Orbital Mechanics (Astrodynamics)
Keplerian Two-Body Problem (The Baseline Model)
The two-body model treats a spacecraft as a point mass under a central gravitational field. It is the foundation for orbit geometry, orbital periods, and energy relationships. In simple terms: it describes the “ideal orbit” before reality adds complexity.
- Conics: circular/elliptic (bound), parabolic/hyperbolic (escape and flyby).
- Energy: specific orbital energy determines orbit size.
- Mean motion: links semi-major axis to orbital period.
Orbital Elements (A Compact Orbit Description)
Orbits are commonly parameterized by a small set of elements (size, shape, orientation, and location). In simple terms: orbital elements are a “coordinate system” for orbits.
- Semi-major axis (a) and eccentricity (e): size and shape.
- Inclination (i), RAAN (Ω), argument of periapsis (ω): orientation.
- True/mean anomaly: where the spacecraft is along the orbit.
Perturbations (Where Reality Deviates)
Real trajectories are influenced by non-ideal forces. For LEO satellites, drag and Earth’s oblateness (J2) often dominate. In simple terms: perturbations slowly “push” the orbit away from the ideal shape.
- Atmospheric drag: decays semi-major axis; depends on density and solar activity.
- J2 effects: nodal regression and periapsis precession.
- Third-body gravity: Sun/Moon effects, critical for cislunar missions.
- Solar radiation pressure: meaningful for high area-to-mass spacecraft.
Maneuvering (Trajectory Control)
Maneuvers change orbital energy and geometry. Basic building blocks include plane changes, Hohmann transfers, and phasing maneuvers. In simple terms: a small velocity change (Δv) can reshape the entire orbit.
- Impulsive vs. low-thrust: short burns vs. long-duration thrusting with optimization.
- Δv budget: a key driver of propulsion sizing and mission feasibility.
- Trajectory optimization: compute-efficient planning for complex missions.
Modern Focus (What Is Getting Important Now)
- Cislunar logistics: transfers, staging, and sustained operations around the Moon.
- Debris management: conjunction screening and maneuver planning at scale.
- Active removal: rendezvous + capture + deorbit; example: ELSA-M concept for end-of-life services.