Editing Space rendezvous (section)

===Methods of approach===

The two most common methods of approach for [[proximity operations]] are in-line with the flight path of the spacecraft (called V-bar, as it is along the velocity vector of the target) and [[orthogonal|perpendicular]] to the flight path along the line of the radius of the orbit (called R-bar, as it is along the radial vector, with respect to Earth, of the target).<ref name=wertz2003>
{{cite journal |last=Wertz|first=James R. |author2=Bell, Robert  |editor-first1=Peter |editor-first2=James |editor-last1=Tchoryk, Jr. |editor-last2=Shoemaker |title=Autonomous Rendezvous and Docking Technologies – Status and Prospects |journal=SPIE AeroSense Symposium |date=2003 |series=Space Systems Technology and Operations Conference, Orlando Florida, April 21–25, 2003 |volume=5088 |page=20 |doi=10.1117/12.498121 |bibcode=2003SPIE.5088...20W |s2cid=64002452 |id=Paper 5088-3 |url=http://microcosminc.com/analysis/spie03.pdf|archive-url=https://web.archive.org/web/20120425122952/http://microcosminc.com/analysis/spie03.pdf|url-status=dead|archive-date=2012-04-25|access-date=August 3, 2019}}</ref>
The chosen method of approach depends on safety, spacecraft / thruster design, mission timeline, and, especially for docking with the ISS, on the location of the assigned docking port.

==== V-bar approach====
The V-bar approach is an approach of the "chaser" horizontally along the passive spacecraft's velocity vector. That is, from behind or from ahead, and in the same direction as the orbital motion of the passive target. The motion is [[wikt:parallel|parallel]] to the target's orbital velocity.<ref name=wertz2003/><ref name="pearson1989">{{cite web | last=Pearson|first=Don J.|date=November 1989 |title=Shuttle Rendezvous and Proximity Operations|url=http://home.comcast.net/~djpearson/rndz/rndzpaper.html|access-date=November 26, 2011|work=originally presented at COLLOQUE: MECANIQUE SPATIALE (SPACE DYNAMICS) TOULOUSE, FRANCE NOVEMBER 1989 |publisher=NASA|archive-date=July 27, 2013|archive-url=https://web.archive.org/web/20130727004238/http://home.comcast.net/~djpearson/rndz/rndzpaper.html|url-status=live}}</ref><!-- ref 'pearson1989' provides examples of V-bar and R-bar approaches, without definitions -->
In the V-bar approach from behind, the chaser fires small thrusters to increase its velocity in the direction of the target. This, of course, also drives the chaser to a higher orbit. To keep the chaser on the V-vector, other thrusters are fired in the radial direction. If this is omitted (for example due to a thruster failure), the chaser will be carried to a higher orbit, which is associated with an orbital velocity lower than the target's. Consequently, the target moves faster than the chaser and the distance between them increases. This is called a ''natural braking effect'', and is a natural safeguard in case of a thruster failure.{{citation needed|date=June 2014}}

[[STS-104]] was the third [[Space Shuttle]] mission to conduct a V-bar arrival at the [[International Space Station]].<ref>
{{cite web | url = http://spaceflight.nasa.gov/shuttle/archives/sts-104/crew/inthobaugh.html | archive-url = https://web.archive.org/web/20020203145933/http://spaceflight.nasa.gov/shuttle/archives/sts-104/crew/inthobaugh.html | url-status = dead | archive-date = 2002-02-03 | title = STS-104 Crew Interviews with Charles Hobaugh, Pilot | publisher = NASA}}</ref>  The V-bar, or [[Orbital state vectors|velocity vector]], extends along a line directly ahead of the station. Shuttles approach the ISS along the V-bar when docking at the [[Pressurized Mating Adapter|PMA-2]] docking port.<ref name=harwood>{{cite web |url=http://spaceflightnow.com/station/stage5a1/010309fd2/ |title=Shuttle Discovery nears rendezvous with station |publisher=SPACEFLIGHT NOW |author=WILLIAM HARWOOD |date=March 9, 2001 |access-date=March 17, 2009 |archive-date=December 2, 2008 |archive-url=https://web.archive.org/web/20081202151744/http://spaceflightnow.com/station/stage5a1/010309fd2/ |url-status=live }}</ref>

==== R-bar approach====
The R-bar approach consists of the chaser moving below or above the target spacecraft, along its radial vector. The motion is [[orthogonal]] to the orbital velocity of the passive spacecraft.<ref name=wertz2003/><ref name=pearson1989/><!-- ref 'pearson1989' provides examples of V-bar and R-bar approaches, without definitions -->
When below the target the chaser fires radial thrusters to close in on the target. By this it increases its altitude. However, the orbital velocity of the chaser remains unchanged (thruster firings in the radial direction have no effect on the orbital velocity). Now in a slightly higher position, but with an orbital velocity that does not correspond to the local circular velocity, the chaser slightly falls behind the target. Small rocket pulses in the orbital velocity direction are necessary to keep the chaser along the radial vector of the target. If these rocket pulses are not executed (for example due to a thruster failure), the chaser will move away from the target. This is a ''natural braking effect''. For the R-bar approach, this effect is stronger than for the V-bar approach, making the R-bar approach the safer one of the two.{{citation needed|date=June 2014}}
Generally, the R-bar approach from below is preferable, as the chaser is in a lower (faster) orbit than the target, and thus "catches up" with it. For the R-bar approach from above, the chaser is in a higher (slower) orbit than the target, and thus has to wait for the target to approach it.{{citation needed|date=June 2014}}

[[Astrotech Corporation|Astrotech]] proposed meeting ISS cargo needs with a vehicle which would approach the station, "using a traditional nadir R-bar approach."<ref>
{{cite conference
 |last        = Johnson
 |first       = Michael D.
 |author2     = Fitts, Richard
 |author3     = Howe, Brock
 |author4     = Hall, Baron
 |author5     = Kutter, Bernard
 |author6     = Zegler, Frank
 |author7     = Foster
 |author8     = Mark
 |title       = Astrotech Research & Conventional Technology Utilization Spacecraft (ARCTUS)
 |book-title  = AIAA SPACE 2007 Conference & Exposition
 |page        = 7
 |place       = Long Beach, California
 |date        = September 18, 2007
 |url         = http://pdf.aiaa.org/preview/CDReadyMSPACE07_1808/PV2007_6130.pdf
 |url-status     = dead
 |archive-url  = https://web.archive.org/web/20080227050750/http://pdf.aiaa.org/preview/CDReadyMSPACE07_1808/PV2007_6130.pdf
 |archive-date = February 27, 2008
 |df          = mdy-all
}}</ref> The nadir R-bar approach is also used for flights to the ISS of [[H-II Transfer Vehicle]]s, and of [[SpaceX Dragon]] vehicles.<ref>''Rendezvous Strategy of the Japanese Logistics Support Vehicle to the International Space Station,'' [http://adsabs.harvard.edu/full/1997ESASP.381..103Y] {{Webarchive|url=https://web.archive.org/web/20210505175034/http://adsabs.harvard.edu/full/1997ESASP.381..103Y|date=May 5, 2021}}</ref><ref>''Success! Space station snags SpaceX Dragon capsule'' [http://news.cnet.com/8301-11386_3-57441570-76/success-space-station-snags-spacex-dragon-capsule/] {{Webarchive|url=https://web.archive.org/web/20120525171424/http://news.cnet.com/8301-11386_3-57441570-76/success-space-station-snags-spacex-dragon-capsule/|date=May 25, 2012}}</ref>

==== Z-bar approach====
An approach of the active, or "chaser", spacecraft horizontally from the side and orthogonal to the [[Orbital elements|orbital plane]] of the passive spacecraft—that is, from the side and out-of-plane of the orbit of the passive spacecraft—is called a Z-bar approach.<ref name=bessel1993>
{{cite journal |last=Bessel|first=James A. |author2=Ceney, James M.  |author3=Crean, David M.  |author4=Ingham, Edward A.  |author5= Pabst, David J.  |title=Prototype Space Fabrication Platform |journal=Air Force Institute of Technology, Wright-Patterson AFB, Ohio – School of Engineering |date=December 1993 |series=Accession number ADA273904 |page=9 |bibcode=1993MsT..........9B |url=http://handle.dtic.mil/100.2/ADA273904 |archive-url=https://web.archive.org/web/20120531101530/http://handle.dtic.mil/100.2/ADA273904 |url-status=dead |archive-date=May 31, 2012 |access-date=November 3, 2011}}</ref><!-- Note: a drawing exists in this US Federal Government publication https://web.archive.org/web/20120531101530/http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA273904&Location=U2&doc=GetTRDoc.pdf that graphically illustrates the R-Bar, V-Bar, and Z-Bar approaches. This could probably be cleaned up and modified to make an illustration for this article. -->