Hour angles and aries lrg

Grunt Productions 2005

Hour Angles and Aries

A Brief By Lance GrindleyA Brief By Lance Grindley


Hour Angles and AriesHour Angles and AriesNautical Almanac:Nautical Almanac:

- in section 6 it was shown that line of position (LOP) - in section 6 it was shown that line of position (LOP) can be determined from a sextant angle (hs) and can be determined from a sextant angle (hs) and geographical position (GP) of bodygeographical position (GP) of body

- GP constantly changes as earth rotates as does GMT- GP constantly changes as earth rotates as does GMT


this section deals with determination of GP of body at this section deals with determination of GP of body at exact GMT of sextant observationexact GMT of sextant observation

- data to make this determination is found in Nautical - data to make this determination is found in Nautical AlmanacAlmanac

- Nautical Almanac is printed every calendar year and - Nautical Almanac is printed every calendar year and is available in fall of previous yearis available in fall of previous year


- Nautical Almanac contains tables that observer can Nautical Almanac contains tables that observer can obtain GP of 4 planets, sun, moon, 57 navigation stars obtain GP of 4 planets, sun, moon, 57 navigation stars and Polaris for every second during yearand Polaris for every second during year

- before determining GP of body, definitions of - before determining GP of body, definitions of declination (DEC) and hour angle necessarydeclination (DEC) and hour angle necessary


Declination (DEC):Declination (DEC):

- on earth’s surface, position of vessel described in terms of - on earth’s surface, position of vessel described in terms of latitude and longitudelatitude and longitude

- in celestial navigation, instead of latitude, declination describes - in celestial navigation, instead of latitude, declination describes whether body is north or south of equatorwhether body is north or south of equator


Declination:Declination:

- stars have fairly constant DEC- stars have fairly constant DEC

- DEC of sun, moon and 4 planets change rapidly from - DEC of sun, moon and 4 planets change rapidly from day to day and significantly from minute to minuteday to day and significantly from minute to minute


Hour Angle:Hour Angle:hour angles are roughly celestial navigation’s equivalent of hour angles are roughly celestial navigation’s equivalent of longitude; there are 3 hour angles that will be introduced:longitude; there are 3 hour angles that will be introduced:

- Greenwich hour angle (GHA) - Greenwich hour angle (GHA)

- local hour angle (LHA)- local hour angle (LHA)

- sidereal hour angle (SHA), generally associated with - sidereal hour angle (SHA), generally associated with starsstars


Hour Angle:Hour Angle:- unlike longitude, hour angles are always measured - unlike longitude, hour angles are always measured westward through 360westward through 360ºº

- hour angle of celestial body when measured from - hour angle of celestial body when measured from Greenwich meridian is known as Greenwich Hour Angle Greenwich meridian is known as Greenwich Hour Angle (GHA)(GHA)


Hour Angle:Hour Angle:E - up to 180º GHA corresponds to Lo; over 180º, Lo = E - up to 180º GHA corresponds to Lo; over 180º, Lo = 360º – GHA360º – GHA

EXAMPLES:EXAMPLES:

GHA 90º, Lo = 90º WGHA 90º, Lo = 90º W

GHA 210º, Lo = 360º - 210º = 150º EGHA 210º, Lo = 360º - 210º = 150º E

GHA 350º, Lo = 360º - 350º = 10ºGHA 350º, Lo = 360º - 350º = 10º


Hour Angle:Hour Angle:- now necessary to relate position of body relative to observer’s - now necessary to relate position of body relative to observer’s position, not Greenwichposition, not Greenwich

- hour angle of celestial body when measured from observer’s - hour angle of celestial body when measured from observer’s meridian is known as Local Hour Angle (LHA)meridian is known as Local Hour Angle (LHA)

- if observer’s Lo and GHA of body are known, then LHA can be - if observer’s Lo and GHA of body are known, then LHA can be calculatedcalculated


Hour Angle:Hour Angle:- if Lo is west, LHA = GHA – Lo- if Lo is west, LHA = GHA – LoWW

- if Lo is east, LHA = GHA + Lo- if Lo is east, LHA = GHA + LoEE

- meridian or great circle passing through a body and poles of - meridian or great circle passing through a body and poles of celestial sphere is known as hour circle of bodycelestial sphere is known as hour circle of body

- hour circles of bodies move with time while celestial meridians - hour circles of bodies move with time while celestial meridians remain fixed with respect to earthremain fixed with respect to earth


in this in this example of example of LoLoWW::

LHALHAstarstar = GHA – = GHA – LoLoWW observer observer

LHALHAmoonmoon==GHA – LoGHA – LoWW observerobserver

Lo


in this in this example of example of LoLoEE::

LHALHAstarstar = GHA = GHA + Lo+ LoEE observer observer

LHALHAmoonmoon==GHA + LoGHA + LoEE observerobserver

Gre

en

wic

h

Obse

rver’

s

GHA

Lo


Aries:Aries:- Nautical Almanac tabulates GHA for sun, moon and - Nautical Almanac tabulates GHA for sun, moon and planets for every hour in yearplanets for every hour in year

- if it tabulated every hour for stars, almanac would be - if it tabulated every hour for stars, almanac would be 10 times thicker10 times thicker

- tabulating every hour not necessary for stars which - tabulating every hour not necessary for stars which are slow movingare slow moving


Aries:Aries:- instead of measuring star hour angles from Greenwich, they are - instead of measuring star hour angles from Greenwich, they are measured from point in sky known as Aries measured from point in sky known as Aries ( )( )

- Aries is hour circle projected on earth’s surface of celestial - Aries is hour circle projected on earth’s surface of celestial position occupied by sun at exact instant sun crosses equator, position occupied by sun at exact instant sun crosses equator, moving north, approximately March 21moving north, approximately March 21stst each year (Vernal each year (Vernal Equinox)Equinox)


Aries:Aries:- this point was in constellation Aries 2000 years ago but due to - this point was in constellation Aries 2000 years ago but due to presession motion of earth spinning on polar axis, it has moved presession motion of earth spinning on polar axis, it has moved 3030º westwardº westward (Bowditch page 230) (Bowditch page 230)

- while this point is still known as first point of Aries, currently is in - while this point is still known as first point of Aries, currently is in constellation of Pisces and will make complete circle in 25,800 constellation of Pisces and will make complete circle in 25,800 yearsyears


Aries:Aries:- selection of this point was arbitrary as was selection - selection of this point was arbitrary as was selection of Greenwich meridian for defining longitudeof Greenwich meridian for defining longitude

- instead of Almanac tabulating GHA for every hour for - instead of Almanac tabulating GHA for every hour for all 57 stars, hour angle known as sidereal hour angle all 57 stars, hour angle known as sidereal hour angle (SHA) is measured from Aries(SHA) is measured from Aries

- Almanac just tabulates GHA of Aries- Almanac just tabulates GHA of Aries


Aries:Aries:

- - SHA of a star rarely varies by more than 0.1’ in a SHA of a star rarely varies by more than 0.1’ in a week and Almanac tabulates stars every 3 daysweek and Almanac tabulates stars every 3 days

GHAGHAstarstar = GHA = GHAAriesAries + SHA + SHAstarstar

- GHA and LHA can be applied to all celestial bodies - GHA and LHA can be applied to all celestial bodies and reference point Aries; SHA routinely used for starsand reference point Aries; SHA routinely used for stars


Aries:Aries:- SHA of navigation planets is shown in Almanac generally to assist - SHA of navigation planets is shown in Almanac generally to assist in use of Star Finder 2102-Din use of Star Finder 2102-D

- by definition, SHA of sun is exactly zero at Vernal Equinox- by definition, SHA of sun is exactly zero at Vernal Equinox


Hour Angle Diagrams:Hour Angle Diagrams:- - to avoid perspective drawings, convention is to use to avoid perspective drawings, convention is to use flat circle, viewed from south poleflat circle, viewed from south pole

- circumference- circumferenceof circle isof circle isequatorequator

- hour angles- hour anglesmeasuredmeasuredwestward, shownwestward, shownanticlockwiseanticlockwise


Hour Angle Diagrams:Hour Angle Diagrams:- top of circle “M” represents observer’s meridian with solid line to - top of circle “M” represents observer’s meridian with solid line to centre of circlecentre of circle

- this solid line- this solid lineknown as upperknown as upperbranchbranch


Hour Angle Diagrams:Hour Angle Diagrams:dashed line drawn at 180dashed line drawn at 180º to M, is called º to M, is called lower branchlower branchand labeled “m”and labeled “m”


Hour Angle Diagrams:Hour Angle Diagrams:- after M located arbitrarily at top of diagram, next locate - after M located arbitrarily at top of diagram, next locate Greenwich “G” meridianGreenwich “G” meridian

- if M has Lo =- if M has Lo =7575ºE, GreenwichºE, Greenwichwill be 75º westwill be 75º westor anti-or anti-clockwise fromclockwise fromM; draw as solidM; draw as solidline to centreline to centre


Hour Angle Diagrams:Hour Angle Diagrams:- draw dashed line opposite from centre of circle at 180- draw dashed line opposite from centre of circle at 180º to Gº to G

- known as “g”- known as “g”or lower branchor lower branchof Gof G

- g represents- g representsInternationalInternationalDate LineDate Line


Hour Angle Diagrams:Hour Angle Diagrams:- for star diagram, add Aries by using Nautical Almanac GHA for - for star diagram, add Aries by using Nautical Almanac GHA for the correct time, measuringthe correct time, measuringfrom Gfrom G

- if diagram for- if diagram forsun, moon orsun, moon orplanets, get GHAplanets, get GHAfrom Almanacfrom Almanacand draw as forand draw as forAriesAries


Hour Angle Diagrams:Hour Angle Diagrams:for star diagram, after add Aries, get star’s SHA from Nautical for star diagram, after add Aries, get star’s SHA from Nautical Almanac for correct day,Almanac for correct day,measuring frommeasuring fromAriesAries

SHA 200º


Hour Hour Angle Diagrams:Angle Diagrams:likewise, same technique is used for a second star with, e.g., SHA likewise, same technique is used for a second star with, e.g., SHA = 60= 60ºº

Hour angles and aries lrg

Education

Transcript of Hour angles and aries lrg