celestial navigator

8/6/2019 Celestial Navigator

1/21


2/21


3/21

HOW TO WORK A SlGHT-An Overview

18 Add rhevooo ll ll ~16ond l7ond looku p m i s wm in ! h e k l b l e s & o m ! h e b o n o m! . n d e r l h e h e o d m g A l T ( C o m p u l e d A & . l u d e )V o ur po in ld eM y . .. r he lo b le sf o,r llls qU Oll"h l y ~ s im p l o li e d b e c o < M y o u k n c . .. .. r h e v o lu ec J th e ot-ved o I I I t u d eA lT IT U D E C O R R E C T IO N SA ND AZ IM U T H

19 Rewdrheomer.. . edsemnlo lhtudereod ing2OfOlIneDipCor,edionnotetneneighrofe)l !. !

I m e l e l l o , l e e I I F o r o o n v e n i e n c e l r . e c o r r e c -liOll,clwoysnegohve,hcsOOenlOblJlated1 0 1I h e S i o lS o n p c ge s 21 to 3 5 . fo < th e S u nandPionelsonpoge66.ondfOilheN'conoopcgss 10 1 and 10 2

2 1 Rec o rd r h es ex la n li in d ex jo o r re c t io n o o \i n gi l l l i gnnegol ive i f r eodon iheorcorpos tl o v e i l 0 1 1 t h e e re

22 Therorlec l lo ruonl ine s '20ond21arecOll l"b i n e d o m : ! a p p l i e d 10 t h e 5 e J < I o n io ~ i l u d eT h e r e w l l l s r h e o p p o r e r > l o l l l l O O e

23 A ~ngleoh"udeco"echon fo r th e SIa" isgivenoopoges 271OJ5,Ia rhe5llnOl'PIonellonpoge66ondlorrheM :xlnonp ag es 1 01 a n d 102

U. T h e o b s e t v e d o~iUIe is o b I a , o e d a!let !h e

T h e N o r e N t . r r C e r s r e l . o 1 s c l o r h e U o e N u m ~o n i h e S i g h l R e d ! . a i o n F o r m ( 5 e e p o g e l 6 8 I , Y o ow . l l 1 i n d ~ n 'I (l f f le l io e n ld l or m o s r o li h e .. .. .n . y o up r o c e e d o o o s s r h e S i g h r R e d o c h o n F o r m r u r h e rf o o n w o r k c o O O . t b y c o k l m n l n o r d e r l o l : . e e pi t l l ! r p O I o r i o n e n o o l O O n ' i n l m u m m o n y o l t h e l O b i e so r e o n o n g e d . n c n l I O O I f a m fphndyrudoroenlrycoincooWltholob.olarecl"" ' -'erhenlOkem e u p p e r i u p t h e p o g e l " ' l l u e o l t h e c o r r e c t i o n1 I n di c ol er ne d o y cl rh ewooko lo n o d de

lionolcheckonlhedoteT h e o o m e 0 1 Ine b o d y o s I d e n l if i e dIllspreferoblelOUleodlgilolrOlnerlnonononologuewclcn; lherell le! .Scoonceo[m o k i n g o r e o d l n g m b l o k e

4 D e 1 e r m i n e r h e l " " l r c h c o r r e c l l o n b y c o m p o l 'i n g r h e w c l C h w i t h o r . o r h e r l i m e p l e c e ~e r ro r i l k n o w n o r with 0 R o d lo T im e S i gn o l.a. V v \ l W l C o I o r o d o ) & V v \ I W I H I IH o w o i llU S A . N 'S f E n g l a n d . Z O O S o u i h .A J r i c o , j lYj op o n & V N G A l .J S I! o l io

S S t o n d o r d T i m e o r Z o n e T i m e , l e " h m er e . f e f r e d l o o g < ' R ! l T l m e Z o o e

6 T i m e Z o n e s . W l r h o 1 e w e x c e p l io n s . rn e o ni n t e g r o i n u m b e r o i l l o u r l

7 T h e d o te 0 1 this G M T . . .. .I c h o o g e I r o m I h o tg l V l 'f l I n l in e 1 u o c i e r r h e f d l o w , n g c i r c u r r r

G H A o n d D e d i n c O O o _ N ~ l o o I o . u pr h e O t l e r p O O b o r l f o c l o r F o o p o g e l 6 6 o n dm u l t i r : i Y i r i s b y v o n d d t o d e l e l m i o e r h e p t < l 'p o rO O n c r lp o ll S , e r c, N o t e h a l n e c h o o g e inO e d i n o l i o o d i s o o l s i g n e d s o b e c o r ~ h o wy o u o p p l y t h e c o r r e d i o n _ R e c o r d r h e c o n e < : l -e d vo lu e so lG H A o o d D e d il lQ l rO O O O " 1e !9o n d 1 5 r e s p e d i v e l yM O Q N , F o r i h e N ' o ; Jn I h e p r t '> C e ! 5 i s i d e n ! i-c a l r o r h o l f a r n e S u n o n d P l o r . e i l e x r : e p l t h o lt h e l a b u l a l e d " ' l l u e s 0 1 ( G H A G N \n o n dD e d l n o l i o o o n p o g e . > 6 6 1 0 9 7 o r e g i v e n o lfNeI ' / 6 h ou rs 0 1 G M T T h e i n l e f p o l o ~ onl a b i e ! a r e 0 0 p o g es 9 6 1 0 100 . T h e f o c to r Fon f X lg e 1 66 naw coverS a p e r i o d c I 6n o u r s . R e c o r d l h e " ' l l u e o l H o r i z o n I o I P o r o l k n lI H ~ g i v e n d a i ~ lf a o s e o o l in e 2 3

10 S e e n o l e 91 1 A d d l in e s 6 .9 o n d lO k l g e lh e r ld o n O i IO b -

T I e d 3 6 0 ' i f th e s u m e xc e e d s 3 60 ') 1 0obIoin th e G H A c i t h e b o dy

1 2 E n l e !t h e D R w l u e c il oo g i tu d e o n d h e e d lh e~ g n c o n v e n l i o o s h o w n i n l h e n O l e l i n r h e l e f t .o o n d m o r g i nD A T A F O R S IG I f T R E DU c n O N

1 3 A d d o r s u lx r o d lh e D R l o o g ii u d et o o b io i n'h e


4/21

lNTRODUCT lONastronomical methods wIll not be the basis for naviga-tion; satellite systems will be the navigator's mainstayfo r p os it io n f ix ing . T he p ru den t nav ig ator, h ow eve r, w illnot rely entirely on satellite systems and electronicdevices, wh1ch may not be always available, but w i l lchoose as well Independent methods such as ared es crib ed h ere .

Th e sk ills req u ired b y th e c eles tia l nevlg a to r c a n b ed iv id ed b ro ad ly I nto th re e a re as :

T his book p rovides , In a com pact form , a ll the es sent ia lInstructions, almanac data, and tables for finding the fat-frude and longitude of a ship by celestial navigation andals o the m eans for m aking a com pass check, for a flve-y ea r p erio d . M any num erica l exam ples th a t illu s tra te th euse of Its methods and tables are provided as well. Thisis especially helpful for the navigator who uses celestialmethods Infrequently.

The difference between this and most other stan-dard works on this sublecr ls that It Is emlrely self-con-tained and yet remarkably compact. With the informa-tion supplied here, the navigator is independent of anyother IndIvidual or agency. No longer will it be neces-sary to purchase separately a book on astronomical nav-lgartcn, a nautical almanac, a set of tables for reducing

I An ability to make reliable Instrumentalobservations.

2 An understanding of how astronomicalcoordinates and other data can beextracted from the almanac section.


5/21

TIlE COMPLETE ON-BoARD CELESTIAL NAVIGATOR

$ou t hP o i e

3 EQU1PMENTIn addition to this book and basic navlganon eculcmentsuch as charts, plotting aids, and a hand-bearing com-pass, the navigator should possess a sextant, a time-piece, and a shortwave radio receiver.3.1 SextantIfyou have a choice when buying a secanc tten a metal

quantity extracted can be Incurred,andtheaverageerror will be a quarter of a unit. If when entering sucha table one flnds the point of entry Is the same asthat given in the table, the upper (that Is, moving upthe page) value of the twO possible data values ischosen.

Before studying celestial navigation, the readermust be conversant with such basic navigational quanti-ties as latitude, longitude, azimuth, etc., and be able toplot the passage of a vessel and flx Its position in acoastal situation.

The figure at left shows the position [latitudeand longitude) of two pclms, Pand Q, on the surfaceof the Earth, considered to be spherical. Latitude ismeasured north or south (0'-90') from the equator,and longitude east or west (0'-1 BO') from theGreenwich meridian. P has a north latitude and westlongitude, whl le Q has a south latitude and an eastlongitude.


6/21

Side ErrorWhen In adjustment, the horizon glass should be per-pendicular to the plane of the sextant. For this test,select and sight a well-defined distant object; a star isIdeal for this purpose. The direct and reflected imagesof the object should pass over one another as you movethe sextant setting across the zero of the graduated arc .If they appear side by side, then use the adjustingscrew(s), usual ly farthest Fromthe graduated arc, on thehorizon glass to correct the error.Index ErrorBefore observations, and preferably afterward as well,the sextant should be checked for index error. To dothis, set the sextant reading to approximately zero, aimat the sea horizon orata clear horizontal line a mile orso dlstant, and bring the direct and reflected Images intocoincidence by operating the micrometer drum, whichacts as a slow-motion screw.

If the sextant reading Is not zero, this amount Is theIndex error. Provided It Is not more than a few minutesof are, do not attempt to adjust it. If the reading isgreater than zero (on the are), then subtract this amountfrom all subsequent readings. If the reading Is belowzero {off the are), then add this amount.

To correct for a large Index error, set the reading tozero and use the adjusting screw at the rear of the hori-zon glass (fixed mirror) close to the graduated are tomake the two Images coincide as nearly as possible.

4. ALMANAC DATA

rather than an analogue type with hour, mlnute. and sec-ond hands, Is preferred for timing observations. Whentiming with the latter, the Incorrect minute may be inad-vertently recorded when the time is near the wholeminute.

The worth of a clock Is not necessarily its ability tokeep time exactly but that the time it keeps can be pre-dlcted accurately over many days, provided that it hasbeen subjected to reasonable changes In temperatureand motion. Ifover a test period the clock gains or losesat a steady rate, then It Is a simple mat t e r to f ind a reli-able clock correction some days after the last clock cor-rection has been made. Clocks that perform erraticallyshould be rejected. Note that It costs little, and it Is agood safeguard, to have twOor more clocks on a vessel.

To test a clock's performance, It should be com-pared with another timepiece of known accuracy oragainst a radio time signal. The latter method Is conve-nient because continuous time signals are broadcastfrom many countries. Perhaps the best known are thesignals that originate from \N'oIN [Fort Collins} and\N'oIN(H} (HawaII) on 2.5, 5, 10, 15, and 20 {FortCollins only} MHz In the USA. Provided Ionosphericconditions are not abnormal and depending on the timeof day, the signals can be heard throughout the world.

Although It will be necessary to flnd the Greenwichmean time (GMT or UTC or Zulu) of celestial observa-tions, It Is not necessary that the clock keep GMT. [ftheclock is set to keep standard time [zone time), It Is a sim-


7/21

THE COMPLETE ON-BoARD CELEST1AL NAVIGATOR

Declinations a r e measured (0 -90} north or southfrom the celestial equator. SHAs are measured(0-360} not from a terrestrial meridian containingGreenwich but west from a celestial meridian contain-Ing "the first point of Aries," often denoted by thezodiacal symbol


8/21

4. ALMANAC DATA

2 Extract the listed GHA at GMTOhrs andlv l of the body on the date.

J Using the given value of GMT and (v),look up the correction to GHA atGMTOhrs In the Interpolation tables onpages 66 and 67. If [v ) Is grearer than60', the correction Is found by addingthe correction for hours to that for min-utes In the table. The required GHA Is:

GHA Sun/p lanet", GM f{an} + GHA a t GM TOh rs + {v }(arm.

To find the declination at the same instant of GMT,us e the same technique as described before, but use (d)Instead of I v l . The required value of dec n n atIon Is:

DedinatianSun/planet.DedinallonatGMTOhrs: tld)(orrn.

4.3 MoonThe GHA-GMT and declination of the Moon are tabu-lated at every six hours of GMT for every day of theyear on pages 68 to 97. Each page lists two months ofdata. The horizontal parallax [HP), se e explanation InSections 6.4 and 6.5, Is given dally. The times of thephases of the Moon (new, first quarter, full, and lastquarter) are summarized at the end of each month. Theprocess of interpolation using the differences of {GHA-

The required value of decUnatIon Is:D eclina tion M oon" , D ed ina tian 01 GM TIO/6/12/18)hrs :t

(d ) (orrn.

4.4 SummaryFrom the preceding text It becomes clear that theprocess of finding the GHA of Aries, stars, Sun, plan-ets, and Moon is very slmflar. The GMT Is convertedfrom time to arc, then the tabulated value of the GHAat GMTOhrs for Aries, Sun, and planets-or at a multi-ple of six hours for the Moon-Is extracted and anInterpolation correction applied. The sum of these com-ponents Is then taken. For stars, the GHA is found byadding the SHA. For declination, all that Is required isan interpolation correction to be applied to the tabulat-ed decUnatlon, except for stars, which do not needInterpolation. In later sections we will often be requiredto find the local hour angle (LHA) of the body, which isa measure of how far the body has progressed since itpassed the observer's meridian [north - south). Thiscan be done by applying the longitude (usually the D Rvalue) to the GHA. The following examples Illustrate thecomplete procedure for all bodies:

EXAMPLESFind the lHAs and declinations for Arcturus, Sun,

Moon, and planets In D R latitude N33'sO', longitude


9/21

THE COMPLETE ON-BoARD CELESTIAL NAVIGATOR

Bo d y ~ " 1 1 V e n k r i 1 .1 '0 " MGM f { O ' c ) 145 '00 ' 145'00' 145 '00 'G I l A ' 16031 .1' 13924 -16' 1 4 3 + S 2 'c.~ . l z l : iMG H A 32532 28417 14716. . . . . W Q ll_ J 1 W Q Z lJ 1 W ! ! l l. . . . llIH A l2tll 21202 Li .Ql

I d l I d l Id lO o c ' NI3'18'+19' N24'42' +10 ' 511'30' -5'C O " " ! l = 10., ~ N2446 ~8 0 d v Jupiter 1 .1 S o l u r n [ .1 M o n n MGMT ( a r ( } 145'00' 145'00' 145 '00 'G H A ' 19727 +46' 17835 +52' 4505-164'(ann ill ill -140(-100)G H A 34245 32356 18825L o o g " W .Q l l . . l i W .Q l1 . l 1 W . Q l 1 . l1IH A 27030 zau ll i .J .Q

I d l I d l [ d lO o c ' N5'40' . . ' Nl1'39 ' .1' N7'23'-60'

4.5 Alternative InterpolationMethodIf a simple four-function calculator Is available, the fol-lowing Interpolation technique may be used Instead ofthe method previously described. A table for this Is onpage 166. The technique Is as follows:

1 lo o k up In the table the value c r a factor[F) that corresponds to the given value ofGMT. For the Moon, use GMT minus themultiple of six hours chosen for extract-ing the Moon's coordinates. There Is noneed tclnterpolate E2 Multiply (v ) and (d) by Ftoobtaln thedesired ccrrecncns.

This method Is slightly more accurate than that pre-viously described. It Is suggested that both methods betried and the one more suited to the user's needs beadopted.

From the following table, a comparison can be madeof the Interpolation corrections found using this and theprevious method.

GMT 9h 40m (ORR N '" F X tvl o r (d )M ( o r m . [ d l C~.

So o 0.41 .1' .1' +19 ' . .'


10/21

of observation. If observations are planned for the timeofclv!1 twilight-that 15, when stars, planets, and thehorizon are visible (see Sectton 5.5)-you may wish todesign an observation routine that optimizes the use ofthe restricted time available.

An example of the calculations Involved is shown Indetail In Secrtcn 4 and 15summarized as follows:

B o d y lH A Oed i n l l l i o nA r l o 2 8 6 ' 4 2 '

5 " " 2 5 3 1 7 N I 3 " 2 6 'M o o " 1 1 6 1 0 N 6 4 6V e n u s 2 1 2 0 2 N 2 4 4 6M o o 7 5 0 1 5 1 1 2 8J u p i t e r 2 7 0 3 0 N 5 4 3S a r u r n 2 5 1 4 1 N i l 4 0Turn now to page II I of the predlcttcn and Identi-

fication tables for latitude N30' (nearest 10'), and Inthe column for LHA of Aries equal to 290' (nearest10') are listed the altitudes and azimuths to the nearestdegree of those stars that are above the horizon at thistime. The altitude Is printed first, followed by a spaceand then the azlmuth-a three-figure number In boldtype. If a body Is below the horizon, u# ###" will beshown, Indicating that the body is not visible. The am -

5. PLANNING AND OBSERVATIONS

tudes the brightness of stars and planets Is diminishedbecause the light has to pass through more atmo-sphere than with those sights taken at high altitudes;there Is a loss of about two magnitudes between thezenith and the horizon. In addition, because the lightrays pass close to the sea's surface, the refraction cor-rection (bending of the light path) Is large and maybe adversely affected by abnormal atmospheric ccndr-nons. At high altitudes, although the refractioncorrection (zero In the zenith) Is small and of greatercertainty, It will be difficult to estimate when the bodyand horizon are In proper coincidence. Bringing abody down to the horizon with the sextant can be adifficult operation.

From the bodies that satisfy the altitude restric-tions, select those that will give a good fix. One obser-vation to each of two bodies, not In nne but preferablyclose to 90 apart In azimuth, will be the minimumrequirement to obtain a fix. Jftlme and opportunity per-mit, observations to a number of bodies are desirable toprovide not only a check on the observations and cal-culmens but an assessment of the quality of theobserved position.

It Is good practice also to select the bodies that arewell distributed In azimuth because even If there Is, say,a constant error In altitude-for example, a poor derer-mlnatlon of the sextant Index correction-the selectedposition should lie within the figure formed by the inter-


11/21

THE COMPLETE ON-BoARD CELESTIAL NAVIGATOR

horizon; the lowest point of the arc Iswhere the altitude Is measured. Perfect thecoincidence b y operating the slow-motionscrew until the body appears to touch thehorizon. Call out "time" to the recorderor, if operating single-handed, startcounting seconds until you can note atime on the watch. The watch readingminus the seconds count Is the time ofobservation. Read the degrees on themain scale and add the reading from themicrometer drum, which Is graduatedfrom 0 to 60 minutes.This technique is suitable for starsand planets, but with the Sun or Moonthe contact of the body with the horizonIs made with either the upper or lowerlimbs (edges]. The following figure showsthe appearance In the field of view of thepath of the Sun's lower 11mband a star asthey touch the horizon at the time ofobservation.

lions from as high a vantage point aspossible.

4 In fog or mist It may be necessary to finda low observation point In order to seethe horizon clearly.

5 When there Is broken cloud, the bodymay appear only fieetlngly; under thesecircumstances the navigator should pre-pare a tist ofaltlrudes for setting the sex-tantand compass bearings to locate thebodies. The prediction and Identificationtables are Invaluable for this purpose. Asa precaution, Ifyou are uncertain. of theIdentity of any body, take a compass bear-ln g to help In l a te r rdent tncanon.

6 When the vessel Is roiling and pitchingheavily, It Is best to take observationsamidships to I1mltthe motion of theobserver and the variability or the heightor eye.

7 Get Into the habit or making observat ionsas early as possible at evening twilight andas late as possible at morning twilight,when the horizon will have Its besr deflnl-tion. At morning twl!lght, however, It Isalltoo easy to walt too long and see thestars disappear as you try to observetheir altitudes.


12/21

5. PLANNING AND OBSERVATIONS

B o d y - . A z im u t hA l p ~ e r o l l ' " 0 7 1 "S(~edDr 3 0 0 3 'P o l o . 3 0 0 0 1, < > < t o b 3 ' 3 "S l J b i k 3 ' 1 1 .H u n k i 3 3 1 8 7. . . . . 3 7 0 9 3T h o i s " o n / y o n e b o o f t , S D h i i ,' ll i lk h h o s l l l l rJ Z i m u t l p ( 2 1 9 " } I h a t i s " c f a y r o t h toIntt" lfd1Ciur,iI .2W(225-IO/.

5.4 Observation MethodsThere are two approaches to making observations'Either (a) make a single observation on a large numberof bcdtes, or (b) make multiple observations on eachof a fe w bodies. It Is also possible to make observa-tions combining both techniques. For (a) there Is anadvantage In that many lines of position (see Section7.3) result from the calculations. These should allintersect closely together. If one or more lines cannotbe plotted or is markedly distant from this network oflines, we should suspect that a mistake has been madeIn the observation or calculation, or the Incorrect bodyhas been observed. ln the latter situation an examina-

nlent verrlcat and horizontal scales for altitude and time,and plot each observat lcn point (see the example onpage 103). Ifthe observations are error free, the obser-vation points wlll follow a steady slope or trend (changeof altitude wIthtime). This slope can be found, using thediagram on page 161, where we see that approximatevalues of latitude and azimuth are required for Its eval-uation. The azimuth Is usually known from a predictionor compass bearing or can be obtained from the pre-diction and Identification tables. Now construct a uneanywhere on the paper corresponding to this slope(dotted line)-posltive upward, negative downward.Then draw a line parallel to It that best fits the observa-tlon points (full line). In the example gIven, It appearsthat the first observation deviates markedly from thegeneral trend of the remaining observations, and forthis reason Ithas been excluded. The navigator may havenoted at the tlme that the observation was cncharacrer-IstIcally poor or a mistake could have been made Inreading the sextant or recording the time.

The best single representative observation is themean of all the accepted observations, which can befound by taking the average of the times and the au t -tudes. Taking averages can be a source of arirhmetkalmistake, which can be avoided by taking Instead a pointon this fine of best fit. A ny c on ve nie nt p oint will do, andthIs best estimate can be used In the calcularlons.

This technique should be used only Ifthe time inter-val between the flrsr and last observation Is smau, t.e.,


13/21


merldlan of the observer. An addltlonal graph gives the S34 20', longitude E 170' 45' [E I I h 23m, pagecorrectton [the equation of time wIth the sign 176J.reversed] to LAT to obtain LMT [local mean timeJ-the local time kept by the mean Sun: a fictitIous body.If It were possible to view the apparent (real) and themean Sun In the sky, we would see the mean Sun trav-eling at a constant rate along the celestial equator andthe apparent Sun sometimes ahead or behind the meanSun. The apparent Sun would be removed from theequator bya distance equal to Its declination.

The following examples Illustrate the use of thesetables In findIng the times of sunrise or sunset and thebeglnningorendofclvlltwlllght:

E X A M P L EFind the standard time (time zone W2h] of sunrise

on 18 August 1999, In latitude N4S' 40', longitudeW033' 30' {W2h 14m, page 176].

lA l of s un ris e I pc gB 1 30 l 4 h S O m( O I r ~ l i o n ( 5 I J mB J H l g e ) "/ t I 1 0 f l Un r i s e 4 54L o n gi tu d e ( + W , -E l W ~G M ' 1 "T i m e l o n e I -W ,+ El W1__5 n rn do rd ~ m e o I t o o r i s e ~

l A l o f aw tw i ' i J t ( p a g e l 3 1 l 1 9 h 2 5 m( o r r e c OO 1 ( s o m e ~ e l ,11LMTo IG v i l Tw f lQ h l 1 9 3 7l o o g i t OO e { +W , - E ) E ! . l . _ _ QG M ' 8 1 4T i m e l c n e ( -W , + E ) E!.?__S looomd f lmeo f ( i v ! 1 tw i l i g n l ~

Special Cases of Rising and SettingIn high latitudes and at certain times of the year, It maynot be possible to Ilnd a point of Interpolation In thediagrams on pages 130 and 131. These special situa-tions are categorized as follows:

1 The Sun willremain continuously abovethe horizon If the latitude and declinationare of the same name-that Is, both northor both south-and their sum Is greaterthan 89' 10'.

2 The Sun will remain continuously belowthe horizon If the latitude and declinationare of opposite names and rhetr sum Is


14/21

6.3 Star and Planet CorrectionsUjlht coming from a celestial body toward an observeron the Earth travels In a straight line through the vacu-um of outer space until it meets the Earth's atmosphere.Unless thIs light comes from directly overhead, uponentering the Earth's atmosphere the light bends In a ver-tical plane containing the observer and the body. Theamount of bending, called astronomical refraction,reaches a maximum of about 34' near the horizon butreduces to about 10' at about S' altitude and to zero Inthe zenith. Tables of astronomical rerracnon correctionare given In many places throughout this work with theapparent altltude as argument. The correction is alwaysnegative.6,4 Sun CorrectionWhen the Sun and Moon are observed, it is not possi-ble to make an accurate pointing on the center of thebody, whIch Is where the astronomical coordinates arereferred. Instead, observations are made to the edges(limbs) of the body. Reducing an observation made tothe upper or lower 11mbwill require a correction equalto the radius [semidlameter, or s.d.) of the body.

In additIon, another phenomenon called parallax Inaltitude, or lust parallax, must be compensated for. Thiscorrection arises because of the simplifying assumptionmade In astronomical calculations that a ll celestial bod-res III'at an Inflnlte distance from the Earth. Allowance

7. THE MARCO ST. HILAIRE METHOD

Because the Moon correction can have Identicalvalues for two different altitudes, the argument may beentered from either side of the columns of tabulatedcorrection. It Is also apparent from the tables that thecorrection Is sensitive to altitude changes at low alti-tudes, and therefore the altitude argument Is given Indegrees and minutes up to about 10' or so when thecorrection reaches a maximum. Between about 10' and20' the correcrlon remains almost constant. At higheraltitudes, the altitude argument Is given only indegrees. The correction may be either positive or neg-arlve.

6.6 SummaryThe process of applying the dip and sextant correction iscommon to all bodies. Only one further correction toaltitude Is necessary to complete the process. This Isobtained directly from the tables appropriate to the body.

The following examples Illustrate the procedures ina variety of situations:

EXAMPLES

B o d y S a l a n l H . 0 1 E . D ip S e x la n l A p p a r e n tA h i t u d e Icm, A l t i t u d e

I.. 18'43' 5 . 1 m -4' .3 ' I S ' 4 2 '1 m 2 5 1 7 I lh -4 -4 1 5 "


15/21

THE COMPLETE ON-SOARO CElEST1AL NAVIGATOR

away from the body. The LOP Is drawn from this pointat right angles to this direction. The position of the ves-sells somewhere along the LOP. Obviously two or moreLOPs, which give a reasonable Intersection, will resolvethat uncertainty. The data required for this process,called sight reduction, are as follows:

I The LHA obtained from the GHA of thebody as described In Section 4, using theDR longitude.

L H A : G H A :I : D R lo ng it ud e ( +e lI st , -w es t)2 The DR latitude.3 The declination of the body as described

In Section 4.

7"1 InterceptFrom the LHA. DR latitude, and declination, an altitudeIs calculated. The observed altitude Is obtained from thesextant alntude after those corrections described inSection 6 have been applied. The Intercept is found fromthe difference "observed minus calculated altitude,"expressed In mInutes of arc (nautical miles)

The sight reduction tables on pages 132 to 151 aredesigned to provide the navigator with a simple, unver-s a t method of calculating the altitude, using a minimumnumber of steps. There are no decimal points, only one

reduction tables, this table requires onlythis one special rule.

Step2 Extract the appropriate quantities underthe headings LHA (local hour angie), LAT(latitude), DEC (declination), and L - Dfrom the sight reduction tables. like stan-dard trignometrlcal tables, these tables a r earranged to use the minutes column onthe left-hand side when entering from thetop of the page, but when entering fromthe bottom use the minutes column on therf gh r-h an d s fd e.

Step 3 Add the tabulated quantities for LHA,LAT, and DEC. This Is labeled SUM.Reenter the tables and flnd under theheading SUM a value as near as posslbleto it. Write down the tabulated value nextto It under the heading RES (Result}. Donot attempt to Interpolate the tables.

Step 4 Add the value of RES found from thetables to the tabulated value for L - Dpreviously extracted and look up this sumIn the tables from the bottom under theheadlngALT. The search for thIs place Inthe tables Is simplified because the valueyou seek Is close to that tabulated for thes ex t an t or observed altitude.

EXAMPLE


16/21

I f o nly a n a p p ro x im ate a z im uth is need ed , tw o o th ert ec hn iq ue s a re a va ila ble :

1 C lo se to th e t im e o f o b s erv a tio n , ta k ec om pa s s b ea ring s to th e va rio us b o d ies .Af ter c o rrec ting fo r c om pa s s erro r [m ag -netic va ria tio n a nd d evia tio n), tru e b ea r-lngs m ay b e fo u nd . Th e reverse p r o ce s so f f ind ing th e c om pa s s erro r f ro m ano b served c om pa s s b ea ring a nd a ca lcu fa t -ed a z lm urh Is a ls o p o s s ib le u s ing o ne o fth e m eth o ds d es c rib ed u nd er "Az f rnu thTa bles ," o n p ag e 1 9,a nd "W eirD ia g ram s," o n p a g e 20 , a nd in Sec t io ns 8a nd 9.1. Th e a cc ura cy o f a zim uth d erivedfrom a c om pa s s b ea ring Is o nly a s g o o d a sth e erro r o f o b serva t io n c om bined w ithth e u nc erta in ty o f th e c om pa s s erro r {m ag -nertc d ev la rlo n a n d v ar ia ti on ).

2 Az im uth s c a rl b e fo und d irec tly f ro m th epredic t ion a nd Id en tllk at io n ta ble s en p a g e s10 4 to 129 . D eta ils o f th e w ay In w h ic hth es e ta b les c a rl b e u s ed w ill b e fo u nd InSect ion 5.1. Th e a cc ura cy o f a zim u th s f oundb y th is m eth o d m ay net b e very h ig h b e-c au se w e h ave c ho sen a la titu de and LH A toth e nea res t 1 0~ ln o rd er to en ter th e ta b les .

7. THE MARCQ ST . HILAIRE METHOOStep 3 ( a ) I f th e d ec lin a tio n h a s th e o p p o s ite nam e

of th e Ia ritu de , th en th e b od y lies In th es o u t h e rn skvln n or th la tit ud es , en d I n t heno rth ern sk y In so uth la titu des . [ b ) I f t hed ec lin a tio n h as th e s a me na me [north o rs o u th -N orS) a s th e la titu d e a nd is g rea terth an th e la titu de , th en In northern l a t i tudesth e b o d y lies In t h e no rth ern sk y a nd Insou t h eml a t l t u d e s l n t h e s o u t h emsky .

If th e am big uity h a s no t b een res o lvedIn th e p revio u s s tep s -th a t Is , th e decllna-t lo n h a s th e sam e nam e a s th e la titu d e b u tIs num eric a lly sm aller-th en p ro ceed a sfo l lows :

Step 4 Ent e r th e ta b le from th e b ottom w ith th ed ec lin a tio n a nd no te th e va lu e Immedfare lyove r th e polnr o f e nt rv {Y] . E nt er th e ta b leag a in from th e lef t-h and s id e w ith th e la tl-tu d e a nd find o n th e s am e line a va lu e th a tm os t nea rly c o rres p o nd s to th a t o f (Y) . Atth e b o t tom o f th is c olum n, rea d o ff th ev alu e o f a lt itu de , w hic h is th e p rim e v ert ic ala ltitu de-th e a ltitu de w hen th e b od y liesd l r e c t l y ea s t o rwes t o f t h eob s e rve r .Acom-p a r l s onbe tween t h eva l u e s o f t h eob s e rve< la nd p rim e v ert ic al a ltitu d es w ill r es olv e t hea mb ig uity o f w heth er th e b od y lies to th eno rth o r s o u th o f th e p rim e vertic a l. A s un -


17/21

THE COMPLETE ON-BoARO CELESTIAL NAVI(jATOR

4 above IsgivenInthe diagrams above:Choose the latitude, north or south,

that corresponds to your situation. Com-pare the declination or prime vertical alti-tude with those given In the diagram todecide whether the body lies In the north-ern or southern azimuth quadrants.

EXAMPLE

'" [ H A X A l l . 1 . , Y A l l . IL(Ok) ( P . V . )5 1 8 " 3 2 5 " m 13 ' N 4r 1 4 4 "N 63 1 1 3 36 0 2 0 "3 7 3 3 6"1 5 2 8 4 9 3 6 1 9 " 1 7 15 9 3 5 ' 0 6 1"2 3 61 8 1 2 3 4 "5 9 39 0 1 7 2 5 9" 1 6 3 0 1 8 1 3 4 5 5 3 0 5 65 5 4 1 0 9 5 5 5 2 4 5 4 2 2 1 75 1 7 8 8 9 5 5 1 1 5 3 6 2 9 2 3 0 2 5 75 8 3 4 5 2 5 6 6 0 5 3 5 1 3 9 14 0 3 1

Weir DiagramsThe accuracy of this method Is superior to that of thosepreviously described. The original Weir diagram as usedby the British Navy (Admiralty Chart No. 5000) has

respect to the vertical line, with the centeron point X and reading off the azimuth onthe protractor scale, or

(b) transferring the direction X-Ytothe center of the dlasram with a parallelruler and reading off the azimuth on theouter azimuth scale.

For practice with this method use theexamples given under 'j\zlmuth Tables,"this page, and those on the diagrams.

7,3 The Position FixEvery timed altitude observation, be Ita single observa-tion or the representative of a set of observations on abody, willgive an LOP.This LOP may be constructed onthe chart from the Intercept-which Is the differencebetween the observed and computed altitudes-and theazimuth of the body. The position of the observer wouldlie somewhere along this line. It Is obvious that Ifwe havemade observations to two bodies at different azimuths,the Intersection of the two lOPs would give a positionfor the observer. Observations to more than two bodiesare destrable because they wJlinot only provide a checkon the observations and calculations but also allow anassessment of the quality of the observed position.

Ifwe would rather not clutter up the chart with a lotof construction lines, we can draw the LOPs and soforth on a plotting sheet (see page 169), and transfer


18/21

which w e r e marked off In step 2. Theselines should be made heavy, to distinguishthem from the azimuth lines with arrow-heads at the ends of the lines and thename of the body written against them.

4 If more than two bodies have beenobserved and the resulting LOPsdo notlntersecr ar a point bu r crisscross closelytogether, we must select a point that bestfits this configuration. In so dclng, try tokeep the selected point as close as possi-ble to all LOPs. Some simple configura-tions are shown as follows:

5 Finally, read the tanruce and longlrude ofthe selected point. If using a plottingsheet, be sure to use the centralvertical

7. THE MARCQ ST. HILAIRE METHOD

tratlon of this; for example, the average of6,7,9, and 615 7 (sum divided byfol.lr)jrhe djfferences, without regard to sign,from the average an d the individual nurn-bersare 1,0,2, and I, and the sum ofthe squares of these differences is 6. Youwill flnd that there is 110 number, otherthan Z, that willgive a smaller sum ofsquares of differences. To become familiarwith the technique of least squares, se tyourself some examples of plots of LOPsat a largescale. Select the point of fix,measure off the distances (errors), andform the sum of their squares. Move thepoint of fix to another position and com-pare the new sum of squares with the pre-v lous value. After a little practice,you willbe able to choose the optimum point with-OUttaking any measurement. Th i s processof selecting the point of fix could be called"eyeball least squares."

EX AM PLE O F A PO SIT IO N FIXTimed sextant altitude observations w e r e made to

four bodies on the mcmtng of 30 May 1999.Determine the vessel's position using the following addi-tional data: DR position NIO' 30', W13S' 50'; watchcorrection ISs fast; time zone W9hj height of eye


19/21


step I. On the same llne on the left-handslde, read off the amplltude on the lati-tude scale. AzImuth Is given as follows:

appearlng and dIsappearing. The accuracy of thismethod Is similar to that described under "AzimuthTables," on page 19.

Given the latltude and the declination of the body,the amplitude (horizontal angle from the east or westpoints) can be derived from a formula or obtainedfrom spedat tables. The azimuth tables on pages 152to ISS, although not Intended for this purpose, canbe used to derive amplitudes conveniently as follows:Step 1 Enter the table at the bonom with the

decl1natlon (N orS) and note the valueImmediately over the point of entry [Pl.

Step 2 Enter the table at the top with the latitude[Ignore the N orS) and find In the verti-cal column where a value occurs thatmost nearly corresponds to (PJ found In

9 POLARlSThe proxlmlty of Pofarts (the "pole star," Cl UrsaeMinoris, magnitude 2.1) to the north celestial polemakes It a good chlect for determining azlmuth and [at-ltude even though the observer's position and the timeof observarton may not be known very accurately. Firstcalculate the lHA of Aries using the procedure InSection 4.4.9.1 Azimuth

AtRinA tim u lh " ,, 09 0 ': :1 : o m p nt ud e

t 'orsoulhdedinolions,-fornorthde


20/21

1 0 . SUN OBSERVATIONS

10 S U N OBSERVATIONS10.1 Running FixesThe Sun is a most useful body for celestial navigation,being bright and available for observation throughoutmost of the day. Methods of calculating the azimuth ofthe Sun are given In Section 7.2.

If a body such as the Sun or Moon is observed ona number of occasions during the day, an LOP can bedrawn from each DRposition where those observationswere taken. When at least two or more of these lOPsare combined, the position of the vessel can then bedetermined by either (a) plotting the lOPs at anyselected DR position on the vessel's run or (b), as Incoastal navigation, advancing previous LOPs by thecourse and distance run between the times of observa-tion and fix. The result Is called a running f ix . lOPs notplotted at the DR position from which they were calcu-lated are called double sights, transferred sights, orsimply transfers, To distinguish them from normalsights, the lOPs are usually marked with a doublearrowhead on each end.

EXAMPLEThe f o l lowlng observations were taken to the lower

11mbof the Sun in the forenoon, near noon, and after-noon of ISluly 1999. Determine the vessel's positionat watch time 16h SOm (time zone E IOh). The watch

gator should be circumspect about relying on makingsuch observations. A plot of an LOP near the middle ofthe day is lust as valuable as a "noon" sight, describedin the next section.10,2 Meridian ObservationsThe Sun will cross the observer's meridian[north-south nne) twice each day, at upper and lowertransit. The Sun at lower transit can be observed onlyat certain times of the year inside the Arctic orAntarctic Circles: an unusually high latitude for ship-ping. If the altitude of the Sun is observed as it makesIts upper transit, it will be noticed that altitudes slowlyincrease to J maximum and then decrease. At the high-est altitude, the Sun Is said to be making its uppermeridian passage at a time called local apparent noon[LAN). This will not occur at "12 hours" but willdepend on the time of the year and the vessel's posi-tion with respect to the standard meridian adopted fortimekeeping; see the following example.

If the longitude Is known with reasonable certaintyand the altitude Is not roo high, a compass bearing atupper transit will provide a useful compass check. Thetime of meridian passage can be calculated as follows:

EXAMPLE


21/21

celestial navigator

Documents