Astrodynamics 102 - DerAstrodynamics.com

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Two Equations and Two Unknowns Gauss Battin Shepperd Gooding Klumpp Theories/ Formulations Lambert Algorithm Developers One Equation and One Unknown Lambert Gauss Battin Lancaster/Blanchard Godal Vinh Sun Lambert Algorithm Characteristics: Implementations/ Iterative Methods Newton, Halley, and Others Everyone (almost) Laguerre and Modified Laguerre Conway Der 1. Most (over 90%) Lambert algorithms apply to zero rev and have singularities 2. Sun/Der Lambert + algorithm applies to multi-rev and rarely has singluarity (simple theory + straightforward implementation = speed, accuracy, robustness)
Osculating Orbital Elements at t o [ r (t ), v (t )] o o Radars / Optical sensors Future look angles ( pointing prediction ) Others . . . . . . Orbit Determination and Prediction/Propagation Object at t r Unsuitable for real-time automatic processing Ephemerides Raw Observation data v Orbit Determination (Estimated future/past) position and velocity vectors Rise/Set Site visibility <strong>Astrodynamics</strong> <strong>102</strong>: Lambert / 103: Gauss/Laplace Initial Orbit Determination Processed Observation data Differential Correction Batch / KF TLE conversion difficulties Singularity difficulties Osc2Mean Analytic algorithms in OD and P/P need to process 100,000+ Objects in less than 12 hours with accuracy of 10 km to centimeters for SSA (Estimated initial) positin and velocity vectors Orbital element set r and v Prediction / Propagation 1 2 SP 3 Numerical SGP4 Integration Kepler+ Close approach (miss distance) [ r , v ] Astro 101: Kepler 1 2 3 SGP4 needs TLE conversion (not efficient for SSA) SP is accurate, but slow for SSA Kepler+ is accurate and fast for SSA
Page 1 and 2: Launch / Impact Point Prediction S
Page 3 and 4: Astrodynamics 102: Lambert+ Algorit
Page 5 and 6: Radar/Laser Weather/Satellite Track
Page 7 and 8: Space Debris Collisions 2007 2009,
Page 9 and 10: 1. What, Why, How What? Satellite r
Page 11 and 12: Physics and Mathematics 2. Physics
Page 13 and 14: direct transfer orbit o (inclinatio
Page 15 and 16: Choice of bounded x, gives a “ver
Page 17 and 18: Classical Kepler (2-Body) Perturbat
Page 19 and 20: Equations of Motion (2-Body) d2 r =
Page 21 and 22: v 2 vv2 vt2 v 2 Initial Step 1 B Ke
Page 23 and 24: Transfer orbit 1: inc_to = 1, i < 9
Page 25: Lambert Problem Given: r (t ) , r (
Page 29 and 30: Applications of Analytic Algorithms
Page 31 and 32: UNCLASSIFIED Applications of Analyt
Page 33 and 34: Astrodynamics 102 Part 2: Verificat
Page 35 and 36: ICBM transfer orbit , Single revolu
Page 37 and 38: Numerical Example 4 High Earth Orbi
Page 39 and 40: Numerical Example 6 ICBM transfer o
Page 41 and 42: Numerical Example 8 Molniya transfe

Astrodynamics 102 - DerAstrodynamics.com

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