Paraxial approximation: Difference between revisions

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en>Srleffler
The accuracy statement is confusing because it follows the second-order cosine expression immediately with a statement about the first-order approximation, without explanation. The whole approximation either passes or fails.
en>Srleffler
m Thanks for the last edit. This edit completes the fix.
 
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{{Starbox begin
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| name=Eta Sagittarii
}}
{{Starbox image
| image =
    <div style="position: relative">[[File:Sagittarius IAU.svg|250px|alt=Diagram showing star positions and boundaries of the Sagittarius constellation and its surroundings]]
    <div style="position: absolute; left: 63.4%; top: 55.6%;">[[File:Cercle rouge 100%.svg|12px]]</div>
    </div>
| caption=Location of η Sagittarii (circled)
}}
{{Starbox observe
| epoch    = J2000
| ra      = {{RA|18|17|37.63505}}<ref name=aaa474_2_653/>
| dec      = {{DEC|&minus;36|45|42.0667}}<ref name=aaa474_2_653/>
| appmag_v = +3.11<ref name=aass34_1/>/+7.8
| constell = [[Sagittarius (constellation)|Sagittarius]]
}}
{{Starbox character
| class    = M2&nbsp;III<ref name=houk1979/> + F7&nbsp;V<ref name=kaler/>
| b-v      = +1.56<ref name=aass34_1/>
| u-b      = +1.71<ref name=aass34_1/>
| variable = [[Irregular variable|Irregular]]<ref name=aaa374_968/>
}}
{{Starbox astrometry
| radial_v = +0.5<ref name=gcsrv/>
| prop_mo_ra  = &minus;129.56<ref name=aaa474_2_653/>
| prop_mo_dec = &minus;166.26<ref name=aaa474_2_653/>
| parallax = 22.35
| p_error  = 0.24
| parallax_footnote = <ref name=aaa474_2_653/>
| absmag_v = &minus;4.90<ref name=aaa374_968/>
}}
{{Starbox detail
| component1 = η Sgr A
| mass    =
| radius  = 57<ref name=lang2006/>
| luminosity  =
| temperature =
| metal_fe =
| gravity  =
| rotational_velocity =
| age      =
}}
{{Starbox catalog
| names = η&nbsp;Sagittarii, η&nbsp;Sgr, Eta&nbsp;Sgr, [[Catalog of Components of Double and Multiple Stars|CCDM]]&nbsp;J18176-3646AB, [[Durchmusterung|CPD]]-36&nbsp;8128, [[Fifth Fundamental Catalogue|FK5]]&nbsp;683, [[Boss General Catalogue|GC]]&nbsp;24944, [[Henry Draper Catalogue|HD]]&nbsp;167618, [[Hipparcos|HIP]]&nbsp;89642, [[Bright Star Catalogue|HR]]&nbsp;6832, [[Index Catalogue of Visual Double Stars|IDS]]&nbsp;18109-3647 AB, [[PPM Star Catalogue|PPM]]&nbsp;297508, [[Smithsonian Astrophysical Observatory Star Catalog|SAO]]&nbsp;209957, [[Washington Double Star Catalog|WDS]]&nbsp;J18176-3646AB.<ref name=SIMBAD/>
}}
{{Starbox end}}
'''Eta Sagittarii''' ('''Eta&nbsp;Sgr''', '''η&nbsp;Sagittarii''', '''η&nbsp;Sgr''') is a [[binary star]] system in the southern [[zodiac]] [[constellation]] of [[Sagittarius (constellation)|Sagittarius]]. Based upon [[parallax]] measurements, it is located at a distance of {{Convert|146|ly|pc|abbr=off|lk=on}} from [[Earth]].<ref name=aaa474_2_653/> It was formerly known as "Beta Telescopii" (&beta;&nbsp;Tel). In India, where part of the constellation of Sagittarius represents an Elephant, this star forms the creature's tail.<ref name=omeara2011/>
 
The primary component, η Sagittarii A, is a [[red giant]] star with a [[stellar classification]] of M2&nbsp;III.<ref name=houk1979/> It is an [[stellar evolution|evolved]] star that is currently at a stage called the [[asymptotic giant branch]], having exhausted both the hydrogen and the helium at its core.<ref name=aj104_1_275/> This star is classified as an oxygen-rich [[irregular variable]],<ref name=aaa374_968/> as it undergoes small [[Apparent magnitude|magnitude]] fluctuations between +3.08 and 3.12.<ref name=kaler/> The measured [[angular diameter]] of this star is {{nowrap|11.9 ± 2.1 [[milliarcsecond|mas]]}}.<ref name=aaa434_3_1201/> At the estimated distance of Eta Draconis,<ref name=aaa474_2_653/> this yields a physical size of about 57 times the [[Solar radius|radius of the Sun]].<ref name=lang2006/>
 
The companion, η Sagittarii B, was first noted by American astronomer [[Sherburne Wesley Burnham|S. W. Burnham]] in 1879. The two stars share a common [[proper motion]] and hence are probably gravitationally bound to each other.<ref name=burnham1978/> The secondary is likely an [[F-type main sequence star]] with an [[apparent magnitude]] of +7.77. It located at an [[angular separation]] of 3.6&nbsp;[[arcsecond]]s from the primary, along a [[position angle]] of 108°.<ref name=aas107_235/> This star is at a projected distance of 165 [[Astronomical Unit]]s from the red giant primary and the pair take a minimum of 1,270 years to complete an [[orbit]].<ref name=kaler/>
 
Within the context of the [[Milky Way]] galaxy, this system is a member of the faint old disk group.<ref name=aaa374_968/> Because of [[proper motion]], this star will move into constellation [[Corona Australis]] around 6300&nbsp;CE.<ref name=moore2011/> Eta Sagittarii has two optical companions that are not physically associated with the system. The first is a 10th magnitude star at an angular separation of 93&nbsp;arcseconds with a position angle of 303°. There is a fainter, 13th magnitude star at an angular separation of 33&nbsp;arcseconds along a position angle of 276°.<ref name=burnham1978/>
 
==Name and etymology==
*This star, together with [[Gamma Sagittarii|γ Sgr]], [[Delta Sagittarii|δ Sgr]] and [[Epsilon Sagittarii|ε Sgr]] were ''Al Naʽām al Wārid'' (النعم الوارد), the Going Ostriches.<ref name=allen1899>{{cite book
| last=Allen | first=R. H. | year=1963
| authorlink=Richard Hinckley Allen
| title=Star Names: Their Lore and Meaning
| url=http://penelope.uchicago.edu/Thayer/E/Gazetteer/Topics/astronomy/_Texts/secondary/ALLSTA/Sagittarius*.html
| accessdate=2012-09-04 | edition=Reprint
| publisher=Dover Publications Inc
| location=New York | isbn=0-486-21079-0 | page=355}}</ref> According to the catalogue of stars in the ''Technical Memorandum 33-507 - A Reduced Star Catalog Containing 537 Named Stars'', ''Al Naʽām al Wārid'' or '''Namalwarid''' was the title for this star<ref>[http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720005197_1972005197.pdf Jack W. Rhoads - ''Technical Memorandum 33-507-A Reduced Star Catalog Containing 537 Named Stars'', Jet Propulsion Laboratory, California Institute of Technology; November 15, 1971]</ref>
*In [[Chinese language|Chinese]], {{lang|zh|箕}} ({{lang|zh-Latn|Jī}}), meaning ''[[Winnowing Basket (Chinese constellation)|Winnowing Basket]]'', refers to an asterism consisting of η Sagittarii, [[Gamma Sagittarii|γ Sagittarii]], [[Delta Sagittarii|δ Sagittarii]] and [[Epsilon Sagittarii|ε Sagittarii]]. Consequently, η Sagittarii itself is known as {{lang|zh|箕宿四}} ({{lang|zh-Latn|Jī Sù sì}}, {{lang-en|the Fourth Star of Winnowing Basket}}.)<ref>{{zh icon}} [http://aeea.nmns.edu.tw/2006/0605/ap060511.html AEEA (Activities of Exhibition and Education in Astronomy) 天文教育資訊網 2006 年 5 月 11 日]</ref>
 
==References==
{{Reflist|30em|refs=
 
<ref name=aaa474_2_653>{{citation | last1=van Leeuwen | first1=F. | title=Validation of the new Hipparcos reduction | journal=Astronomy and Astrophysics | volume=474 | issue=2 |date=November 2007 | pages=653–664 | doi=10.1051/0004-6361:20078357 | bibcode=2007A&A...474..653V | arxiv=0708.1752 | postscript=. }}</ref>
 
<ref name=houk1979>{{citation | title=Michigan catalogue of two-dimensional spectral types for the HD stars | volume=3 | last1=Houk | first1=Nancy | publication-place=Ann Arbor, Michigan | publisher=Dept. of Astronomy, University of Michigan | year=1979 | bibcode=1982mcts.book.....H | postscript=. }}</ref>
 
<ref name=gcsrv>{{citation | last=Wilson | first=R. E. | year=1953 | title=General Catalogue of Stellar Radial Velocities | publisher=Carnegie Institute of Washington D.C. | bibcode=1953GCRV..C......0W | postscript=. }}</ref>
 
<ref name=aass34_1>{{citation | last1=Nicolet | first1=B. | year=1978 | title=Photoelectric photometric Catalogue of homogeneous measurements in the UBV System | journal=Astronomy and Astrophysics Supplement Series | volume=34 | pages=1–49 | bibcode=1978A&AS...34....1N | postscript=. }}</ref>
 
<ref name=SIMBAD>{{citation | title=HD 167618 -- Variable Star | work=SIMBAD Astronomical Database  | url=http://simbad.u-strasbg.fr/sim-id.pl?protocol=html&Ident=eta+sagittarii | accessdate=2007-03-29 | postscript=. }}</ref>
 
<ref name=moore2011>{{citation | page=296, | url=http://books.google.com/books?id=2FNfjWKBZx8C | title=Patrick Moore's Data Book of Astronomy | first1=Patrick | last1=Moore | first2=Robin | last2=Rees | publication-place=Cambridge | publisher=Cambridge University Press | year=2011 | postscript=. }}</ref>
 
<ref name=aaa374_968>{{citation | display-authors=1 | last1=Mennessier | first1=M. O. | last2=Mowlavi | first2=N. | last3=Alvarez | first3=R. | last4=Luri | first4=X. | title=Long period variable stars: galactic populations and infrared luminosity calibrations | journal=Astronomy and Astrophysics | volume=374 | pages=968–979 |date=August 2001 | doi=10.1051/0004-6361:20010764 | bibcode=2001A&A...374..968M | arxiv=astro-ph/0105552 | postscript=. }}</ref>
 
<ref name=aj104_1_275>{{citation | last1=Eggen | first1=Olin J. | title=Asymptotic giant branch stars near the sun | journal=Astronomical Journal | volume=104 | issue=1 | pages=275–313 |date=July 1992 | doi=10.1086/116239 | bibcode=1992AJ....104..275E | postscript=. }}</ref>
 
<ref name=aas107_235>{{citation | last1=Jasinta | first1=D. M. D. | last2=Soegiartini | first2=E. | title=Photographic observations of visual double stars | journal=Astronomy and Astrophysics Supplement | volume=107 | pages=235–241 |date=October 1994 | bibcode=1994A&AS..107..235 | postscript=. }}</ref>
 
<ref name=kaler>{{citation | first1=James B. | last=Kaler | title=Eta Sagittarii | work=Stars | publisher=University of Illinois | url=http://stars.astro.illinois.edu/sow/etasgr.html | accessdate=2012-02-10 | postscript=. }}</ref>
 
<ref name=omeara2011>{{citation | first1=Stephen James | last1=O'Meara | title=Deep-Sky Companions: The Secret Deep | publisher=Cambridge University Press | year=2011 | isbn=0-521-19876-3 | page=341 | url=http://books.google.com/books?id=v859bKO0A4gC&pg=PA341 | postscript=. }}</ref>
 
<ref name=burnham1978>{{citation | first1=Robert | last1=Burnham | title=Burnham's Celestial Handbook: an observer's guide to the universe beyond the solar system | volume=3 | series=Dover books explaining science | edition=2nd | publisher=Courier Dover Publications | year=1978 | isbn=0-486-23673-0 | url=http://books.google.com/books?id=PJzIt3SIlkUC&pg=PA1564 | postscript=. }}</ref>
 
<ref name=lang2006>{{citation | first1=Kenneth R. | last1=Lang | title=Astrophysical formulae | volume=1 | series=Astronomy and astrophysics library | edition=3 | publisher=Birkhäuser | year=2006 | isbn=3-540-29692-1 | url=http://books.google.com/books?id=OvTjLcQ4MCQC&pg=PA41 | postscript=. }} The radius (R<sub>*</sub>) is given by:
:<math>\begin{align} 2\cdot R_*
& = \frac{(44.7\cdot 11.9\cdot 10^{-3})\ \text{AU}}{0.0046491\ \text{AU}/R_{\bigodot}} \\
& \approx 114\cdot R_{\bigodot}
\end{align}</math></ref>
 
<ref name=aaa434_3_1201>{{citation | last1=Richichi | first1=A. | last2=Percheron | first2=I. | title=First results from the ESO VLTI calibrators program | journal=Astronomy and Astrophysics | volume=434 | issue=3 | pages=1201–1209 |date=May 2005 | doi=10.1051/0004-6361:20042257 | bibcode=2005A&A...434.1201R |arxiv = astro-ph/0501532 }}</ref>
 
}}
 
{{Stars of Sagittarius}}
 
[[Category:Bayer objects|Sagittarii, Eta]]
[[Category:Henry Draper Catalogue objects|167618]]
[[Category:Hipparcos objects|089642]]
[[Category:Irregular variables]]
[[Category:Multiple star systems|4]]
[[Category:M-type giants]]
[[Category:Sagittarius (constellation)]]
[[Category:F-type main-sequence stars]]

Latest revision as of 04:30, 27 August 2014

Andrew Berryhill is what his spouse loves to contact him and he completely digs that title. He is an information officer. Her family members lives in Alaska but her spouse wants them to move. To perform lacross is the thing I love most of all.

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