Expert-level orbital mechanics covering Keplerian orbits, orbital maneuvers, Hohmann transfers, rendezvous, interplanetary trajectories, and perturbations.
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| name | orbital-mechanics-expert |
| version | 1.0.0 |
| description | Expert-level orbital mechanics covering Keplerian orbits, orbital maneuvers, Hohmann transfers, rendezvous, interplanetary trajectories, and perturbations. |
| author | luo-kai |
| tags | ["orbital mechanics","Kepler","Hohmann transfer","rendezvous","perturbations","delta-V"] |
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 |
