Expert-level orbital mechanics covering Keplerian orbits, orbital maneuvers, Hohmann transfers, rendezvous, interplanetary trajectories, and perturbations.
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Six orbital elements: semi-major axis, eccentricity, inclination, RAAN, argument of perigee, true anomaly. Vis-viva equation: v squared = GM times 2 over r minus 1 over a. Orbital period: T = 2 pi sqrt a cubed over GM. Orbit types: circular, elliptical, parabolic, hyperbolic based on eccentricity. Specific energy: epsilon = minus GM over 2a, negative for bound orbits.
Hohmann transfer: minimum energy transfer between circular orbits, two burns. Delta-V: velocity change required for maneuver, determines propellant mass. Plane change: expensive maneuver, best done at low velocity near apogee. Bielliptic transfer: three burns, more efficient than Hohmann for large ratio orbits. Phasing orbit: adjust timing for rendezvous by changing orbital period.
Clohessy-Wiltshire equations: relative motion near circular reference orbit. V-bar approach: approach along velocity vector, passive abort safe. R-bar approach: approach along radial direction, natural drift used. Hold points: stable relative positions for inspection before docking.
J2 effect: Earth oblateness causes nodal regression and perigee rotation. Atmospheric drag: lowers perigee, causes orbit decay for LEO satellites. Solar radiation pressure: significant for large area-to-mass ratio spacecraft. Third body: Moon and Sun perturb high Earth orbits.
| Pitfall | Fix |
|---|---|
| Two-body assumption for long missions | Include perturbations for accurate long-term propagation |
| Ignoring J2 in sun-synchronous design | J2 regression rate must equal Earth orbit rate |
| Wrong reference frame | Clarify ECI vs ECEF vs RTN before calculations |
| Underestimating delta-V margins | Add 10-15% margin for navigation and dispersions |
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Expert-level abstract algebra knowledge. Use when working with groups, rings, fields, modules, Galois theory, representation theory, or algebraic structures. Also use when the user mentions 'group', 'ring', 'field', 'homomorphism', 'isomorphism', 'normal subgroup', 'quotient group', 'Sylow theorem', 'Galois theory', 'polynomial ring', 'ideal', 'module', 'vector space', or 'representation theory'.
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Expert-level acoustics knowledge. Use when working with sound waves, acoustic propagation, resonance, standing waves, Doppler effect, room acoustics, ultrasound, noise control, musical acoustics, or architectural acoustics. Also use when the user mentions 'sound wave', 'decibel', 'frequency', 'resonance', 'standing wave', 'Doppler effect', 'acoustic impedance', 'reverberation', 'ultrasound', 'noise control', 'harmonics', or 'sound intensity'.
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Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.
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Expert-level air quality engineering covering pollutant sources, atmospheric dispersion, air quality standards, emission controls, and air quality modeling.
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Expert-level aircraft structures covering structural design philosophy, wing and fuselage analysis, fatigue and damage tolerance, composite structures, and certification.
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Expert-level algorithms and complexity theory covering sorting, searching, graph algorithms, dynamic programming, greedy algorithms, NP-completeness, and algorithm design paradigms.
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