Fundamentals of astrodynamics and applications 4th Edition (2013)

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THE SPACE TECHNOLOGY LIBRARYPublished jointly by Microcosm Press and SpringerAn Introduction to Mission Design for Geostationary Satellites, J. J. PochaSpace Mission Analysis and Design, 3 rd edition, James R. Wertz and Wiley J. LarsonSpace Mission Engineering, James R. WertzHandbook of Geostationary Orbits, E. M. SoopSpacecraft Structures and Mechanisms, From Concept to Launch, Thomas P. SarafinSpaceflight Life Support and Biospherics, Peter EckartReducing Space Mission Cost, James R. Wertz and Wiley J. LarsonThe Logic of Microspace, Rick FleeterSpace Marketing: A European Perspective, Walter A. R. PeetersOrbit and Constellation Design and Management, James R. WertzInfluence of Psychological Factors on Product Development, Eginaldo Shizuo KamataEssential Spaceflight Dynamics and Magnetospherics, Boris Rauschenbakh,Michael Ovchinnikov, and Susan McKenna-LawlorSpace Psychology and Psychiatry, Nick Kanas and Dietrich ManzeyFundamentals of Space Medicine, Gilles ClémentFundamentals of Space Biology, Gilles Clément and Klaus SlenzkaMicrogravity Two-Phase Flow and Heat Transfer, Kamiel GabrielArtificial Gravity, Gilles Clément and Angelia BuckleyThe Space Technology Library Editorial BoardManaging Editor:Editorial Board:James R. Wertz, Microcosm, Inc., Hawthorne, CARoland Doré, International Space University, Strasbourg, FranceWiley J. Larson, United States Air Force AcademyTom Logsdon, Rockwell International (retired)Landis Markley, Goddard Space Flight CenterRobert G. Melton, Pennsylvania State UniversityKeiken Ninomiya, Institute of Space & Astronautical Science, JapanJehangir J. Pocha, Matra Marconi Space, Stevenage, EnglandGael Squibb, Jet Propulsion LaboratoryMartin Sweeting, University of Surrey, EnglandAbout the AuthorDavid Vallado is currently a Senior Research Astrodynamicist with Analytical Graphics, Inc. inColorado Springs, Colorado. He holds a BS degree in Astrodynamics Engineering from the U. S.Air Force Academy and MS from the Air Force Institute of Technology. He also holds an MS inSystems Management from the University of Southern California. He is a retired Air Force LieutenantColonel. His Air Force experience includes: Stage 1 Project Manager for MX missile, SACHeadquarters Analysis Division, U. S. Air Force instructor, Air Force Research Laboratory Scientist,and Headquarters U. S. Space Command Analysis Office. He has also worked as a principalengineer with Raytheon in Denver, Colorado.
Fundamentals of Astrodynamicsand ApplicationsFourth EditionDavid A. ValladoAnalytical Graphics Inc.with technical contributions byWayne D. McClainCharles Stark Draper LaboratorySpace Technology LibraryPublished byMicrocosm PressHawthorne, CA
Page 2 and 3: Common Two-body EquationsSpecific A
Page 5: CircleEllipse Parabola HyperbolaEqu
Page 9: FUNDAMENTALS OF ASTRODYNAMICS AND A
Page 13: To God from whom all blessings and
Page 16 and 17: viii3.3 Coordinate Systems 1453.3.1
Page 18 and 19: x7.4.2 Range-only Processing 4527.5
Page 20 and 21: xii11.2.2 Mission Planning 85211.3
Page 22 and 23: xivAlgorithm SummaryAlgorithm 1 Fin
Page 24 and 25: xviForwardAt Microcosm, when an ast
Page 26 and 27: xviiineed,” only to find that you
Page 28 and 29: xxAcknowledgmentsI credit numerous
Page 30 and 31: xxiiald Dichmann, John Douglass, Te
Page 32 and 33: 2 EQUATIONS OF MOTION 1.1one, . . .
Page 34 and 35: 4 EQUATIONS OF MOTION 1.1modern tec
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Page 42 and 43: 12 EQUATIONS OF MOTION 1.21.1.5 Oth
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Page 52 and 53: 22 EQUATIONS OF MOTION 1.3r K sat=
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30 EQUATIONS OF MOTION 1.3The perio
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32 EQUATIONS OF MOTION 1.3(1) Using
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34 EQUATIONS OF MOTION 1.4EarthThir
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36 EQUATIONS OF MOTION 1.4geometry.
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38 EQUATIONS OF MOTION 1.4ni = 1.m
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40 EQUATIONS OF MOTION 1.4n1 2 1 my
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42 KEPLER’S EQUATION AND KEPLER
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130 COORDINATE AND TIME SYSTEMS 3.1
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242 OBSERVATIONS 4.2numerals, effec
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244 OBSERVATIONS 4.2t s-rect s-tran
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246 OBSERVATIONS 4.2SEZObserved Pla
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248 OBSERVATIONS 4.24.2.3 Types of
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250 OBSERVATIONS 4.3egories: dedica
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252 OBSERVATIONS 4.3which have corn
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254 OBSERVATIONS 4.4TABLE 4-3. Phys
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256 OBSERVATIONS 4.4ClearCavalierSo
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258 OBSERVATIONS 4.4ṙ COS( d)COS(
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260 OBSERVATIONS 4.4fixed orientati
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262 OBSERVATIONS 4.4.. - ṙ COS( e
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264 OBSERVATIONS 4.4Notice several
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266 OBSERVATIONS 4.4RAZEL is simply
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268 OBSERVATIONS 4.4SIN( b)SIN( LHA
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270 OBSERVATIONS 4.4This equation y
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272 OBSERVATIONS 4.420181614Inclina
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274 OBSERVATIONS 4.4d = -20°49'24.
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276 OBSERVATIONS 4.4Problems1. You
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278 CELESTIAL PHENOMENA 5.1K^eZ^Ecl
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280 CELESTIAL PHENOMENA 5.1M L = 35
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282 CELESTIAL PHENOMENA 5.1SunLunar
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284 CELESTIAL PHENOMENA 5.1TAN( a L
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286 CELESTIAL PHENOMENA 5.25.2.1 Ap
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288 CELESTIAL PHENOMENA 5.2ALGORITH
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290 CELESTIAL PHENOMENA 5.25.2.2 Ap
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292 CELESTIAL PHENOMENA 5.2JD temp
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294 CELESTIAL PHENOMENA 5.3Set GHA
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296 CELESTIAL PHENOMENA 5.3e = 0.04
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298 CELESTIAL PHENOMENA 5.32-6 3Q =
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300 CELESTIAL PHENOMENA 5.3minutes
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302 CELESTIAL PHENOMENA 5.3SAT hori
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304 CELESTIAL PHENOMENA 5.3Unfortun
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306 CELESTIAL PHENOMENA 5.3lite has
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308 CELESTIAL PHENOMENA 5.3c( t min
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310 CELESTIAL PHENOMENA 5.3L 1 = l
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312 CELESTIAL PHENOMENA 5.3the sola
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314 CELESTIAL PHENOMENA 5.3a6378SIN
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316 CELESTIAL PHENOMENA 5.3Problems
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318 ORBITAL MANEUVERING 6.2After so
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320 ORBITAL MANEUVERING 6.3The subs
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322 ORBITAL MANEUVERING 6.3v transb
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324 ORBITAL MANEUVERING 6.3Trans 1b
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326 ORBITAL MANEUVERING 6.3ALGORITH
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328 ORBITAL MANEUVERING 6.32mm21 (
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330 ORBITAL MANEUVERING 6.3R* = 15.
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332 ORBITAL MANEUVERING 6.3Substitu
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334 ORBITAL MANEUVERING 6.3COS( E)=
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336 ORBITAL MANEUVERING 6.3TABLE 6-
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338 ORBITAL MANEUVERING 6.4close to
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340 ORBITAL MANEUVERING 6.480Latitu
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342 ORBITAL MANEUVERING 6.46.4.2 In
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344 ORBITAL MANEUVERING 6.4ALGORITH
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346 ORBITAL MANEUVERING 6.4K^v fina
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348 ORBITAL MANEUVERING 6.46.4.4 Ch
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350 ORBITAL MANEUVERING 6.5Up to th
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352 ORBITAL MANEUVERING 6.5change t
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354 ORBITAL MANEUVERING 6.5TABLE 6-
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356 ORBITAL MANEUVERING 6.5COS( g)=
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358 ORBITAL MANEUVERING 6.6Sec. 7.6
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360 ORBITAL MANEUVERING 6.6tions. F
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362 ORBITAL MANEUVERING 6.6c = a L
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364 ORBITAL MANEUVERING 6.6Δv= 2(
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366 ORBITAL MANEUVERING 6.6solution
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368 ORBITAL MANEUVERING 6.6node wit
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370 ORBITAL MANEUVERING 6.6^J^KInte
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372 ORBITAL MANEUVERING 6.7or physi
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374 ORBITAL MANEUVERING 6.7For gene
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376 ORBITAL MANEUVERING 6.7Because
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378 ORBITAL MANEUVERING 6.710Accumu
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380 ORBITAL MANEUVERING 6.7Then, fi
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382 ORBITAL MANEUVERING 6.7c(v p )
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384 ORBITAL MANEUVERING 6.7Now find
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386 ORBITAL MANEUVERING 6.7Numerica
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388 ORBITAL MANEUVERING 6.8Δv acc
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390 ORBITAL MANEUVERING 6.8.. mr= -
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392 ORBITAL MANEUVERING 6.8..r I=..
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394 ORBITAL MANEUVERING 6.8Take the
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396 ORBITAL MANEUVERING 6.8yt ()=..
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398 ORBITAL MANEUVERING 6.8. .ẋ()
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400 ORBITAL MANEUVERING 6.8Now, rew
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402 ORBITAL MANEUVERING 6.8150x(m)1
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404 ORBITAL MANEUVERING 6.8velocity
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406 ORBITAL MANEUVERING 6.8x(m)2000
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408 ORBITAL MANEUVERING 6.8Intercep
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410 ORBITAL MANEUVERING 6.8. - 2qx
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412 ORBITAL MANEUVERING 6.8presente
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414 ORBITAL MANEUVERING 6.8point 2
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416 ORBITAL MANEUVERING 6.8z= -----
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418 ORBITAL MANEUVERING 6.810.000y
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420 ORBITAL MANEUVERING 6.8Problems
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422 ORBITAL MANEUVERING 6.8
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424 INITIAL ORBIT DETERMINATION 7.1
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518 SPECIAL PERTURBATION TECHNIQUES
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610 GENERAL PERTURBATION TECHNIQUES
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732 ORBIT DETERMINATION AND ESTIMAT
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838 MISSION ANALYSIS 11.1developing
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840 MISSION ANALYSIS 11.1Today, the
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842 MISSION ANALYSIS 11.1tasked to
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844 MISSION ANALYSIS 11.1Upgrades s
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846 MISSION ANALYSIS 11.2The eccent
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848 MISSION ANALYSIS 11.22000100000
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850 MISSION ANALYSIS 11.2TABLE 11-2
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852 MISSION ANALYSIS 11.2An importa
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854 MISSION ANALYSIS 11.3applies to
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856 MISSION ANALYSIS 11.3eral speci
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858 MISSION ANALYSIS 11.3r horizong
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860 MISSION ANALYSIS 11.3Use these
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862 MISSION ANALYSIS 11.4SIN 2 ( L)
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864 MISSION ANALYSIS 11.4^KSun1200A
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866 MISSION ANALYSIS 11.4where usin
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868 MISSION ANALYSIS 11.4drift to t
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870 MISSION ANALYSIS 11.4ascending
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872 MISSION ANALYSIS 11.4Rev 17Rev
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874 MISSION ANALYSIS 11.4motion. Fo
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876 MISSION ANALYSIS 11.4Δλ rev=
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878 MISSION ANALYSIS 11.4If we take
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880 MISSION ANALYSIS 11.411.4.3 Min
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882 MISSION ANALYSIS 11.4the most e
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884 MISSION ANALYSIS 11.4∂ 2 r---
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886 MISSION ANALYSIS 11.4dq-------d
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888 MISSION ANALYSIS 11.4tories for
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890 MISSION ANALYSIS 11.4The mean m
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892 MISSION ANALYSIS 11.4When you d
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894 MISSION ANALYSIS 11.42π-----Q1
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896 MISSION ANALYSIS 11.5Longitude
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898 MISSION ANALYSIS 11.5the precis
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900 MISSION ANALYSIS 11.5•••
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902 MISSION ANALYSIS 11.5Pseudorang
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904 MISSION ANALYSIS 11.5an integer
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906 MISSION ANALYSIS 11.5of code ps
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908 MISSION ANALYSIS 11.6known rece
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910 MISSION ANALYSIS 11.6the interv
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912 MISSION ANALYSIS 11.6DAT, x p ,
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914 MISSION ANALYSIS 11.6TABLE 11-4
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916 MISSION ANALYSIS 11.690Elevatio
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918 MISSION ANALYSIS 11.6f range ()
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920 MISSION ANALYSIS 11.7Satellite
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922 MISSION ANALYSIS 11.7For this d
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924 MISSION ANALYSIS 11.7Woodburn e
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926 MISSION ANALYSIS 11.7t close (
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928 MISSION ANALYSIS 11.7straight a
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930 MISSION ANALYSIS 11.7for the P
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932 MISSION ANALYSIS 11.7riance ell
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934 MISSION ANALYSIS 11.7If the cal
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936 MISSION ANALYSIS 11.7d close=P2
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938 MISSION ANALYSIS 11.7the correc
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940 MISSION ANALYSIS 11.7
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942 INTERPLANETARY MISSION ANALYSIS
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990 APPENDIX Aaaa iâ iacc iSemimaj
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992 APPENDIX Att acct dirftt mt pt
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994 APPENDIX AG mpG pHHHH dH pq'Ecc
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996 APPENDIX AbbAzimuth, measured p
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998 APPENDIX At iDelta time between
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Dictionary of Symbols
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1002 APPENDIX B180.0° rLHA L-----
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1004 APPENDIX BB.1.3Evaluating Dens
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1006 APPENDIX Bf=35 4 R2-----------
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1008 APPENDIX BWe also need the par
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1010 APPENDIX B( Δlog 10 r) He0.65
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1012 APPENDIX BTime lags are used f
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1014 APPENDIX BTABLE B-7. Russian D
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1016 APPENDIX BTABLE B-9. Russian D
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1018 APPENDIX Cerf( z)=z------2e t2
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1020 APPENDIX Cy= C T X z = A T X +
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1022 APPENDIX CSIN( a+b)= SIN( a)CO
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1024 APPENDIX CFor the right triang
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1026 APPENDIX CcACbBaFigure C-4.Obl
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1028 APPENDIX CNow find the constan
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1030 APPENDIX Ca=1-- 3( P32 - 4R) -
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1032 APPENDIX Cfunctions, for which
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1034 APPENDIX Cfirst equation of Eq
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1036 APPENDIX CIF a c0 < 0.0 and MA
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1038 APPENDIX Cno such roots exist
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1040 APPENDIX DTABLE D-2. Selected
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1042 APPENDIX DTABLE D-4. Mean Plan
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1044 APPENDIX DTABLE D-7. Largest I
Page 1076 and 1077:
1046 APPENDIX DD.4 Planetary Epheme
Page 1078 and 1079:
1048 APPENDIX Dq˜2= 173.005 159°
Page 1080 and 1081:
1050 APPENDIX DNeptunei23= 1.769 95
Page 1082 and 1083:
1052 APPENDIX Dannual period, AnnPe
Page 1084 and 1085:
1054 APPENDIX DCurrent Yearyyyy.vm(
Page 1086 and 1087:
1056 APPENDIX DObservational Data:R
Page 1088 and 1089:
1058 APPENDIX D| CROSS CROSS produc
Page 1090 and 1091:
1060 APPENDIX DTABLE D-10. Orbit De
Page 1092 and 1093:
1062 REFERENCESAllan, R. R., and G.
Page 1094 and 1095:
1064 REFERENCESBrewer, J.A., and D.
Page 1096 and 1097:
1066 REFERENCESChilulli, Roy M. 199
Page 1098 and 1099:
1068 REFERENCESEscobal, Pedro R. [1
Page 1100 and 1101:
1070 REFERENCES———. 1997. A N
Page 1102 and 1103:
1072 REFERENCESHoots, Felix R., Lin
Page 1104 and 1105:
1074 REFERENCESKnowles, Stephen H.
Page 1106 and 1107:
1076 REFERENCESMcCarthy, Dennis. 19
Page 1108 and 1109:
1078 REFERENCESNostrand, Philip M.
Page 1110 and 1111:
1080 REFERENCESSchumacher, Paul W.,
Page 1112 and 1113:
1082 REFERENCESSutton, Eric K., Jef
Page 1114 and 1115:
1084 REFERENCESVallado, David A., a
Page 1116 and 1117:
1086 REFERENCESZarchan, Paul. 1994.
Page 1118 and 1119:
1088 INDEXRussian GOST, 571Soviet C
Page 1120 and 1121:
1090 INDEXDay of the yearderiving,
Page 1122 and 1123:
1092 INDEXEquinoctial elements, 108
Page 1124 and 1125:
1094 INDEXdetermining period, 122ec
Page 1126 and 1127:
1096 INDEXLAGEOS See Laser Geodynam
Page 1128 and 1129:
1098 INDEXNewton, Isaac 41, 129, 31
Page 1130 and 1131:
1100 INDEXPerturbation effectscentr
Page 1132 and 1133:
1102 INDEX853Rectification point, 5
Page 1134 and 1135:
1104 INDEXSpecific force, 522Specif
Page 1136 and 1137:
1106 INDEXVariational equations 803
Page 1138:
Constants & ConversionsWe can use t
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