbit and a final burn to reach the target orbit.
- Plane Change Maneuver: Altering the inclination of an orbit, typically requiring a significant Δv.
- Rendezvous Maneuver: Precisely matching the position and velocity of two orbiting objects.
Types of Orbits
- Geostationary Orbit (GEO): An orbit around Earth with a period matching Earth's rotation, appearing stationary from the ground.
- Geosynchronous Orbit: An orbit around Earth with a period matching Earth's rotation, but not necessarily circular or with zero inclination.
- Low Earth Orbit (LEO): An orbit around Earth at a relatively low altitude (typically below 2,000 km).
- Polar Orbit: An orbit that passes over or close to the poles of a planet.
- Sun-synchronous Orbit: A near-polar orbit that maintains a consistent relationship with the sun, useful for Earth observation satellites.
- Highly Elliptical Orbit (HEO): An orbit with a high eccentricity, resulting in large variations in altitude.
Perturbations
Deviations from an idealized Keplerian orbit caused by various forces.
- Atmospheric Drag: Resistance encountered by satellites in low Earth orbit due to the Earth's atmosphere.
- Non-spherical Earth: The Earth's oblateness causes perturbations in satellite orbits.
- Third-body Gravitational Effects: Gravitational influence from the Sun, Moon, and other celestial bodies.
- Solar Radiation Pressure: Force exerted by photons from the Sun on a satellite's surface.