WordNet

the angular distance of a point in an orbit past the point of periapsis measured in degrees
rightly so called; "true courage"; "a spirit which true men have always admired"; "a true friend"
proper alignment; the property possessed by something that is in correct or proper alignment; "out of true"
as acknowledged; "true, she is the smartest in her class" (同)admittedly, avowedly, confessedly
accurately placed or thrown; "his aim was true"; "he was dead on target" (同)dead on target
having a legally established claim; "the legitimate heir"; "the true and lawful king" (同)lawful, rightful
accurately fitted; level; "the window frame isnt quite true" (同)straight
make level, square, balanced, or concentric; "true up the cylinder of an engine" (同)true up
conforming to definitive criteria; "the horseshoe crab is not a true crab"; "Pythagoras was the first true mathematician"
consistent with fact or reality; not false; "the story is true"; "it is undesirable to believe a proposition when there is no ground whatever for supposing it true"- B. Russell; "the true meaning of the statement"
determined with reference to the earths axis rather than the magnetic poles; "true north is geographic north"
devoted (sometimes fanatically) to a cause or concept or truth; "true believers bonded together against all who disagreed with them"
deviation from the normal or common order or form or rule (同)anomalousness
a person who is unusual (同)unusual person
(astronomy) position of a planet as defined by its angular distance from its perihelion (as observed from the sun)

PrepTutorEJDIC

『ほんとうの』,真実の / 『本物の』,正真正銘の(real) / 『誠実な』,忠実な,忠誠な(faithful) / 心からの,うそ偽りのない / 寸分違わない,正確に一致する,適合する / 正当な,適正な,正しい(proper) / 間違いない,確実な / 〈機械・器具などが〉正確にできた,正しい位置にある;〈声などが〉正しい調子の / うそをつかないで,正直に / 寸分違わないように,確実に / 先祖の型どおりに / …‘を'正しく調整する《+up+名,+名+up》
〈U〉〈C〉変則,例外;異常 / 〈C〉変則的な事態,異例な人(物)

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2013/12/16 12:08:18」(JST)

wiki en

The true anomaly of point P is the angle . Also shown is the eccentric anomaly of point P, which is the angle E. The center of the ellipse is point C, and the focus is point F. The radial position vector r is taken from the focus F, not from the center of coordinates C. Auxiliary circle has radius a; minor auxiliary circle has radius b.

In celestial mechanics, true anomaly is an angular parameter that defines the position of a body moving along a Keplerian orbit. It is the angle between the direction of periapsis and the current position of the body, as seen from the main focus of the ellipse (the point around which the object orbits).

The true anomaly is usually denoted by the Greek letters or , or the Latin letter .

The true anomaly is one of three angular parameters ("anomalies") that define a position along an orbit, the other two being the eccentric anomaly and the mean anomaly.

Formulas[edit]

From state vectors[edit]

For elliptic orbits true anomaly can be calculated from orbital state vectors as:

(if then replace by )

where:

is orbital velocity vector of the orbiting body,
is eccentricity vector,
is orbital position vector (segment fp) of the orbiting body.

Circular orbit[edit]

For circular orbits the true anomaly is undefined because circular orbits do not have a uniquely determined periapsis. Instead one uses the argument of latitude :

(if then replace by )

where:

is vector pointing towards the ascending node (i.e. the z-component of is zero).

Circular orbit with zero inclination[edit]

For circular orbits with zero inclination the argument of latitude is also undefined, because there is no uniquely determined line of nodes. One uses the true longitude instead:

(if then replace by )

where:

is x-component of orbital position vector ,
is x-component of orbital velocity vector .

From the eccentric anomaly[edit]

The relation between the true anomaly and the eccentric anomaly E is:

or equivalently

Therefore

where is the polar argument of the vector (available in many programming languages as the library function atan2(y, x) in Fortran and MATLAB, or as ArcTan(x, y) in Wolfram Mathematica).

Radius from true anomaly[edit]

The radius (distance from the focus of attraction and the orbiting body) is related to the true anomaly by the formula

where a is the orbit's semi-major axis (segment cz).

References[edit]

Murray, C. D. & Dermott, S. F. 1999, Solar System Dynamics, Cambridge University Press, Cambridge.
Plummer, H.C., 1960, An Introductory treatise on Dynamical Astronomy, Dover Publications, New York. (Reprint of the 1918 Cambridge University Press edition.)

UpToDate Contents

全文を閲覧するには購読必要です。 To read the full text you will need to subscribe.

1. 三尖弁のエプスタイン奇形 ebsteins anomaly of the tricuspid valve
2. 好中球増多症の原因 causes of neutrophilia
3. 胎児腹壁破裂および総排泄腔外反症 body stalk anomaly and cloacal exstrophy
4. 視神経の先天性および後天性異常 congenital anomalies and acquired abnormalities of the optic nerve
5. 三尖弁の心エコー評価 echocardiographic evaluation of the tricuspid valve

English Journal

High-resolution calorimetric study of pb(mg_{1/3}nb_{2/3})o_{3} single crystal.

Novak N, Pirc R, Wencka M, Kutnjak Z.SourceInstitute Jožef Stefan, Jamova 39, 1000 Ljubljana, Slovenia.
Physical review letters.Phys Rev Lett.2012 Jul 20;109(3):037601. Epub 2012 Jul 16.
Motivated by the long-standing unresolved enigma of the relaxor ferroelectric ground state, we performed a high-resolution heat capacity and polarization study of the field-induced phase transition in the relaxor ferroelectric single crystal Pb(Mg_{1/3}Nb_{2/3})O_{3} (PMN) oriented along the [110] d
PMID 22861896

Developmental venous anomaly coexisting with a true arteriovenous malformation: a rare clinical entity.

Erdem E, Amole AO, Akdol MS, Samant RS, Yaşargil GM.SourceDepartment of Radiology, University of Arkansas for Medical Sciences, Little Rock, Arkansas, USA.
Journal of neurointerventional surgery.J Neurointerv Surg.2012 Jul;4(4):e19. Epub 2011 Jul 29.
Two patients diagnosed with arteriovenous malformation (AVM) in close association with a developmental venous anomaly (DVA) are reported. The first patient presented with episodes of left extremity weakness and numbness as well as chronic headaches. The second patient presented with spontaneous intr
PMID 21990487

Japanese Journal

4. 小児外科領域におけるNCDの利活用 : NCDがもたらす小児外科医療のパラダイム・シフト(<特集>National Clinical Databaseの現状とこれから)

前田貢作
日本外科学会雑誌 115(1), 13-16, 2014-01-01
NAID 110009688498

Capability Assessment of the Space-Based Optical Measurement for LEO Debris

TAGAWA Makoto,YANAGISAWA Toshifumi,MATSUMOTO Haruhisa,KUROSAKI Hirohisa,ODA Hiroshi,HANADA Toshiya,KITAZAWA Yukihito
TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES, AEROSPACE TECHNOLOGY JAPAN 11(0), 109-115, 2013
… This paper summarizes assessment results in terms of the number of passing objects, imaged objects, image moving velocity in pixels, apparent magnitude, observation occurrence frequency with respect to the observers true anomaly, and the relationship between the observation count and interval. …
NAID 130003385874

Is Mainstream Economics a Slave Morality?: An Analysis of the Longstanding Anomalies of Mainstream Economics within the Evolutionary Framework of Multiple Moralities

Jiang Zhixiong,Bao Lili,Liu Hanqing
Evolutionary and Institutional Economics Review 10(1), 107-129, 2013
… We argue this perplexing situation has arisen because each anomaly, despite an apparent illogic, has practical utility as a rhetorical instrument of real world interests. … Rhetorical instruments may elicit a set of behaviors desired of the believer that true theory would not. … First, we show how the theoretical function of each anomaly may be explained from this perspective with standard economics theory. …
NAID 130003364766