liminfoOrbital Mechanics Reference
Free reference guide: Orbital Mechanics Reference
About Orbital Mechanics Reference
The Orbital Mechanics Reference is a comprehensive, searchable quick-reference covering fundamental astrodynamics formulas and data needed by aerospace engineers, mission designers, and students. It includes Kepler's three laws with polar coordinate equations, the vis-viva equation for computing orbital velocities, specific orbital energy classifications, and the six classical orbital elements (a, e, i, RAAN, omega, true anomaly) with representative values for ISS, GPS, GEO, and other well-known satellites.
Beyond fundamentals, this reference provides detailed coverage of orbital transfer maneuvers including Hohmann transfers with step-by-step delta-V calculations, bi-elliptic transfers for large orbit ratios (r2/r1 > 11.94), plane change maneuvers with combined strategies, and phasing maneuvers for rendezvous operations. Each entry includes the governing equations, worked numerical examples, and practical engineering tips.
The reference also covers operational topics essential for satellite mission planning: complete Earth-based delta-V budgets from surface to LEO through interplanetary trajectories, the Tsiolkovsky rocket equation with representative Isp values for different propulsion systems, TLE (Two-Line Element) format decoding, ground station visibility calculations, orbital perturbation sources (J2, drag, SRP, third-body), and atmospheric reentry dynamics including thermal protection strategies.
Key Features
- Kepler's three laws with polar coordinate equations and worked ISS orbital period examples
- Vis-viva equation and specific orbital energy with circular, escape, and bound orbit cases
- Six classical orbital elements (COEs) with representative values for ISS, GPS, GEO, and Moon orbits
- Hohmann, bi-elliptic, plane change, and phasing transfer maneuver formulas with delta-V calculations
- Complete delta-V budget from Earth surface through LEO, GEO, Moon, and Mars trajectories
- Tsiolkovsky rocket equation with Isp values for solid, RP-1, LH2, ion, and Hall thrusters
- TLE format field-by-field decoding, ground station visibility, and orbital perturbation analysis
- Atmospheric reentry dynamics covering flight path angles, heating models, and thermal protection systems
Frequently Asked Questions
What orbital mechanics formulas does this reference cover?
The reference covers Kepler's three laws (elliptic orbits, equal areas, harmonic law), the vis-viva equation (v squared = mu times (2/r - 1/a)), specific orbital energy, all six classical orbital elements, and their relationships to orbital period, velocity, and energy.
How do I calculate delta-V for a Hohmann transfer?
The reference provides the complete Hohmann transfer formulas: transfer semi-major axis at = (r1 + r2)/2, first burn dv1 = sqrt(mu/r1) times (sqrt(2r2/(r1+r2)) - 1), and second burn dv2 = sqrt(mu/r2) times (1 - sqrt(2r1/(r1+r2))). A worked example for LEO to GEO (3,935 m/s total) is included.
Does it explain the TLE (Two-Line Element) format?
Yes, the reference includes a complete field-by-field breakdown of the TLE format using ISS as an example. It explains the catalog number, international designator, epoch, mean motion derivative, B-star drag coefficient, inclination, RAAN, eccentricity, argument of perigee, mean anomaly, and mean motion.
What orbit types are covered in this reference?
The reference covers LEO (200-2,000 km), GEO (35,786 km altitude), SSO (sun-synchronous, 600-800 km), and MEO/GPS orbits with specific parameters including altitude, period, velocity, inclination, and representative satellites for each orbit type.
Can I find interplanetary transfer data here?
Yes, the reference includes Earth-to-planet delta-V budgets for Venus, Mars, Jupiter, and Saturn using Hohmann transfers, along with transfer times, launch window intervals, and information about gravity assist techniques used by missions like Voyager and Cassini.
What perturbation sources are covered?
The reference covers five major perturbation sources: Earth oblateness (J2 effect causing RAAN precession used for SSO), atmospheric drag (significant below 800 km), solar radiation pressure (for high area-to-mass ratio satellites), third-body gravity (Moon/Sun at GEO and beyond), and relativistic effects (important for GPS time corrections).
How is this reference useful for rocket equation calculations?
The Tsiolkovsky equation section provides dv = Isp times g0 times ln(m0/mf) with mass ratio formulas, plus representative specific impulse values: solid rockets (260 s), RP-1/LOX like Merlin (310 s), LH2/LOX like RS-25 (450 s), ion thrusters (3,000 s), and Hall thrusters (1,500 s).
Does it cover atmospheric reentry?
Yes, the reference includes reentry interface altitude (122 km), velocities for LEO (7.8 km/s), lunar return (11 km/s), and Mars return (12+ km/s), flight path angle corridors for crewed missions, stagnation point heat flux formulas, and thermal protection system types (ablative, insulative, and radiative).