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Thitut (คุย | ส่วนร่วม)
หน้าใหม่: {{short description|Elliptical orbit used to transfer between two orbits of different altitudes, in the same plane}} File:Hohmann transfer orbit.svg|thumb|Hohmann tran...
 
Thitut (คุย | ส่วนร่วม)
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{{short description|วงโคจรรีที่ใช้ในการถ่ายโอนระหว่างสองวงโคจรที่มีความสูงแตกต่างกัน ที่อยู่ในระนาบเดียวกัน}}
{{short description|Elliptical orbit used to transfer between two orbits of different altitudes, in the same plane}}
[[File:Hohmann transfer orbit.svg|thumb|Hohmann transfer orbit, labelledวงโคจรถ่ายโอนโฮมันน์ (2,) from an orbitจากวงโคจรระดับต่ำ (1) to a higher orbitไปยังวงโคจรที่สูงขึ้น (3)]]
[[File:Animation of InSight trajectory.gif|thumb |right |Anตัวอย่างของวงโคจรถ่ายโอนโฮมันน์ระหว่างโลก example of a Hohmann transfer orbit between Earth and Mars, as used by theและดาวอังคาร อย่างที่ถูกใช้โดยยาน[[NASAอินไซต์]] ของ[[InSightนาซา]] probe.<br/>{{legend2legend2|magenta| Hohmannวงโคจรถ่ายโอนโฮมันน์}}{{·}}{{legend2legend2| RoyalBlue |[[Earthโลก]]}}{{·}}{{legend2legend2| Lime |[[Marsดาวอังคาร]]}}]]
{{Astrodynamics}}
ใน[[กลศาสตร์วงโคจร]] '''วงโคจรถ่ายโอนโฮมันน์''' เป็น[[วงโคจรรี]]ที่ใช้เพื่อถ่ายโอนระหว่าง[[วงโคจรกลม]]สองวงที่มีรัศมีจากวัตถุศูนย์กลางต่างกัน แต่อยู่ใน[[ระนาบ]]เดียวกัน การถ่ายโอนโฮมันน์มักจะเป็นวิธีที่ใช้เชื้อเพลิงน้อยที่สุดในการเดินทางระหว่างวงโคจร แต่[[วงโคจรถ่ายโอนสองวงรี|การถ่ายโอนสองวงรี]]สามารถใช้เชื้อเพลิงน้อยกว่าในบางกรณี
In [[orbital mechanics]], the '''Hohmann transfer orbit''' ({{IPAc-en|ˈ|h|oʊ|m|ə|n}}) is an [[elliptical orbit]] used to transfer between two [[circular orbit]]s of different radii around a central body in the same [[Plane (geometry)|plane]]. The Hohmann transfer often uses the lowest possible amount of [[propellant]] in traveling between these orbits, but [[bi-elliptic transfer]]s can use less in some cases.
 
[[การเคลื่อนย้ายวงโคจร]]เพื่อทำการถ่ายโอนโฮมันน์ ใช้การจุดเครื่องยนต์สองครั้ง ครั้งแรกเพื่อเคลื่อน[[ยานอวกาศ]]เข้าสู่วงโคจรถ่ายโอน และครั้งที่สองเพื่อเคลื่อนออกจากวงโคจรถ่ายโอน การเคลื่อนย้ายนี้ถูกตั้งชื่อตาม [[วอลเตอร์ โฮมันน์]] นักวิทยาศาสตร์ชาว[[เยอรมันนี|เยอรมัน]]ผู้ตีพิมพ์คำอธิบายลักษณะวงโคจรในหนังสือของเขา ''Die Erreichbarkeit der Himmelskörper'' (''ความเป็นไปได้ของเทหวัตถุ'') ที่ตีพิมพ์ในปี 1925<ref>Walter Hohmann, ''The Attainability of Heavenly Bodies'' (Washington: NASA Technical Translation F-44, 1960) [https://archive.org/details/nasa_techdoc_19980230631 Internet Archive].</ref> โฮมันน์ได้รับอิทธิพลในบางส่วนจากกวีนิยายวิทยาศาสตร์ชาวเยอรมัน เคิร์ด ลัสวิทซ์ และจากหนังสือ''[[สองดาวเคราะห์]]'' ที่ตีพิมพ์ในปี 1897 ของเขา
The [[orbital maneuver]] to perform the Hohmann transfer uses two engine impulses, one to move a [[spacecraft]] onto the [[transfer orbit]] and a second to move off it. This maneuver was named after [[Walter Hohmann]], the [[Germany|German]] scientist who published a description of it in his 1925 book ''Die Erreichbarkeit der Himmelskörper'' (''The Attainability of Celestial Bodies'').<ref>Walter Hohmann, ''The Attainability of Heavenly Bodies'' (Washington: NASA Technical Translation F-44, 1960) [https://archive.org/details/nasa_techdoc_19980230631 Internet Archive].</ref> Hohmann was influenced in part by the German science fiction author [[Kurd Lasswitz]] and his 1897 book ''[[Two Planets]]''.
 
The elliptic transfer orbits between different bodies (planets, moons etc.) are often referred to as Hohmann transfer orbits. When used for traveling between celestial bodies, a Hohmann transfer orbit requires that the starting and destination points be at particular locations in their orbits relative to each other. Space missions using a Hohmann transfer must wait for this required alignment to occur, which opens a so-called [[launch window]]. For a space mission between [[Earth]] and [[Mars]], for example, these launch windows occur every 26 months. A Hohmann transfer orbit also determines a fixed time required to travel between the starting and destination points; for an Earth-Mars journey this travel time is about 9 months. When transfer is performed between orbits close to celestial bodies with significant gravitation, much less [[delta-v]] is usually required, as the [[Oberth effect]] may be employed for the burns.
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They are also often used for these situations, but [[low-energy transfer]]s which take into account the thrust limitations of real engines, and take advantage of the gravity wells of both planets can be more fuel efficient.<ref>{{Cite web|url=https://www.universetoday.com/117615/making-the-trip-to-mars-cheaper-and-easier-the-case-for-ballistic-capture/|title=Making the Trip to Mars Cheaper and Easier: The Case for Ballistic Capture|last=Williams|first=Matt|date=2014-12-26|website=Universe Today|language=en-US|access-date=2019-07-29}}</ref><ref>{{Cite web|url=https://www.scientificamerican.com/article/a-new-way-to-reach-mars-safely-anytime-and-on-the-cheap/|title=A New Way to Reach Mars Safely, Anytime and on the Cheap|last=Hadhazy|first=Adam|website=Scientific American|language=en|access-date=2019-07-29}}</ref><ref>{{Cite web|url=https://gereshes.com/2019/04/08/an-introduction-to-beresheet-and-its-trajectory-to-the-moon/|title=An Introduction to Beresheet and Its Trajectory to the Moon|date=2019-04-08|website=Gereshes|language=en-US|access-date=2019-07-29}}</ref>
 
==คำอธิบาย==
== Explanation ==
The diagram shows a Hohmann transfer orbit to bring a spacecraft from a lower circular orbit into a higher one. It is one half of an [[elliptic orbit]] that touches both the lower circular orbit the spacecraft wishes to leave (green and labeled ''1'' on diagram) and the higher circular orbit that it wishes to reach (red and labeled ''3'' on diagram). The transfer (yellow and labeled ''2'' on diagram) is initiated by firing the spacecraft's engine to accelerate it so that it will follow the elliptical orbit. This adds energy to the spacecraft's orbit. When the spacecraft has reached its destination orbit, its orbital speed (and hence its orbital energy) must be increased again to change the elliptic orbit to the larger circular one.
 
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The Hohmann transfer orbit is based on two [[Impulse function|instantaneous]] velocity changes. Extra fuel is required to compensate for the fact that the bursts take time; this is minimized by using high-thrust engines to minimize the duration of the bursts. For transfers in Earth orbit, the two burns are labelled the ''perigee burn'' and the ''apogee burn'' (or '[[Apogee kick motor|'apogee kick'']]<ref>Jonathan McDowell, "[https://arc.aiaa.org/doi/pdf/10.2514/6.1997-3133 Kick In the Apogee: 40 years of upper stage applications for solid rocket motors, 1957-1997]", 33rd AIAA Joint Propulsion Conference, July 4, 1997. [https://arc.aiaa.org/doi/abs/10.2514/6.1997-3133 abstract]. Retrieved 18 July 2017.</ref>); more generally, they are labelled ''periapsis'' and ''apoapsis'' burns. Alternately, the second burn to circularize the orbit may be referred to as a ''circularization burn''.
 
===ประเภท 1 และประเภท 2===
===Type I and Type II===
 
An ideal Hohmann transfer orbit transfers between two circular orbits in the same plane and traverses exactly 180° around the primary. In the real world, the destination orbit may not be circular, and may not be coplanar with the initial orbit. Real world transfer orbits may traverse slightly more, or slightly less, than 180° around the primary. An orbit which traverses less than 180° around the primary is called a "Type I" Hohmann transfer, while an orbit which traverses more than 180° is called a "Type II" Hohmann transfer.<ref name= "NASA-trajectories">NASA, ''Basics of Space Flight'', Section 1, Chapter 4, "[https://solarsystem.nasa.gov/basics/chapter4-1 Trajectories]". Retrieved 26 July 2017. Also available [https://spaceodyssey.dmns.org/media/57432/hohmann_transfer_orbits.pdf spaceodyssey.dmns.org].</ref><ref>Tyson Sparks, [http://ccar.colorado.edu/asen5050/projects/projects_2015/Students/Alpert_Brian/interplanetary_transfer.html Trajectories to Mars], Colorado Center for Astrodynamics Research, 12/14/2012. Retrieved 25 July 2017.</ref>
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Transfer orbits can go more than 360° around the sun. These multiple-revolution transfers are sometimes referred to as Type III and Type IV, where a Type III is a Type I plus 360°, and a Type IV is a Type II plus 360°.<ref>Langevin, Y. (2005). "Design issues for Space Science Missions," ''Payload and Mission Definition in Space Sciences'', V. Mártínez Pillet, A. Aparicio, and F. Sánchez, eds., Cambridge University Press, p. 30. {{ISBN|052185802X}}, 9780521858021</ref>
 
==การคำนวณ==
== Calculation ==
For a small body orbiting another much larger body, such as a satellite orbiting Earth, the total energy of the smaller body is the sum of its [[kinetic energy]] and [[potential energy]], and this total energy also equals half the potential at the [[Semi-major axis#Average distance|
average distance]] <math>a</math> (the [[semi-major axis]]):
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:<math> \alpha = \pi - \omega_2 t_\text{H} = \pi\left(1 -\frac{1}{2\sqrt{2}}\sqrt{\left(\frac{r_1}{r_2} + 1\right)^3}\right). </math>
 
==ตัวอย่าง==
== Example ==
[[File:Total energy during Hohmann transfer.png|thumb|upright=1.2|Total energy balance during a Hohmann transfer between two circular orbits with first radius <math>r_p</math> and second radius <math>r_a</math>]]
Consider a [[geostationary transfer orbit]], beginning at ''r''<sub>1</sub> = 6,678&nbsp;km (altitude 300&nbsp;km) and ending in a [[geostationary orbit]] with ''r''<sub>2</sub> = 42,164&nbsp;km (altitude 35,786&nbsp;km).
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This is ''greater'' than the Δv required for an [[escape orbit]]: 10.93&nbsp;−&nbsp;7.73 = 3.20&nbsp;km/s. Applying a Δv at the [[Low Earth orbit]] (LEO) of only 0.78&nbsp;km/s more (3.20−2.42) would give the rocket the [[escape speed]], which is less than the Δv of 1.46&nbsp;km/s required to circularize the geosynchronous orbit. This illustrates the [[Oberth effect]] that at large speeds the same Δv provides more [[specific orbital energy]], and energy increase is maximized if one spends the Δv as quickly as possible, rather than spending some, being decelerated by gravity, and then spending some more to overcome the deceleration (of course, the objective of a Hohmann transfer orbit is different).
 
==กรณีเลวร้ายที่สุด เดลตา-''วี'' สูงสุด==
== Worst case, maximum delta-''v'' ==
As the example above demonstrates, the Δ''v'' required to perform a Hohmann transfer between two circular orbits is not the greatest when the destination radius is infinite. (Escape speed is {{radic|2}} times orbital speed, so the Δv required to escape is {{radic|2}}&nbsp;−&nbsp;1 (41.4%) of the orbital speed.) The Δv required is greatest (53.0% of smaller orbital speed) when the radius of the larger orbit is 15.5817... times that of the smaller orbit.<ref>{{Cite book |last=Vallado |first=David Anthony |title=Fundamentals of Astrodynamics and Applications |page=317 |publisher=Springer |date=2001 |isbn=0-7923-6903-3 |url=https://books.google.com/books?id=PJLlWzMBKjkC}}</ref> This number is the positive root of &nbsp;x<sup>3</sup>&nbsp;−&nbsp;15&nbsp;x<sup>2</sup>&nbsp;−&nbsp;9&nbsp;x&nbsp;−&nbsp;1&nbsp;=&nbsp;0, which is&nbsp; <math>5+4\,\sqrt{7}\cos\left({1\over 3}\arctan{\sqrt{3}\over 37}\right)</math>. For higher orbit ratios the Δ''v'' required for the second burn decreases faster than the first increases.
 
==การประยุกต์ใช้สำหรับการเดินทางระหว่างดาวเคราะห์==
== Application to interplanetary travel ==
 
When used to move a spacecraft from orbiting one planet to orbiting another, the situation becomes somewhat more complex, but much less delta-''v'' is required, due to the [[Oberth effect]], than the sum of the delta-''v'' required to escape the first planet plus the delta-''v'' required for a Hohmann transfer to the second planet.
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To get to the Sun, it is actually not necessary to use a Δ''v'' of 24&nbsp;km/s. One can use 8.8&nbsp;km/s to go very far away from the Sun, then use a negligible Δ''v'' to bring the angular momentum to zero, and then fall into the Sun. This can be considered a sequence of two Hohmann transfers, one up and one down. Also, the table does not give the values that would apply when using the Moon for a [[gravity assist]]. There are also possibilities of using one planet, like Venus which is the easiest to get to, to assist getting to other planets or the Sun.
 
==การเปรียบเทียบกับการถ่ายโอนแบบอื่น==
==Comparison to other transfers==
 
===การถ่ายโอนสองวงรี===
=== Bi-elliptic transfer ===
{{main|วงโคจรถ่ายโอนสองวงรี}}
{{main|Bi-elliptic transfer}}
The bi-elliptic transfer consists of two half-[[elliptic orbit]]s. From the initial orbit, a first burn expends delta-v to boost the spacecraft into the first transfer orbit with an [[apoapsis]] at some point <math>r_b</math> away from the [[central body]]. At this point a second burn sends the spacecraft into the second elliptical orbit with [[periapsis]] at the radius of the final desired orbit, where a third burn is performed, injecting the spacecraft into the desired orbit.<ref name="Curtis">{{Cite book | last = Curtis | first = Howard | title = Orbital Mechanics for Engineering Students | page = 264 | publisher = [[Elsevier]] | year = 2005 | isbn = 0-7506-6169-0 | url = https://books.google.com/books?id=6aO9aGNBAgIC}}</ref>
 
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{{Citation |last=Sternfeld |first=Ary {{sic|J.|expected=A.}} |title=Sur les trajectoires permettant d'approcher d'un corps attractif central à partir d'une orbite keplérienne donnée |language=French |trans-title=On the allowed trajectories for approaching a central attractive body from a given Keplerian orbit |url=http://gallica.bnf.fr/ark:/12148/bpt6k31506/f711.image.langEN |journal=Comptes rendus de l'Académie des sciences |location=Paris |volume=198 |number=1 |date=1934-02-12 |pages=711–713}}.</ref>
 
===การถ่ายโอนแรงผลักดันต่ำ===
=== Low-thrust transfer ===
{{main|Low thrust relative orbital transfer}}
Low-thrust engines can perform an approximation of a Hohmann transfer orbit, by creating a gradual enlargement of the initial circular orbit through carefully timed engine firings. This requires a [[Delta-v|change in velocity (delta-''v'')]] that is greater than the two-impulse transfer orbit<ref name="MIT_16.522">MIT, ''16.522: Space Propulsion'', Session 6, "[https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-522-space-propulsion-spring-2015/lecture-notes/MIT16_522S15_Lecture6.pdf Analytical Approximations for Low Thrust Maneuvers]", Spring 2015 (retrieved 26 July 2017)
</ref> and takes longer to complete.
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Transfer orbits using electrical propulsion or low-thrust engines optimize the transfer time to reach the final orbit and not the delta-v as in the Hohmann transfer orbit. For geostationary orbit, the initial orbit is set to be supersynchronous and by thrusting continuously in the direction of the velocity at apogee, the transfer orbit transforms to a circular geosynchronous one. This method however takes much longer to achieve due to the low thrust injected into the orbit.<ref>{{Cite book | last = Spitzer | first = Arnon | title = Optimal Transfer Orbit Trajectory using Electric Propulsion | publisher = [[USPTO]] | date = 1997 | url = http://www.google.com/patents/US5595360}}</ref>
 
===เครือข่ายขนส่งระหว่างดาวเคราะห์===
===Interplanetary Transport Network===
{{main article|เครือข่ายขนส่งระหว่างดาวเคราะห์}}
{{main article|Interplanetary Transport Network}}
In 1997, a set of orbits known as the Interplanetary Transport Network (ITN) was published, providing even lower propulsive delta-''v'' (though much slower and longer) paths between different orbits than Hohmann transfer orbits.<ref>{{cite web |last1= Lo |first1= M. W. |author1-link= Martin Lo |first2= S. D. |last2= Ross |title= Surfing the Solar System: Invariant Manifolds and the Dynamics of the Solar System |publisher= [[JPL]] |work= Technical Report |series= IOM |id= 312/97 |pages= 2–4 |date= 1997 |url= http://www.gg.caltech.edu/~mwl/publications/publications2.htm }}</ref> The Interplanetary Transport Network is different in nature than Hohmann transfers because Hohmann transfers assume only one large body whereas the Interplanetary Transport Network does not. The Interplanetary Transport Network is able to achieve the use of less propulsive delta-''v'' by employing [[gravity assist]] from the planets.{{citation needed|date=January 2016}}
 
==ดูเพิ่ม==
== See also ==
{{Portal|Spaceflightการบินอวกาศ}}
*[[Bi-elliptic transfer]]
*[[Delta-v budget]]
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*[[Orbital mechanics]]
 
==อ้างอิง==
== Citations==
{{reflist}}
 
==Sourcesที่มา==
*{{cite book | author= Walter Hohmann | title = Die Erreichbarkeit der Himmelskörper
|publisher= Verlag Oldenbourg in München | date = 1925 | isbn = 3-486-23106-5}}
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* {{cite book|author=Battin, R.H.|title=An Introduction to the Mathematics and Methods of Astrodynamics|publisher = American Institute of Aeronautics & Ast, Washington, DC|date=1999|isbn=978-1-56347-342-5}}
 
==ลิงค์ภายนอก==
== External links ==
* {{cite web |url= http://www.braeunig.us/space/orbmech.htm |title= Orbital Mechanics |website= Rocket and Space Technology |publisher= Robert A. Braeunig |access-date= 2005-08-17 |archive-url= https://web.archive.org/web/20120204054322/http://www.braeunig.us/space/orbmech.htm |archive-date= 2012-02-04 |url-status= dead }}
* {{cite book |chapter-url=https://solarsystem.nasa.gov/basics/chapter4-1 |title= Basics of Spaceflight |chapter= 4. Interplanetary Trajectories |publisher= [[NASA]] |location= JPL }}