Orbitalna mehanika — разлика између измена

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Orbitalna mehanika ili astrodinamika je primena balistike^[1] i nebeske mehanike^[2]^[3] na praktične probleme koji se tiču kretanja raketa i drugih svemirskih letelica. Kretanje ovih objekata se obično izračunava iz Njutnovih zakona kretanja^[4] i zakona univerzalne gravitacije.^[5]^[6]^[7] Orbitalna mehanika je sržna disciplina unutar dizajna i kontrole svemirskih misija.

Nebeska mehanika šire tretira orbitalnu dinamiku sistema pod uticajem gravitacije, uključujući svemirske letelice i prirodna astronomska tela poput zvezdanih sistema, planeta, meseca i kometa. Orbitalna mehanika se fokusira na putanje svemirskih letelica, uključujući orbitalne manevre, promene orbitalne ravni i međuplanetarne transfere, i planeri misija je koriste da predvide rezultate propulzivnih manevara. Opšta relativnost je tačnija teorija od Njutnovih zakona za izračunavanje orbita, a ponekad je neophodna i za veću tačnost ili u visoko-gravitacijskim situacijama (npr. orbite blizu Sunca).

Istorija

Sve do uspona svemirskih putovanja u dvadesetom veku, postojala je mala razlika između orbitalne i nebeske mehanike. U vreme Sputnika polje se nazivalo „svemirskom dinamikom”.^[8] Fundamentalne tehnike, poput onih koje se koriste za rešavanje Keplerovog problema (određivanja položaja kao funkcije vremena), stoga su iste u obe oblasti. Pored toga, istorija polja je gotovo u potpunosti zajednička.

Johan Kepler je bio prvi koji je uspešno modelovao planetarne orbite sa visokim stepenom tačnosti, objavivši svoje zakone 1605. Isak Njutn objavio je više opštih zakona nebeskog kretanja u prvom izdanju svog dela Philosophiæ Naturalis Principia Mathematica (1687), koji su dali metodu za pronalaženje orbite tela sledeći parabolični put iz tri opservacije.^[9] Ovo je iskoristio Edmund Halej za uspostavljanje orbita raznih kometa, uključujući i onu koja nosi njegovo ime. Njutnova metoda sukcesivne aproksimacije formalizovana je u analitičku metodu Ojlerovim doprinosom iz 1744. godine, čiji je rad zatim bio generalizovan na eliptične i hiperboličke orbite Lambertovim doprinosom tokom 1761-1777.^[10]^[11]

Druga prekretnica u određivanju orbite bila je pomoć Karla Fridriha Gausa u otkriću patuljaste planete Ceres 1801. godine. Gausova metoda je mogla da koristi samo tri opažanja (u obliku parova rektascenzije i deklinacije) da pronađe šest orbitalnih elemenata koji u potpunosti opisuju orbitu. Teorija određivanja orbite je kasnije razvijena do tačke u kojoj se danas primenjuje u GPS prijemnicima, kao i u praćenju i katalogizaciji tek promatranih malih planeta. Moderno određivanje i predviđanje orbite koriste se za rad svih tipova satelita i svemirskih sondi, jer je potrebno znati njihove buduće položaje sa visokom tačnošću.

Astrodinamiku je razvio astronom Samjuel Herik početkom 1930-ih. On se konsultovao sa raketnim naučnika Robertom Godardom i bio je ohrabren je da nastavi svoj rad na svemirskim navigacionim tehnikama, jer je Godard verovao da će one biti potrebne u budućnosti. Numeričke tehnike astrodinamike bile su povezane sa novim moćnim računarima 1960-ih godina i čovek je bio spreman da putuje na Mesec i da se vrati.

Reference

^ Herbst, Judith (2005). The History of Weapons. Lerner Publications. ISBN 9780822538059. Приступљено 16. 3. 2018 — преко Google Books.
^ Forest R. Moulton, Introduction to Celestial Mechanics, 1984, Dover, ISBN 0-486-64687-4
^ John E. Prussing, Bruce A. Conway, Orbital Mechanics, 1993, Oxford Univ. Press
^ Newton, Sir Isaac; Machin, John (1729). Principia. 1 (1729 translation изд.). стр. 19.
^ Fritz Rohrlich (25. 8. 1989). From Paradox to Reality: Our Basic Concepts of the Physical World. Cambridge University Press. стр. 28—. ISBN 978-0-521-37605-1.
^ Klaus Mainzer (2. 12. 2013). Symmetries of Nature: A Handbook for Philosophy of Nature and Science. Walter de Gruyter. стр. 8—. ISBN 978-3-11-088693-1.
^ „Physics: Fundamental Forces and the Synthesis of Theory | Encyclopedia.com”. www.encyclopedia.com.
^ Thomson, William T. (1961). Introduction to Space Dynamics. New York: Wiley.
^ Bate, R. R.; Mueller, D. D.; White, J. E. (1971). Fundamentals of Astrodynamics. Courier Corporation. стр. 5. ISBN 978-0-486-60061-1.
^ Browne, Michael E. (јул 1999). Schaum's outline of theory and problems of physics for engineering and science (Series: Schaum's Outline Series). McGraw-Hill Companies. стр. 58. ISBN 978-0-07-008498-8.
^ Holzner, Steven (децембар 2005). Physics for Dummies. Wiley, John & Sons, Incorporated. стр. 64. Bibcode:2005pfd..book.....H. ISBN 978-0-7645-5433-9.

Literatura

Curtis, Howard D. (2009). Orbital Mechanics for Engineering Students, 2e. New York: Elsevier. ISBN 978-0-12-374778-5.
Bate, Roger R.; Mueller, Donald D.; White, Jerry E. (1971). Fundamentals of Astrodynamics. New York: Dover Publications. ISBN 0-486-60061-0.
Sellers, Jerry J.; Astore, William J.; Giffen, Robert B.; Larson, Wiley J. (2004). Kirkpatrick, Douglas H., ур. Understanding Space: An Introduction to Astronautics (2 изд.). McGraw Hill. стр. 228. ISBN 0-07-242468-0.
„Air University Space Primer, Chapter 8 - Orbital Mechanics” (PDF). USAF. Архивирано из оригинала (PDF) 2013-02-14. г. Приступљено 2007-10-13.
Bate, R.R.; Mueller, D.D.; White, J.E. (1971). Fundamentals of Astrodynamics. Dover Publications, New York. ISBN 978-0-486-60061-1.
Vallado, D. A. (2001). Fundamentals of Astrodynamics and Applications (2nd изд.). Springer. ISBN 978-0-7923-6903-5.
Battin, R.H. (1999). An Introduction to the Mathematics and Methods of Astrodynamics. American Institute of Aeronautics & Ast, Washington, D.C. ISBN 978-1-56347-342-5.
Chobotov, V.A., ур. (2002). Orbital Mechanics (3rd изд.). American Institute of Aeronautics & Ast, Washington, D.C. ISBN 978-1-56347-537-5.
Herrick, S. (1971). Astrodynamics: Orbit Determination, Space Navigation, Celestial Mechanics, Volume 1. Van Nostrand Reinhold, London. ISBN 978-0-442-03370-5.
Herrick, S. (1972). Astrodynamics: Orbit Correction, Perturbation Theory, Integration, Volume 2. Van Nostrand Reinhold, London. ISBN 978-0-442-03371-2.
Kaplan, M.H. (1976). Modern Spacecraft Dynamics and Controls. Wiley, New York. ISBN 978-0-471-45703-9.
Tom Logsdon (1997). Orbital Mechanics. Wiley-Interscience, New York. ISBN 978-0-471-14636-0.
John E. Prussing & Bruce A. Conway (1993). Orbital Mechanics. Oxford University Press, New York. ISBN 978-0-19-507834-3.
M.J. Sidi (2000). Spacecraft Dynamics and Control. Cambridge University Press, New York. ISBN 978-0-521-78780-2.
W.E. Wiesel (1996). Spaceflight Dynamics (2nd изд.). McGraw-Hill, New York. ISBN 978-0-07-070110-6.
J.P. Vinti (1998). Orbital and Celestial Mechanics. American Institute of Aeronautics & Ast, Reston, Virginia. ISBN 978-1-56347-256-5.
P. Gurfil (2006). Modern Astrodynamics. Butterworth-Heinemann. ISBN 978-0-12-373562-1.
Baez, John. „Mysteries of the gravitational 2-body problem”. Архивирано из оригинала 2008-10-21. г. Приступљено 2004-12-11.
D'Eliseo, M. M. (2007). „The first-order orbital equation”. American Journal of Physics. 75 (4): 352—355. Bibcode:2007AmJPh..75..352D. doi:10.1119/1.2432126.
Hall, Brian C. (2013), Quantum Theory for Mathematicians, Graduate Texts in Mathematics, 267, Springer, ISBN 978-1461471158 .
Leach, P. G. L.; G. P. Flessas (2003). „Generalisations of the Laplace–Runge–Lenz vector”. J. Nonlinear Math. Phys. 10 (3): 340—423. Bibcode:2003JNMP...10..340L. arXiv:math-ph/0403028 . doi:10.2991/jnmp.2003.10.3.6.
US Army (фебруар 1965), Interior Ballistics of Guns (PDF), Engineering Design Handbook: Ballistics Series, United States Army Materiel Command, AMCP 706-150, Архивирано из оригинала (PDF) 24. 9. 2020. г.
Gurstelle, William (2004), The art of the catapult: build Greek ballista, Roman onagers, English trebuchets, and more ancient artillery, Chicago: Chicago Review Press, ISBN 978-1-55652-526-1, OCLC 54529037
Liddell, Henry George; Scott, Robert, A Greek-English Lexicon (definition), Perseus, Tufts , κατά πάλλω
Marsden, Eric William (1969), Greek and Roman Artillery: Historical Development, Oxford: Clarendon, ISBN 978-0-19-814268-3 .
MSFC History Office (2000), Rockets in Ancient Times (100 B.C. to 17th Century), Marshall Space Flight Center History Office, Архивирано из оригинала 2009-07-09. г., Приступљено 2016-06-09
„catapult”, Dictionaries (definition), Oxford, Архивирано из оригинала 7. 7. 2011. г.
Schellenberg, Hans Michael (2006), „Diodor von Sizilien 14,42,1 und die Erfindung der Artillerie im Mittelmeerraum” (PDF), Frankfurter Elektronische Rundschau zur Altertumskunde, 3: 14—23
Sutton, George (2001), Rocket Propulsion Elements (7th изд.), Chichester: John Wiley & Sons, ISBN 978-0-471-32642-7
William M. Smart, Celestial Mechanics, 1961, John Wiley.
Doggett, LeRoy E. (1997), „Celestial Mechanics”, Ур.: Lankford, John, History of Astronomy: An Encyclopedia, New York: Taylor & Francis, стр. 131—140, ISBN 9780815303220
J.M.A. Danby, Fundamentals of Celestial Mechanics, 1992, Willmann-Bell
Alessandra Celletti, Ettore Perozzi, Celestial Mechanics: The Waltz of the Planets, 2007, Springer-Praxis, ISBN 0-387-30777-X.
Michael Efroimsky. 2005. Gauge Freedom in Orbital Mechanics. Annals of the New York Academy of Sciences, Vol. 1065, pp. 346-374
Alessandra Celletti, Stability and Chaos in Celestial Mechanics. Springer-Praxis 2010, XVI, 264 p., Hardcover ISBN 978-3-540-85145-5
Calvert, James B. (2003-03-28), Celestial Mechanics, University of Denver, Архивирано из оригинала 2006-09-07. г., Приступљено 2006-08-21

Spoljašnje veze

ORBITAL MECHANICS (Rocket and Space Technology)
Java Astrodynamics Toolkit
Astrodynamics-based Space Traffic and Event Knowledge Graph
Newtonian Dynamics Undergraduate level course by Richard Fitzpatrick. This includes Lagrangian and Hamiltonian Dynamics and applications to celestial mechanics, gravitational potential theory, the 3-body problem and Lunar motion (an example of the 3-body problem with the Sun, Moon, and the Earth).
Marshall Hampton's research page: Central configurations in the n-body problem
Celestial Mechanics is a Planetarium Artwork created by D. S. Hessels and G. Dunne
Professor Tatum's course notes at the University of Victoria
Italian Celestial Mechanics and Astrodynamics Association

[Herbst-1] Herbst, Judith (2005). The History of Weapons. Lerner Publications. ISBN 9780822538059. Приступљено 16. 3. 2018 — преко Google Books.

[2] Forest R. Moulton, Introduction to Celestial Mechanics, 1984, Dover, ISBN 0-486-64687-4

[3] John E. Prussing, Bruce A. Conway, Orbital Mechanics, 1993, Oxford Univ. Press

[4] Newton, Sir Isaac; Machin, John (1729). Principia. 1 (1729 translation изд.). стр. 19.

[5] Fritz Rohrlich (25. 8. 1989). From Paradox to Reality: Our Basic Concepts of the Physical World. Cambridge University Press. стр. 28—. ISBN 978-0-521-37605-1.

[6] Klaus Mainzer (2. 12. 2013). Symmetries of Nature: A Handbook for Philosophy of Nature and Science. Walter de Gruyter. стр. 8—. ISBN 978-3-11-088693-1.

[7] „Physics: Fundamental Forces and the Synthesis of Theory | Encyclopedia.com”. www.encyclopedia.com.

[8] Thomson, William T. (1961). Introduction to Space Dynamics. New York: Wiley.

[9] Bate, R. R.; Mueller, D. D.; White, J. E. (1971). Fundamentals of Astrodynamics. Courier Corporation. стр. 5. ISBN 978-0-486-60061-1.

[first-law-shaums-10] Browne, Michael E. (јул 1999). Schaum's outline of theory and problems of physics for engineering and science (Series: Schaum's Outline Series). McGraw-Hill Companies. стр. 58. ISBN 978-0-07-008498-8.

[first-law-dmmy-11] Holzner, Steven (децембар 2005). Physics for Dummies. Wiley, John & Sons, Incorporated. стр. 64. Bibcode:2005pfd..book.....H. ISBN 978-0-7645-5433-9.

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@@ Ред 2: / Ред 2: @@
 [[File:Orbital motion.gif|thumb|261px|A satellite orbiting the earth has a [[Speed#Tangential speed|tangential velocity]] and an inward [[acceleration]].]]
-'''Orbitalna mehanika''' ili '''astrodinamika''' je primena [[ballistics|balistike]] i [[celestial mechanics|nebeske mehanike]] na praktične probleme koji se tiču kretanja [[raketa]] i drugih [[spacecraft|svemirskih letelica]]. Kretanje ovih objekata se obično izračunava iz [[Newton's laws of motion|Njutnovih zakona kretanja]] i [[Newton's law of universal gravitation|zakona univerzalne gravitacije]]. Orbitalna mehanika je sržna disciplina unutar dizajna i kontrole [[space exploration|svemirskih misija]].
+'''Orbitalna mehanika''' ili '''astrodinamika''' je primena [[ballistics|balistike]]<ref name="Herbst">{{cite book|url=https://books.google.com/books?id=U-5T2Zs5qG8C&pg=PA8|title=The History of Weapons|first=Judith|last=Herbst|year=2005|publisher=Lerner Publications|isbn=9780822538059|access-date=16 March 2018|via=Google Books}}</ref> i [[celestial mechanics|nebeske mehanike]]<ref>Forest R. Moulton, ''Introduction to Celestial Mechanics'', 1984, Dover, {{ISBN|0-486-64687-4}}</ref><ref>John E. Prussing, Bruce A. Conway, ''Orbital Mechanics'', 1993, Oxford Univ. Press</ref> na praktične probleme koji se tiču kretanja [[raketa]] i drugih [[spacecraft|svemirskih letelica]]. Kretanje ovih objekata se obično izračunava iz [[Newton's laws of motion|Njutnovih zakona kretanja]]<ref>{{Cite book |url=https://books.google.com/books?id=Tm0FAAAAQAAJ&pg=PA19 |page=19 |volume=1 |edition=1729 translation |title=Principia |last1=Newton |first1=Sir Isaac |last2=Machin |first2=John |year=1729 }}</ref> i [[Newton's law of universal gravitation|zakona univerzalne gravitacije]].<ref>{{cite book|author=Fritz Rohrlich|title=From Paradox to Reality: Our Basic Concepts of the Physical World|url=https://books.google.com/books?id=3TqA1394OVcC&pg=PA28|date=25 August 1989|publisher=Cambridge University Press|isbn=978-0-521-37605-1|pages=28–}}</ref><ref>{{cite book|author=Klaus Mainzer|title=Symmetries of Nature: A Handbook for Philosophy of Nature and Science|url=https://books.google.com/books?id=QekhAAAAQBAJ&pg=PA8|date=2 December 2013|publisher=Walter de Gruyter|isbn=978-3-11-088693-1|pages=8–}}</ref><ref>{{Cite web|url=https://www.encyclopedia.com/science/science-magazines/physics-fundamental-forces-and-synthesis-theory|title=Physics: Fundamental Forces and the Synthesis of Theory &#124; Encyclopedia.com|website=www.encyclopedia.com}}</ref> Orbitalna mehanika je sržna disciplina unutar dizajna i kontrole [[space exploration|svemirskih misija]].
 [[Nebeska mehanika]] šire tretira [[Орбита|orbitalnu]] dinamiku sistema pod uticajem [[gravity|gravitacije]], uključujući svemirske letelice i prirodna [[astronomical object|astronomska tela]] poput [[Звездани систем|zvezdanih sistema]], [[planeta]], [[mesec]]a i [[kometa]]. Orbitalna mehanika se fokusira na [[Путања|putanje]] svemirskih letelica, uključujući [[Orbital maneuver|orbitalne manevre]], promene [[Orbital plane (astronomy)|orbitalne ravni]] i međuplanetarne transfere, i planeri misija je koriste da predvide rezultate [[Spacecraft propulsion|propulzivnih manevara]]. [[Opšta relativnost]] je tačnija teorija od Njutnovih zakona za izračunavanje orbita, a ponekad je neophodna i za veću tačnost ili u visoko-gravitacijskim situacijama (npr. orbite blizu Sunca).
@@ Ред 10: / Ред 10: @@
 Sve do uspona svemirskih putovanja u dvadesetom veku, postojala je mala razlika između orbitalne i nebeske mehanike. U vreme [[Sputnik]]a polje se nazivalo „svemirskom dinamikom”.<ref>{{cite book|last1=Thomson|first1=William T.|title=Introduction to Space Dynamics|date=1961|publisher=Wiley|location=New York}}</ref> Fundamentalne tehnike, poput onih koje se koriste za rešavanje [[Kepler problem|Keplerovog problema]] (određivanja položaja kao funkcije vremena), stoga su iste u obe oblasti. Pored toga, istorija polja je gotovo u potpunosti zajednička.
-[[Johan Kepler]] je bio prvi koji je uspešno modelovao planetarne orbite sa visokim stepenom tačnosti, objavivši [[Kepler's laws of planetary motion|svoje zakone]] 1605. [[Isak Njutn]] objavio je više opštih zakona nebeskog kretanja u prvom izdanju svog dela -{''[[Philosophiæ Naturalis Principia Mathematica]]''}- (1687), koji su dali metodu za pronalaženje orbite tela sledeći [[parabola|parabolični]] put iz tri opservacije.<ref>{{cite book|last1=Bate|first1=R. R.|last2=Mueller|first2=D. D.|last3=White|first3=J. E.|title=Fundamentals of Astrodynamics|url=https://books.google.com/books?id=UtJK8cetqGkC&pg=PR5|year=1971|publisher=Courier Corporation|isbn=978-0-486-60061-1|page=5}}</ref> Ovo je iskoristio [[Edmund Halej]] za uspostavljanje orbita raznih [[kometa]], uključujući i onu koja nosi njegovo ime. Njutnova metoda sukcesivne aproksimacije formalizovana je u analitičku metodu [[Леонард Ојлер|Ojlerovim]] doprinosom iz 1744. godine, čiji je rad zatim bio generalizovan na eliptične i hiperboličke orbite [[Јохан Хајнрих Ламберт|Lambertovim]] doprinosom tokom 1761-1777.
+[[Johan Kepler]] je bio prvi koji je uspešno modelovao planetarne orbite sa visokim stepenom tačnosti, objavivši [[Kepler's laws of planetary motion|svoje zakone]] 1605. [[Isak Njutn]] objavio je više opštih zakona nebeskog kretanja u prvom izdanju svog dela -{''[[Philosophiæ Naturalis Principia Mathematica]]''}- (1687), koji su dali metodu za pronalaženje orbite tela sledeći [[parabola|parabolični]] put iz tri opservacije.<ref>{{cite book|last1=Bate|first1=R. R.|last2=Mueller|first2=D. D.|last3=White|first3=J. E.|title=Fundamentals of Astrodynamics|url=https://books.google.com/books?id=UtJK8cetqGkC&pg=PR5|year=1971|publisher=Courier Corporation|isbn=978-0-486-60061-1|page=5}}</ref> Ovo je iskoristio [[Edmund Halej]] za uspostavljanje orbita raznih [[kometa]], uključujući i onu koja nosi njegovo ime. Njutnova metoda sukcesivne aproksimacije formalizovana je u analitičku metodu [[Леонард Ојлер|Ojlerovim]] doprinosom iz 1744. godine, čiji je rad zatim bio generalizovan na eliptične i hiperboličke orbite [[Јохан Хајнрих Ламберт|Lambertovim]] doprinosom tokom 1761-1777.<ref name="first-law-shaums">{{Cite book| last = Browne| first =Michael E.| title =Schaum's outline of theory and problems of physics for engineering and science| publisher = McGraw-Hill Companies| date=јул 1999| format =Series: Schaum's Outline Series| page =[https://archive.org/details/schaumsoutlineof00brow/page/58 58]| url =https://archive.org/details/schaumsoutlineof00brow| url-access = registration| isbn =978-0-07-008498-8}}</ref><ref name="first-law-dmmy">{{Cite book| last = Holzner| first = Steven | title =Physics for Dummies| publisher =Wiley, John & Sons, Incorporated| date=децембар 2005| page =[https://archive.org/details/physicsfordummie00holz/page/64 64]| url =https://archive.org/details/physicsfordummie00holz| url-access = registration| isbn =978-0-7645-5433-9| bibcode = 2005pfd..book.....H }}</ref>
 Druga prekretnica u određivanju orbite bila je pomoć [[Carl Friedrich Gauss|Karla Fridriha Gausa]] u otkriću [[dwarf planet|patuljaste planete]] [[Ceres (dwarf planet)|Ceres]] 1801. godine. [[Gausova metoda]] je mogla da koristi samo tri opažanja (u obliku parova [[Rektascenzija|rektascenzije]] i [[Deklinacija (astronomija)|deklinacije]]) da pronađe šest [[Орбитални елементи|orbitalnih elemenata]] koji u potpunosti opisuju orbitu. Teorija određivanja orbite je kasnije razvijena do tačke u kojoj se danas primenjuje u GPS prijemnicima, kao i u praćenju i katalogizaciji tek promatranih [[Minor planet|malih planeta]]. Moderno određivanje i predviđanje orbite koriste se za rad svih tipova satelita i svemirskih sondi, jer je potrebno znati njihove buduće položaje sa visokom tačnošću.
@@ Ред 16: / Ред 16: @@
 Astrodinamiku je razvio astronom [[Samuel Herrick (astronomer)|Samjuel Herik]] početkom 1930-ih. On se konsultovao sa raketnim naučnika [[Роберт Хачинс Годард|Robertom Godardom]] i bio je ohrabren je da nastavi svoj rad na svemirskim navigacionim tehnikama, jer je Godard verovao da će one biti potrebne u budućnosti. Numeričke tehnike astrodinamike bile su povezane sa novim moćnim računarima 1960-ih godina i čovek je bio spreman da putuje na [[Mesec]] i da se vrati.
-==Reference==
+== Reference ==
 {{Reflist}}
@@ Ред 22: / Ред 22: @@
 {{Refbegin|30em}}
 * {{cite book|author=Curtis, Howard D.|title=Orbital Mechanics for Engineering Students, 2e|publisher=Elsevier|location=New York|date=2009|isbn=978-0-12-374778-5}}
+* {{cite book |last=Bate |first=Roger R. |author2=Mueller, Donald D. |author3=White, Jerry E. |title=Fundamentals of Astrodynamics |date=1971 |publisher=Dover Publications |location=New York |isbn=0-486-60061-0 |pages= |url=https://archive.org/details/fundamentalsofas00bate }}
-* {{cite book
+* {{cite book |last=Sellers |first=Jerry J. |author2=Astore, William J. |author3=Giffen, Robert B. |author4=Larson, Wiley J. |editor=Kirkpatrick, Douglas H. |title=Understanding Space: An Introduction to Astronautics |url=https://archive.org/details/understandingspa00sell |edition=2 |date=2004 |publisher=McGraw Hill |isbn=0-07-242468-0 |pages=[https://archive.org/details/understandingspa00sell/page/n245 228]}}
-|last=Bate
-|first=Roger R.
-|author2=Mueller, Donald D.
-|author3=White, Jerry E.
-|title=Fundamentals of Astrodynamics
-|date=1971
-|publisher=Dover Publications
-|location=New York
-|isbn=0-486-60061-0
-|pages=
-|url=https://archive.org/details/fundamentalsofas00bate
-}}
-* {{cite book
-|last=Sellers
-|first=Jerry J.
-|author2=Astore, William J. |author3=Giffen, Robert B. |author4=Larson, Wiley J.
-|editor=Kirkpatrick, Douglas H.
-|title=Understanding Space: An Introduction to Astronautics
-|url=https://archive.org/details/understandingspa00sell
-|edition=2
-|date=2004
-|publisher=McGraw Hill
-|isbn=0-07-242468-0
-|pages=[https://archive.org/details/understandingspa00sell/page/n245 228]}}
 * {{cite web |url=http://space.au.af.mil/primer/orbital_mechanics.pdf |title=Air University Space Primer, Chapter 8 - Orbital Mechanics |publisher=USAF |access-date=2007-10-13 |archive-url=https://web.archive.org/web/20130214090912/http://space.au.af.mil/primer/orbital_mechanics.pdf |archive-date=2013-02-14 |url-status=dead }}
 * {{cite book|author=Bate, R.R.|author2=Mueller, D.D.|author3=White, J.E.|title=Fundamentals of Astrodynamics|publisher=Dover Publications, New York|date=1971|isbn=978-0-486-60061-1|url=https://archive.org/details/fundamentalsofas00bate}}
@@ Ред 65: / Ред 42: @@
 * {{citation|first=Brian C.|last=Hall|title=Quantum Theory for Mathematicians|series=Graduate Texts in Mathematics|volume=267 |publisher=Springer|year=2013|isbn=978-1461471158}}.
 * {{cite journal | first=P. G. L. |last=Leach |author2=G. P. Flessas  | title=Generalisations of the Laplace–Runge–Lenz vector | journal=J. Nonlinear Math. Phys. | volume=10 |issue=3 | date=2003 | pages=340–423 | arxiv=math-ph/0403028 | doi=10.2991/jnmp.2003.10.3.6 |bibcode = 2003JNMP...10..340L }}
+* {{Citation |author=US Army |date=February 1965  |title=Interior Ballistics of Guns |series=Engineering Design Handbook: Ballistics Series |id=AMCP 706-150 |publisher=United States Army Materiel Command |url=https://apps.dtic.mil/dtic/tr/fulltext/u2/462060.pdf |archive-url=https://web.archive.org/web/20200924032323/https://apps.dtic.mil/dtic/tr/fulltext/u2/462060.pdf |url-status=dead |archive-date=September 24, 2020 }}
+* {{Citation |last= Gurstelle |first= William |author-link= William Gurstelle |year= 2004 |title= The art of the catapult: build Greek ballista, Roman onagers, English trebuchets, and more ancient artillery |publisher= Chicago Review Press |location= Chicago |isbn= 978-1-55652-526-1 |oclc= 54529037 |url-access= registration |url= https://archive.org/details/artofcatapult00will }}
+* {{Citation |last1=Liddell |first1=Henry George |last2=Scott |first2=Robert |title=A Greek-English Lexicon |type=definition |series=Perseus |publisher=Tufts }}, [https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Dkata%2F1 κατά]  [https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Dpa%2Fllw πάλλω]
+* {{Citation |last=Marsden  |first=Eric William  |year=1969  |title=Greek and Roman Artillery: Historical Development |publisher=Clarendon |place=Oxford|isbn=978-0-19-814268-3}}.
+* {{Citation |author=MSFC History Office |year=2000 |title=Rockets in Ancient Times (100 B.C. to 17th Century) |publisher=[[Marshall Space Flight Center]] History Office |url=http://history.msfc.nasa.gov/rocketry/tl1.html |access-date=2016-06-09 |archive-url=https://web.archive.org/web/20090709042712/http://history.msfc.nasa.gov/rocketry/tl1.html |archive-date=2009-07-09 |url-status=dead }}
+* {{Citation |ref={{harvid|Oxford Dic}}|url=http://oxforddictionaries.com/definition/catapult |archive-url=https://web.archive.org/web/20110707113215/http://oxforddictionaries.com/definition/catapult |url-status=dead |archive-date=July 7, 2011 |contribution=catapult |publisher=Oxford |title=Dictionaries |type=definition}}
+* {{Citation |last=Schellenberg |first=Hans Michael |year=2006 |url=http://s145739614.online.de/fera/ausgabe3/Schellenberg.pdf |title=Diodor von Sizilien 14,42,1 und die Erfindung der Artillerie im Mittelmeerraum |journal=Frankfurter Elektronische Rundschau zur Altertumskunde |volume=3 |pages=14–23}}
+* {{Citation |last=Sutton |first=George |title=Rocket Propulsion Elements |edition=7th |url=https://books.google.com/books?id=LQbDOxg3XZcC |publisher=John Wiley & Sons |location=Chichester |year=2001 |isbn=978-0-471-32642-7 }}
+* William M. Smart, ''Celestial Mechanics'', 1961, John Wiley.
+* {{ Citation | last = Doggett | first = LeRoy E. | editor-last = Lankford | editor-first = John | date = 1997 | title = History of Astronomy: An Encyclopedia | chapter = Celestial Mechanics | publisher = Taylor & Francis | place = New York | pages = 131–140 | isbn = 9780815303220 | url = https://books.google.com/books?id=fIzMMe3VczkC }}
+* J.M.A. Danby, ''Fundamentals of Celestial Mechanics'', 1992, Willmann-Bell
+* Alessandra Celletti, Ettore Perozzi, ''Celestial Mechanics: The Waltz of the Planets'', 2007, Springer-Praxis, {{ISBN|0-387-30777-X}}.
+* Michael Efroimsky. 2005. ''Gauge Freedom in Orbital Mechanics.'' [https://archive.today/2013.01.05-074903/http://www3.interscience.wiley.com/journal/118692589/abstract?CRETRY=1&SRETRY=0 Annals of the New York Academy of Sciences, Vol. 1065, pp. 346-374]
+* Alessandra Celletti, ''Stability and Chaos in Celestial Mechanics.'' Springer-Praxis 2010, XVI, 264 p., Hardcover {{ISBN|978-3-540-85145-5}}
+* {{Citation | last = Calvert | first = James B. | date = 2003-03-28 | url = http://www.du.edu/~jcalvert/phys/orbits.htm | title = Celestial Mechanics | publisher = University of Denver | access-date = 2006-08-21 | archive-url = https://web.archive.org/web/20060907120741/http://www.du.edu/~jcalvert/phys/orbits.htm | archive-date = 2006-09-07 | url-status = dead }}
 {{refend}}
@@ Ред 72: / Ред 65: @@
 * -{[http://jat.sourceforge.net Java Astrodynamics Toolkit]}-
 * -{[http://astria.tacc.utexas.edu/AstriaGraph/ Astrodynamics-based Space Traffic and Event Knowledge Graph]}-
+* [http://farside.ph.utexas.edu/teaching/336k/Newton.pdf Newtonian Dynamics] Undergraduate level course by Richard Fitzpatrick. This includes Lagrangian and Hamiltonian Dynamics and applications to celestial mechanics, gravitational potential theory, the 3-body problem and Lunar motion (an example of the 3-body problem with the Sun, Moon, and the Earth).
+* [http://www.math.washington.edu/~hampton/research.html Marshall Hampton's research page: Central configurations in the n-body problem]
+* [https://web.archive.org/web/20190428072152/http://www.cmlab.com/ Celestial Mechanics is a Planetarium Artwork created by D. S. Hessels and G. Dunne]
+* [http://orca.phys.uvic.ca/~tatum/celmechs.html Professor Tatum's course notes at the University of Victoria]
+* [http://www.mat.uniroma2.it/simca/english.html Italian Celestial Mechanics and Astrodynamics Association]
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