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Languages of the Isle of Man
From Wikipedia, the free encyclopedia
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Languages of Isle of Man
Main languages
English
(Manx English)
Main immigrant languages
Irish
Main foreign languages
French, German
Revived national language(s)
Manx
The main language of the Isle of Man is English, predominantly the Manx English dialect. Manx, the historical language of the island, is still maintained by a very small speaker population.
Both English and Manx are official languages in Tynwald.
Contents
[hide]
1 Manx
2 English language
3 Other minority languages
4 Extinct languages of the Isle of Man
4.1 Historical forms of "Irish"
4.2 Old Norse
4.3 Brythonic
4.4 Latin and French
5 References
Manx[edit]
A bilingual English/Manx welcome sign in Douglas.
Main article: Manx language
The Manx language is a Celtic language of the Goidelic subdivision, and descendant of Old Irish. It is sometimes called Manx Gaelic to distinguish it from the local variety of English.
The language was historically the dominant one on the island, but fell out of use during the twentieth century, and is considered to have become extinct in 1974 after the death of Ned Maddrell.[1] At the present time, less than one hundred children receive their education exclusively in Manx. There are an additional 1,689 second-language speakers, comprising 2.2% of the population of the Isle of Man. The language has been offered in public schools since 1992, and has been mandatory since 2001.
English language[edit]
Main articles: British English and Manx English
The English language has replaced Manx as the dominant language on the island. The native dialect is known as Anglo-Manx or Manx English, and has been employed by a number of the island's more notable writers such as T.E. Brown and "Cushag". which distinguishes itself by considerable influence and a large number of loanwords and phrases from Manx Gaelic. However, this dialect is being supplanted by other dialects of English, especially from north west England.
For formal purposes British English is the usual form of English used in the Isle of Man. For many years, the BBC has been the main broadcaster to the island, and many English people have settled in the IOM.
Forms of Irish English can also be heard on the island, from both Dublin and Belfast. The island has traditionally had many Irish tourists, and settlers.
Other minority languages[edit]
There are a few people in the island who speak other languages habitually. These include Irish speakers. French, German and Spanish are also taught in the island's schools.
Extinct languages of the Isle of Man[edit]
The Coat of arms of the Isle of Man, which uses the motto "Quocunque Jeceris Stabit" (Wherever you throw it, it will stand), a reference to the triskelion on the shield
Historical forms of "Irish"[edit]
Old Irish and Middle Irish are the ancestors of today's Manx language. Neither of these became extinct, so much as evolved, and Manx diverged from Scottish and Irish forms.
During the Middle Ages, the three Gaelic languages maintained a single standard for higher registers and poetry. This is sometimes misleadingly referred to as "Classical Irish" - despite the fact it was much in use in Scotland and presumably the Isle of Man. It is also known as Classical Gaelic.
Old Norse[edit]
Many of the island's placenames are Norse in origin, e.g. Laxey, Ramsey, and so are some of the island's institutions e.g. Tynwald (Þingvóllr). A few Norse inscriptions remain.
Brythonic[edit]
There seems to be evidence that the island once spoke a form of P-Celtic before it became Gaelicised. There is little evidence of this in placenames however.
Latin and French[edit]
Latin and French have been used in ceremonial purposes, e.g. legal use, and mottos, as in the UK.
References[edit]
Jump up ^ "Manx". Ethnologue. 1999-02-19. Retrieved 2014-08-23.
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Chelsea F.C.–Tottenham Hotspur F.C. rivalry
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Chelsea and Tottenham Hotspur rivalry
Chelsea and Tottenham Hotspur contesting the 2015 Football League Cup Final.
Other names
Chelsea F.C. vs. Tottenham Hotspur F.C.
Locale
London
Teams
Chelsea
Tottenham Hotspur
First meeting
Chelsea 2–1 Tottenham Hotspur
1909–10 First Division
(18 December 1909)
Latest meeting
Tottenham Hotspur 1–2 Chelsea
Premier League
(20 August 2017)
Next meeting
Chelsea v Tottenham Hotspur
Premier League
(31 March 2018)
Statistics
Meetings total
159
Most wins
Chelsea (68)
All-time series
Chelsea: 68
Drawn: 40
Tottenham Hotspur: 51
Largest victory
Tottenham Hotspur 5–0 Chelsea
First Division
(9 October 1920)
Tottenham Hotspur 1–6 Chelsea
Premier League
(6 December 1997)
The rivalry between Chelsea and Tottenham Hotspur is based on the football derby match in London between the two clubs. Chelsea play their home games at Stamford Bridge, while Tottenham play their home games at Wembley Stadium.
Contents
[hide]
1 Background
2 History
3 Honours
4 Highest attendances
5 See also
6 References
Background[edit]
While they never considered each other primary rivals, as two of the top clubs in London there has always been strong needle between the fans dating back from the 1967 FA Cup Final. Matches between them would often attract large attendances and would sometimes end up in violent clashes between supporters.
According to a 2004 survey by Planetfootball.com, Chelsea and Tottenham fans consider each other as their second rival, after Arsenal.[1]
However, a new 2012 survey has shown that Chelsea fans consider Tottenham to be their main rival, above Arsenal and Manchester United. In the same survey, it's shown that Tottenham fans still consider Chelsea their second rival, below Arsenal.[2]
History[edit]
The first league meeting between the two teams took place on 18 December 1909 at Stamford Bridge as Tottenham only joined the Football League in 1908 and won promotion to the Football League First Division in 1909, and the match was won by Chelsea 2–1. Both teams however struggled in the 1909–10 season, and they met again at White Hart Lane on 30 April 1910 in the final match of season, with both fighting for survival in Division One. Spurs beat Chelsea 2–1, sending Chelsea down, with the winning goal scored by a former Chelsea player Percy Humphreys.[3]
However, the rivalry itself dates back from the 1967 FA Cup final, which was the competition's first final to be contested between two teams from London, and is thus often dubbed the Cockney Cup Final. Tottenham won it 2–1.[4] For Chelsea fans, it was a major blow to see two of their former players, Jimmy Greaves and Terry Venables, win the FA Cup with Tottenham.[5]
The rivalry was further stoked during the 1974–75 season, one in which Tottenham and Chelsea fought out a bitter battle against relegation from the First Division. Before the direct match, Tottenham were in the relegation zone and Chelsea were one point ahead of them. Tottenham ultimately won 2–0. Then, Chelsea could not win either of their remaining two games and were ultimately relegated from the First Division with Tottenham staying up via a solitary point.[6]
Since the 1990s, Chelsea become dominant in the meetings with Tottenham, remaining unbeaten by their rivals for over a decade, culminating in a 6–1 win on White Hart Lane.[7]
On 5 November 2006, Tottenham beat Chelsea 2–1 on White Hart Lane, ending a 16-year period without victory against the Blues in the league. Spurs did, however, beat Chelsea in 2002 during a 5–1 win in the second leg of the league cup after a 2–1 defeat at Stamford Bridge, resulting in an aggregate score of 6–3.[8]
On 11 March 2007, Chelsea and Tottenham met in the FA Cup quarter-finals, with Chelsea coming to 3–3 down from 1–3 and earning a replay. The next day, hooligans of Tottenham and Chelsea clashed in the streets of London, a fight in which 10 fans were knifed.[9] Chelsea eventually won the replay by 2–1, progressing in the semi-finals. In the next season, the two sides have met in the 2008 Football League Cup Final, with Tottenham winning the trophy after a 2–1 victory.[10]
Chelsea and Tottenham players before the FA Cup semi-final in 2017
On 1 March 2015, Chelsea won the 2015 Football League Cup Final 2–0 against Tottenham, with goals provided by John Terry and Diego Costa. After the match, fans clashed on the Underground.[11] After this final, Chelsea surpassed Tottenham in number of trophies won.
On 2 May 2016, Chelsea and Tottenham met at Stamford Bridge. The first two goals were scored by Harry Kane and Son Heung-min. In the second half, Gary Cahill and Eden Hazard scored the two goals for Chelsea. It ended as a 2–2 draw which automatically gave Leicester City their first ever Premier League title.[12][13] This was arguably the closest Tottenham had ever come to winning the league since their last title in 1961 and since their last third-place finish in 1990. This match re-ignited the rivalry between the two clubs as players violently attacked each other on the pitch, resulting in a record nine yellow cards for Tottenham, and another three for Chelsea. As a result, both clubs had to pay three FA charges for failing to control their players.[14]
On 20 August 2017, Tottenham and Chelsea contested in the second round of the 2017–18 Premier League, with Tottenham playing their first-ever home Premier League match at the Wembley Stadium. Chelsea won the match 2–1 with two goals scored by Marcos Alonso, ending Tottenham's 19-game home Premier League unbeaten run.[15]
Honours[edit]
[16][17]
International competitions
Chelsea
Tottenham Hotspur
UEFA Champions League 1 0
UEFA Cup / UEFA Europa League 1 2
UEFA Cup Winners' Cup 2 1
UEFA Super Cup 1 —
National competitions
Chelsea
Tottenham Hotspur
First Division / Premier League 6 2
FA Cup 7 8
League Cup 5 4
FA Community Shield 4 7
Total 27 24
Highest attendances[edit]
100,000, Tottenham 2–1 Chelsea, 20 May 1967, FA Cup, Wembley[18][19]
89,294, Chelsea 2–0 Tottenham, 1 March 2015, Football League Cup, Wembley[20]
87,660, Chelsea 1–2 Tottenham, 24 February 2008, Football League Cup, Wembley[21]
86,355, Chelsea 4–2 Tottenham, 22 April 2017, FA Cup, Wembley[22]
85,731, Tottenham 1–5 Chelsea, 15 April 2012, FA Cup, Wembley[23]
76,000, Chelsea 0–4 Tottenham, 16 October 1920, First Division, Stamford Bridge[24]
73,587, Tottenham 1–2 Chelsea, 20 August 2017, Premier League, Wembley[25]
66,398, Tottenham 4–0 Chelsea, 26 January 1957, FA Cup, White Hart Lane[26]
See also[edit]
English football portal
London portal
North London derby
West London derby
Chelsea F.C.–Leeds United F.C. rivalry
Arsenal F.C.–Chelsea F.C. rivalry
References[edit]
General
"Complete head-to-head results and statistics". 11v11.com. Retrieved 21 August 2017.
Specific
Jump up ^ "Football Rivalries: The Complete Results". Planetfootball.com. Retrieved 2 January 2007.
Jump up ^ "Football Rivalries: The Survey". The Daisy Cutter. Retrieved 14 September 2012.
Jump up ^ Welch, Julie (7 September 2015). "Chapter 5: The Human Chain of Lightning". The Biography of Tottenham Hotspur. Vision Sports Publishing. ISBN 9781909534506.
Jump up ^ "Tottenham Hotspur 2–1 Chelsea (1966–67 FA Cup Final)". Thechels.com.
Jump up ^ "Chelsea History Series: Why exactly do we hate Tottenham Hotspur?". Reddit.com.
Jump up ^ "The Chelsea – Tottenham Rivalry in a Nutshell". Cffcathy.wordpress.com. Retrieved 18 October 2012.
Jump up ^ "Tottenham Hotspur 1–6 Chelsea (1997–98 FA Premier League)". Thechels.com.
Jump up ^ "Premiership: Tottenham 2 – 1 Chelsea". The Guardian. Retrieved 6 November 2006.
Jump up ^ "10 fans knifed in Chelsea battle". Evening Standard. Retrieved 12 March 2007.
Jump up ^ Jonathan Stevenson (24 February 2008). "Tottenham 2–1 Chelsea". BBC Sport. Retrieved 21 August 2017.
Jump up ^ "WARNING VIOLENT SCENES: Chelsea and Spurs fans clash after Capital One Cup final". Daily Star. Retrieved 6 March 2015.
Jump up ^ Lewis, Aimee (2016-05-02). "Chelsea 2–2 Tottenham Hotspur". BBC Sport. Retrieved 2016-11-27.
Jump up ^ "Leicester City win Premier League title after Tottenham draw at Chelsea". BBC Sport. 2016-05-02. Retrieved 2016-11-27.
Jump up ^ Jeremy Wilson (16 May 2016). "Chelsea and Tottenham fined total of £600,000 by FA after Stamford Bridge chaos". Telegraph. Retrieved 21 August 2017.
Jump up ^ Phil McNulty (20 August 2017). "Tottenham 1–2 Chelsea". BBC Sport. Retrieved 21 August 2017.
Jump up ^ "Trophy Cabinet". Chelsea F.C. chelseafc.com. Retrieved 21 August 2017.
Jump up ^ "Club Honours". Tottenham Hotspur F.C. tottenhamhotspur.com. Retrieved 21 August 2017.
Jump up ^ Tottenham full results
Jump up ^ My Football Facts
Jump up ^ "Chelsea v Tottenham Hotspur, 01 March 2015". 11v11.com. Retrieved 21 August 2017.
Jump up ^ "Chelsea v Tottenham Hotspur, 24 February 2008". 11v11.com. Retrieved 21 August 2017.
Jump up ^ "Chelsea v Tottenham Hotspur, 22 April 2017". 11v11.com. Retrieved 21 August 2017.
Jump up ^ "Tottenham Hotspur v Chelsea, 15 April 2012". 11v11.com. Retrieved 21 August 2017.
Jump up ^ "Chelsea v Tottenham Hotspur, 16 October 1920". 11v11.com. Retrieved 21 August 2017.
Jump up ^ "Tottenham Hotspur v Chelsea, 20 August 2017". 11v11.com. Retrieved 21 August 2017.
Jump up ^ "Tottenham Hotspur v Chelsea, 26 January 1957". 11v11.com. Retrieved 21 August 2017.
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Grace Adler
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This article describes a work or element of fiction in a primarily in-universe style. Please help rewrite it to explain the fiction more clearly and provide non-fictional perspective. (August 2011) (Learn how and when to remove this template message)
Grace Adler
Will & Grace character
First appearance
"Pilot"
(episode 1.01)
Created by
David Kohan
Max Mutchnick
Portrayed by
Debra Messing
Information
Full name
Grace Elizabeth Adler
(birth name)
Grace Elizabeth Adler-Markus
(former married name)
Nickname(s)
Gracie, G, Gracious
Gender
Female
Occupation
Interior designer
Family
Martin Adler
(father)
Bobbi Adler
(mother, deceased)
Janet Adler
(sister)
Joyce Adler
(sister)
Spouse(s)
James Hanson
(husband; annulled)
Dr. Marvin "Leo" Markus
(husband; 1st time [divorced])
(husband; 2nd time [divorced])
Children
Laila Markus[1]
(daughter, with Leo, in the flash-forward; removed from the revival)
Relatives
Dr. Jay Markus
(former father-in-law)
Eleanor Markus
(former mother-in-law)
Religion
Judaism
Grace Elizabeth Adler (formerly Adler-Markus) is a fictional character in the American sitcom Will & Grace, portrayed by Debra Messing.[2][3][4] A Jewish interior designer living in New York City, she lives with her gay best friend, Will Truman (played by Eric McCormack), for a majority of the series.[5] She is also the employer of Karen Walker (Megan Mullally) and the friend and neighbor of Jack McFarland (Sean Hayes).
Contents
[hide]
1 Character overview
2 Relationships
2.1 Romantic relationships
3 See also
4 References
Character overview[edit]
Grace was born on April 26, 1967, in Schenectady, New York.[citation needed] She has been particularly influenced by her mother, Bobbi (Debbie Reynolds), a flamboyant actress from whom she inherited her many neuroses.[6] Grace also constantly strives for the affection of her father Martin (Alan Arkin and Robert Klein), competing with her two sisters (one younger, one older), who have more obvious problems than she (Joyce, played by Sara Rue, is a mentally disabled compulsive overeater, while Janet, portrayed by Geena Davis, is rarely employed and promiscuous). Grace herself is decidedly selfish and neurotic, but this is usually played for laughs, like when her husband Leo asks, "You want me to be happy, right?" and she sweetly replies "Not if it affects me negatively in any way."[7] She is also somewhat vain, once declaring herself to be a "frickin' bombshell" and believing that she bears a strong resemblance to red-haired celebrities like Rita Hayworth (once even thinking a photo of Hayworth was one of herself) and Nicole Kidman. This, however, leads to her being taken down a peg, and she is usually the butt of numerous jokes by other characters. In one episode, while in Los Angeles, she is repeatedly mistaken for Kathy Griffin by tourists.[8] She is a Democrat[9] and a graduate of Columbia University and the Fashion Institute.
Grace's quirks and physical abnormalities are often fodder for the show's antics. She has very large feet, even for her height, and she's often ridiculed for them. She comments on the fact "feet the size of canoes" were the only things her father ever gave her. When Will pulls out a pair of over-sized slippers out of a box of her childhood memorabilia, she remarks "Those are my ballet slippers from fourth grade! I went from a four to an eight in a month!"
There is a general running joke of her being slovenly and unladylike, which contrasts with Will's fastidiousness, usually for purposes of comedy. She is very cheap and often hoards on free things (such as pretending to have a drinking problem in order to get free food at Alcoholics Anonymous meetings) and even steals. She once mentions selling Will's college term papers for a profit, of which Will had no knowledge.
Relationships[edit]
Grace's best friend since college is Will Truman, and their relationship is the focus of the show. They met at a college party at Columbia University. Through the third-season episode "Lows in the Mid-Eighties," we see they began dating and Grace did not realize that Will was gay at the time, and Will had not come out of the closet yet. When Will met Jack McFarland at a party, Jack made him confront his homosexuality. Will "proposed" to Grace during Thanksgiving, in an effort to postpone actually having sex with her. When he finally came out to her hours later, Grace was so angry with him that she didn't speak to him for a year. They ran into each other at a grocery store a year later and made up, and became inseparable best friends. Grace moves into Will's apartment in season one when she breaks up with her fiance Danny.[10] She moves out in season 2 to declare her independence - albeit only to an apartment across the hall.[11] She moves back in the 3rd season.[12] She eventually moves to Brooklyn in season five when she marries Leo but moves back in with Will in season 7 when she gets divorced.
Her closeness to Will is a running joke throughout the series; many other characters refer to them as a married couple. They can finish each other's sentences, which helps them in their fast rounds in trivia and parlor games. They can also be quite dysfunctional and co-dependent, sometimes even requiring the other's approval of clothing and boyfriends. When Will begins dating his future husband Vince D'Angelo (Bobby Cannavale) in season 6, Will is nervous about Grace's opinion of him, noting that he has ended relationships because Grace disliked one detail about them (one example given is that all Grace had to say about one such boyfriend was "mock turtleneck," and the relationship was ruined).[13] Despite this, they are generally caring and supportive of each other.
Aside from Will, Grace also has a close relationship with her assistant, Karen Walker, a rich, alcoholic socialite who does virtually no work. Karen is nevertheless useful to Grace, as she pays for her employer's health insurance, gives Grace holiday bonuses, and occasionally uses her society connections to help Grace get work. Otherwise, Karen spends her "work" hours drinking and belittling Grace. Karen routinely criticizes Grace's choices in fashion (usually by disdainfully asking, "Honey, what's this all about?") and men. Karen doesn't exactly withhold her judgments; in one episode, when Will calls Grace at work and Karen answers, she puts him on hold and says "Grace, the reason you're not in a relationship is on line one." Nonetheless, Grace and Karen become close friends over the years. Grace eventually learns to look past Karen's faults, and Karen occasionally does stop ridiculing her to reveal a softer, more caring side. In one episode, Grace stands up to Milo (played by Andy García) who refuses to go on a second date with Karen, who was going through a divorce with her husband Stan and was very vulnerable at the time. In another instance, Karen turns down Grace's proposal for a business loan to protect Grace, who didn't really have a strong business plan.
Grace also has a close bond with Will's other best friend, Jack McFarland. Early in the series, Jack and Grace dislike each other, seeing each other as a rival for Will's affections. However, after they spend time together while Will is in the Cayman Islands between Seasons two and three, they develop a closer friendship. They still antagonize one another, however, often leading to Grace striking Jack in some manner.
Romantic relationships[edit]
Grace has a string of boyfriends throughout the series, many played by guest stars such as Woody Harrelson and Gregory Hines. Grace marries the Jewish doctor Leo Markus, played by Harry Connick, Jr., on November 21, 2002, but the marriage ends when he has a one-night stand with a doctor from the Red Cross while working in Cambodia with Doctors Without Borders. In season 8, the two reunite briefly during a flight to London when they coincidentally met on the plane. Their mile high tryst leads to Grace getting pregnant, but she doesn't tell Leo because he is engaged to another woman. However, in the series finale, she and Leo remarry and raise the baby, a girl named Laila, together. Laila is born in Rome, where Leo is working at a hospital as a researcher. After one year in Rome the family moves back to New York, to their apartment in Brooklyn. Laila goes on to attend college and there meets Will and Vince's son, Ben. Laila and Ben are living in dorm rooms opposite each other's while at college; the same scenario that Will and Grace found themselves in while they attended college. Ben and Laila marry soon afterward.[14]
When the series was revived in 2017, the events of the season finale - in which Grace gives birth to Leo's child and drifts apart from Will - are effectively retconned as one of Karen's alcohol-induced hallucinations. In this continuity, Grace has recently got divorced from Leo, has never had children, and has moved back in with Will while she recovers from the divorce.[15] When Leo reappears sometime later, it is revealed that the marriage ended because of Grace's close friendship with Will as well as her inability to trust Leo not to cheat on her again. Despite the couple trying months of therapy and taking up golf together, they couldn't make it work and Grace, unable to forgive Leo, turned to Will for comfort.
Grace also has a reputation for "turning" men gay. Several of her boyfriends – such as Will himself, and her second-season boyfriend Josh – ended up gay or bisexual, and she has a recurring fear that this will happen again. (At one point she entered a room to find her boyfriend Nathan (played by Woody Harrelson) passed out on a bed with Jack and Will, and moans, "Oh, no, I turned another one.") In season 8, she takes this to a new level when she briefly marries James Hanson, Will's Canadian boyfriend in search of a green card. They annul the marriage a few days later because of James' callousness and manipulative behavior.[16]
See also[edit]
List of fictitious Jews
References[edit]
Jump up ^ "Will & Grace: The Big Finale Is Full of Surprises! | canceled + renewed TV shows". TV Series Finale. Retrieved 2013-09-07.
Jump up ^ Gairola, Rahul. "Will & Grace". Pop Matters Television. Retrieved 12 August 2013.
Jump up ^ Keveney, Bill (17 May 2006). "NBC's 'Will' bows out gracefully". USA TODAY. Retrieved 12 August 2013.
Jump up ^ JICHA, Tom. "Top Notch". SunSentinel. Retrieved 12 August 2013.
Jump up ^ Wells, Matt (16 December 2004). "The American gay". The Age. Melbourne. Retrieved 12 August 2013.
Jump up ^ "The Unsinkable Mommy Adler". Will & Grace. Season 1. Episode 13. February 9, 1999. NBC.
Jump up ^ "24". Will & Grace. Season 5. Episode 24. May 15, 2003. NBC.
Jump up ^ "I Love L. Gay". Will & Grace. Season 8. Episode 14. February 2, 2006. NBC.
Jump up ^ "Boo! Humbug". Will & Grace. Season 1. Episode 5. October 26, 1998. NBC.
Jump up ^ "A New Lease on Life". Will & Grace. Season 1. Episode 2. September 21, 1998. NBC.
Jump up ^ "Guess Who's Not Coming to Dinner". Will & Grace. Season 2. Episode 1. September 21, 1999. NBC.
Jump up ^ "Fear and Clothing". Will & Grace. Season 3. Episode 2. October 19, 2000. NBC.
Jump up ^ "Fred Astaire and Ginger Chicken". Will & Grace. Season 6. Episode 20. April 1, 2004. NBC.
Jump up ^ "The Finale". Will & Grace. Season 8. Episode 23. May 18, 2006. NBC.
Jump up ^ Framke, Caroline (September 28, 2017). "Will & Grace, despite what NBC says, isn't the same show that ended 11 years ago. Good". vox.com. Retrieved September 29, 2017.
Jump up ^ "Grace Expectations". Will & Grace. Season 8. Episode 16. March 16, 2006. NBC.
[hide]
v
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Will & Grace
Seasons
1
2
3
4
5
6
7
8
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Characters
Will Truman
Grace Adler
Jack McFarland
Karen Walker
Rosario Salazar
Supporting characters
Episodes
"Pilot"
"Grace, Replaced"
"Gypsies, Tramps and Weed"
"A Chorus Lie"
"Fagel Attraction"
"Marry Me a Little, Marry Me a Little More"
"Dolls and Dolls"
"Back Up, Dancer"
"Alive and Schticking"
"Buy, Buy Baby"
"The Finale"
"11 Years Later"
Related
Awards
Retrieved from "https://en.wikipedia.org/w/index.php?title=Grace_Adler&oldid=827639305"
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text:
Semi-major and semi-minor axes
From Wikipedia, the free encyclopedia
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This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (March 2017) (Learn how and when to remove this template message)
The semi-major (a) and semi-minor axis (b) of an ellipse
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the widest points of the perimeter. The semi-major axis is one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. Essentially, it is the radius of an orbit at the orbit's two most distant points. For the special case of a circle, the semi-major axis is the radius. One can think of the semi-major axis as an ellipse's long radius.
The length of the semi-major axis a {\displaystyle a} of an ellipse is related to the semi-minor axis's length b {\displaystyle b} through the eccentricity e {\displaystyle e} and the semi-latus rectum ℓ {\displaystyle \ell } , as follows:
b = a 1 − e 2 , ℓ = a ( 1 − e 2 ) , a ℓ = b 2 . {\displaystyle {\begin{aligned}b&=a{\sqrt {1-e^{2}}},\,\\\ell &=a\left(1-e^{2}\right),\,\\a\ell &=b^{2}.\,\end{aligned}}}
The semi-major axis of a hyperbola is, depending on the convention, plus or minus one half of the distance between the two branches. Thus it is the distance from the center to either vertex (turning point) of the hyperbola.
A parabola can be obtained as the limit of a sequence of ellipses where one focus is kept fixed as the other is allowed to move arbitrarily far away in one direction, keeping ℓ {\displaystyle \ell } fixed. Thus a {\displaystyle a} and b {\displaystyle b} tend to infinity, a {\displaystyle a} faster than b {\displaystyle b} .
The semi-minor axis of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section.
The major and minor axes are the axes of symmetry for the curve: in an ellipse, the minor axis is the shorter one; in a hyperbola, it is the one that does not intersect the hyperbola.
Contents
[hide]
1 Ellipse
2 Hyperbola
3 Astronomy
3.1 Orbital period
3.2 Average distance
3.3 Energy; calculation of semi-major axis from state vectors
4 References
5 External links
Ellipse[edit]
The semi-major axis is the mean value of the maximum and minimum distances r max {\displaystyle r_{\max }} and r min {\displaystyle r_{\min }} of the ellipse from a focus — that is, of the distances from a focus to the endpoints of the major axis. In astronomy these extreme points are called apsides.
a = r max + r min 2 . {\displaystyle a={\frac {r_{\max }+r_{\min }}{2}}.}
The semi-minor axis of an ellipse is the geometric mean of these distances:
b = r max r min . {\displaystyle b={\sqrt {r_{\max }r_{\min }}}.}
The eccentricity of an ellipse is defined as
e = 1 − b 2 a 2 {\displaystyle e={\sqrt {1-{\frac {b^{2}}{a^{2}}}}}} so r min = a ( 1 − e ) , r max = a ( 1 + e ) {\displaystyle r_{\min }=a(1-e),r_{\max }=a(1+e)} .
Now consider the equation in polar coordinates, with one focus at the origin and the other on the negative x-axis,
r ( 1 + e cos  θ ) = ℓ . {\displaystyle r(1+e\cos \theta )=\ell .\,}
The mean value of r = ℓ / ( 1 − e ) {\displaystyle r=\ell /(1-e)} and r = ℓ / ( 1 + e ) {\displaystyle r=\ell /(1+e)} , for θ = π {\displaystyle \theta =\pi } and θ = 0 {\displaystyle \theta =0} is
a = ℓ 1 − e 2 . {\displaystyle a={\ell \over 1-e^{2}}.\,}
In an ellipse, the semi-major axis is the geometric mean of the distance from the center to either focus and the distance from the center to either directrix.
The semi-minor axis of an ellipse runs from the center of the ellipse (a point halfway between and on the line running between the foci) to the edge of the ellipse. The semi-minor axis is half of the minor axis. The minor axis is the longest line segment perpendicular to the major axis that connects two points on the ellipse's edge.
The semi-minor axis b {\displaystyle b} is related to the semi-major axis a {\displaystyle a} through the eccentricity e {\displaystyle e} and the semi-latus rectum ℓ {\displaystyle \ell } , as follows:
b = a 1 − e 2 a ℓ = b 2 . {\displaystyle {\begin{aligned}b&=a{\sqrt {1-e^{2}}}\,\!\\a\ell &=b^{2}.\,\!\end{aligned}}}
A parabola can be obtained as the limit of a sequence of ellipses where one focus is kept fixed as the other is allowed to move arbitrarily far away in one direction, keeping ℓ {\displaystyle \ell } fixed. Thus a {\displaystyle a} and b {\displaystyle b} tend to infinity, a {\displaystyle a} faster than b {\displaystyle b} .
The length of the semi-minor axis could also be found using the following formula,[1]
2 b = ( p + q ) 2 − f 2 {\displaystyle 2b={\sqrt {(p+q)^{2}-f^{2}}}}
where f {\displaystyle f} is the distance between the foci, p {\displaystyle p} and q {\displaystyle q} are the distances from each focus to any point in the ellipse.
Hyperbola[edit]
The semi-major axis of a hyperbola is, depending on the convention, plus or minus one half of the distance between the two branches; if this is a {\displaystyle a} in the x-direction the equation is:
( x − h ) 2 a 2 − ( y − k ) 2 b 2 = 1. {\displaystyle {\frac {\left(x-h\right)^{2}}{a^{2}}}-{\frac {\left(y-k\right)^{2}}{b^{2}}}=1.}
In terms of the semi-latus rectum and the eccentricity we have
a = ℓ 1 − e 2 . {\displaystyle a={\ell \over 1-e^{2}}.}
The transverse axis of a hyperbola coincides with the major axis.[2]
In a hyperbola, a conjugate axis or minor axis of length 2 b {\displaystyle 2b} , corresponding to the minor axis of an ellipse, can be drawn perpendicular to the transverse axis or major axis, the latter connecting the two vertices (turning points) of the hyperbola, with the two axes intersecting at the center of the hyperbola. The endpoints ( 0 , ± b ) {\displaystyle (0,\pm b)} of the minor axis lie at the height of the asymptotes over/under the hyperbola's vertices. Either half of the minor axis is called the semi-minor axis, of length b {\displaystyle b} . Denoting the semi-major axis length (distance from the center to a vertex) as a {\displaystyle a} , the semi-minor and semi-major axes' lengths appear in the equation of the hyperbola relative to these axes as follows:
x 2 a 2 − y 2 b 2 = 1. {\displaystyle {\frac {x^{2}}{a^{2}}}-{\frac {y^{2}}{b^{2}}}=1.}
The semi-minor axis is also the distance from one of focuses of the hyperbola to an asymptote. Often called the impact parameter, this is important in physics and astronomy, and measure the distance a particle will miss the focus by if its journey is unperturbed by the body at the focus.
The semi-minor axis and the semi-major axis are related through the eccentricity, as follows:
b = a e 2 − 1 . {\displaystyle b=a{\sqrt {e^{2}-1}}.} [3]
Note that in a hyperbola b {\displaystyle b} can be larger than a {\displaystyle a} . [1]
Astronomy[edit]
Orbital period[edit]
In astrodynamics the orbital period T {\displaystyle T} of a small body orbiting a central body in a circular or elliptical orbit is:
T = 2 π a 3 μ {\displaystyle T=2\pi {\sqrt {a^{3} \over \mu }}}
where:
a {\displaystyle a} is the length of the orbit's semi-major axis
μ {\displaystyle \mu } is the standard gravitational parameter of the central body
Note that for all ellipses with a given semi-major axis, the orbital period is the same, regardless of eccentricity.
The specific angular momentum H {\displaystyle H} of a small body orbiting a central body in a circular or elliptical orbit is:
H = a ⋅ μ ⋅ ( 1 − e 2 ) {\displaystyle H={\sqrt {a\cdot \mu \cdot \left(1-e^{2}\right)}}}
where:
a {\displaystyle a} and μ {\displaystyle \mu } are as defined above
e {\displaystyle e} is the eccentricity of the orbit
In astronomy, the semi-major axis is one of the most important orbital elements of an orbit, along with its orbital period. For Solar System objects, the semi-major axis is related to the period of the orbit by Kepler's third law (originally empirically derived),
T 2 ∝ a 3 {\displaystyle T^{2}\propto a^{3}\,}
where T {\displaystyle T} is the period and a {\displaystyle a} is the semi-major axis. This form turns out to be a simplification of the general form for the two-body problem, as determined by Newton:
T 2 = 4 π 2 G ( M + m ) a 3 {\displaystyle T^{2}={\frac {4\pi ^{2}}{G(M+m)}}a^{3}\,}
where G {\displaystyle G} is the gravitational constant, M {\displaystyle M} is the mass of the central body, and m {\displaystyle m} is the mass of the orbiting body. Typically, the central body's mass is so much greater than the orbiting body's, that m {\displaystyle m} may be ignored. Making that assumption and using typical astronomy units results in the simpler form Kepler discovered.
The orbiting body's path around the barycentre and its path relative to its primary are both ellipses. The semi-major axis is sometimes used in astronomy as the primary-to-secondary distance when the mass ratio of the primary to the secondary is significantly large ( M ≫ m {\displaystyle M\gg m} ); thus, the orbital parameters of the planets are given in heliocentric terms. The difference between the primocentric and "absolute" orbits may best be illustrated by looking at the Earth–Moon system. The mass ratio in this case is 7001813005900000000♠81.30059. The Earth–Moon characteristic distance, the semi-major axis of the geocentric lunar orbit, is 384,400 km. The barycentric lunar orbit, on the other hand, has a semi-major axis of 379,700 km, the Earth's counter-orbit taking up the difference, 4,700 km. The Moon's average barycentric orbital speed is 1.010 km/s, whilst the Earth's is 0.012 km/s. The total of these speeds gives a geocentric lunar average orbital speed of 1.022 km/s; the same value may be obtained by considering just the geocentric semi-major axis value.
Average distance[edit]
It is often said that the semi-major axis is the "average" distance between the primary focus of the ellipse and the orbiting body. This is not quite accurate, because it depends on what the average is taken over.
averaging the distance over the eccentric anomaly (q.v.) indeed results in the semi-major axis.
averaging over the true anomaly (the true orbital angle, measured at the focus) results, oddly enough, in the semi-minor axis b = a 1 − e 2 {\displaystyle b=a{\sqrt {1-e^{2}}}} .
averaging over the mean anomaly (the fraction of the orbital period that has elapsed since pericentre, expressed as an angle), finally, gives the time-average a ( 1 + e 2 2 ) . {\displaystyle a\left(1+{\frac {e^{2}}{2}}\right).\,}
The time-averaged value of the reciprocal of the radius, r − 1 {\displaystyle r^{-1}} , is a − 1 {\displaystyle a^{-1}} .
Energy; calculation of semi-major axis from state vectors[edit]
In astrodynamics, the semi-major axis a {\displaystyle a} can be calculated from orbital state vectors:
a = − μ 2 ε {\displaystyle a=-{\mu \over {2\varepsilon }}\,}
for an elliptical orbit and, depending on the convention, the same or
a = μ 2 ε {\displaystyle a={\mu \over {2\varepsilon }}\,}
for a hyperbolic trajectory
and
ε = v 2 2 − μ | r | {\displaystyle \varepsilon ={v^{2} \over {2}}-{\mu \over \left|\mathbf {r} \right|}}
(specific orbital energy)
and
μ = G M {\displaystyle \mu =GM\,}
(standard gravitational parameter), where:
v {\displaystyle v} is orbital velocity from velocity vector of an orbiting object,
r is a cartesian position vector of an orbiting object in coordinates of a reference frame with respect to which the elements of the orbit are to be calculated (e.g. geocentric equatorial for an orbit around Earth, or heliocentric ecliptic for an orbit around the Sun),
G {\displaystyle G} is the gravitational constant,
M {\displaystyle M} is the mass of the gravitating body, and
ε {\displaystyle \varepsilon } is the specific energy of the orbiting body.
Note that for a given amount of total mass, the specific energy and the semi-major axis are always the same, regardless of eccentricity or the ratio of the masses. Conversely, for a given total mass and semi-major axis, the total specific orbital energy is always the same. This statement will always be true under any given conditions.
References[edit]
Jump up ^ http://www.mathopenref.com/ellipseaxes.html,"Major / Minor axis of an ellipse",Math Open Reference, 12 May 2013
Jump up ^ "7.1 Alternative Characterization". www.geom.uiuc.edu.
Jump up ^ "The Geometry of Orbits: Ellipses, Parabolas, and Hyperbolas". www.bogan.ca.
External links[edit]
Semi-major and semi-minor axes of an ellipse With interactive animation
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