at 5 17h00' 590
penr III:
SurveY
: 6 at 18h00' :
scaled from a n
-r8'44'r'.
-18"44'8',
Operatlons
local apparent noon' the and' at 17'6006h'G'C'T' of local apparent The change is -0'7' per hour Aj : -.9'4''s1 that 6 at 17'6006h oris given only to chanse would be (-0'?7;;(0 declination the Nautical Almanac' noo., : -18'44'5''N*tj;il;;'; tenths of minutes' error' Theprecedingcalculationsusealinearinterpolationtoobtainthedeclinationfor otdit' Cont"qu""tlv l-T:':mall the sun, which actuallt;;;il;nontin"u'
usu
Sections 10.33 determined frot triangle can be
inwhicht=l s-,
(r-\
L-l
auy insigninc ant
the foilowing
6or,
I"$; ;: {; } "'.} i'. * :cl*"r"j #."1,:TtirllTiil two-point interpolation equatlon
(6ron
llffi
,
0=) aThe azimuth
:
6or,
*
-
60h)(G'C'T ''o"l?4)
+ (0'0000395)(606)
sin [(7'5)(G'C'T''b")]
t
in decimal hours' in which the G.C'T' is expressed : l8'44'2g'g'+ (0'0000395)(-18'55775) sin [(7'5)(17'6006)]
6"0,
For this example'
l.
When the
AN: Z'\
-
2. When
Arv
6ou.
:
-18o44'2g'g' -2'O"
=
-18o44'31'9'
:
the
180'
TheMicasoftwarepackage|ordeterminingephemerisdatawasnotusedintheprevidata for celestial ousexamples,soat.ew"o,n,i"n*inthisrespeciu..upp'op.iate.The.Micalnteractrve ,.-"rtrf .i f.; ;;;"#*g tables-andw1y of pull-down Astronomical Almanac ;;^il by sfecify, 10.10, for instance, o".].oofO and, by proper use or observations. In Example *fri.fr the declination was desired the year, Aut", unl menus,
The azin
horizontal an device to be
WWV orW'
In each
case'
"-"i.. il;i;c{;,:"g'rxTl"Ji$.::1ffi trl
time for that instant or deta' concerning this
ested user needs a
rrrituUiJunOt
".'",rr".
and the user,s guide
t.""
the software package' calculator o. p"rroiut computer' et Mica user's Guide'' arld Elgin "ld u.s. Naval observu,o.yiio. ,tt.
r"i *ur" pu"tug"r-io, i"n.ruting
Hffi ?ffi:":;tllX,n'"t*}::iiii'",:" ephemerides' The interwn
ephemeris be rererenced to the Sokkia
be determine stoPwatch be sun can be rr This oPerati'
timing
accut
;i:
th:U:$n3ffii"1",Tfi'*?apter
Nautical Almanac'
Next, tl station at oI recommend
compensato
and
horizontal
c
circle. At
tl
loittiltut"
""gi" -"rtt"a
By DrREcr soLAR oBsERvArroN
and the altitude method'
eyePiece sut
horizontal
<
sights to the
Azimuthfromdirectsolarobservationscanbedeterminedbytwoprocedures:thehour-
given in Se using eit 'er
When
Procedure L: Hour-Angle Method
Thehour-anglemethodrequiresveryaccuratedeterminationoftimeandnozenithor ;sed little because of the difficulty t our-angle vertical angle. In tt " piri-tir. "r.th;J;;t for getting accurate time signals' u.Jrrrut" time. with pr"t rn.J."."iuers calcuof obtaining higmy digital watche. ,t u,
illustrated i pointings r sured, so it hair at a P<
is pressed
1
*oi"res usable in pocket p"irrii*".o.olng sprit tlmei,^anJ,itn" a problem' tirn" ioiong"t is such a horizontal angle lators, acquisition ot "*"t"" git",, ri"" by;; h";t:;ngle method' To determine is recorded' It also is "'iltiit "r " *r't;;#;.ed and th";;;;iobservation be
from the line to the
necessary to know
,* iil;;Jlongitude oi-iL
can ,tutlon of observation' which
grouP of 1 reversed P checking. Wher with the t' other met
scaled from a map, found by GPS observations, or determined by the methods outlined in
591
rn, the
,parent
Sections 10.33 and 10.34. Then, using the declination of the sun at the given instant, as determined from data in the ephemeris (Section 10.30, Examples 10.10 and 10.11), the PZS triangle can be solved.by Equation 10.13, which is repeated here for convenience,
cHl.prBn 10:
Introduction to
Astronomy
)nly to
ion for
-sin tanZ: tanDcosd- sin$cost
in which
/
(r0.13)
error,
ruracy,
Lnual):
d: Z:
r : L.H.A. of the sun (Section 10.5) 5 : declination of the sun at instant of observation
latitude of the place of observation clockwise or counterclockwise angle from north in the astronomical triangle
A7,,,
)]
""0,
The azimuth of the sun from the north,
is determined from Z as follows:
prevractive
1. When the sun is east of the meridian (L.H.A. is 180'-360") and tan Z is positive, Ax : Z. When tan Z is negative, AN : Z + 180'. 2. When the sun is west of the meridian (L.H.A. is 0"-180") and tan Z is positive, Arv : 180' + Z.If tan Zis negative' Aw : 360" + Z. The azimuth of the line is computed from the azimuth of the sun and the observed horizontal angle. The usual procedure is as follows. Prior to going into the field, the timing device to be used should be checked very carefully and set using the time signals from WWV or WWVH, received either from a shortwave radio or by calling [phone]. In each case, the DUT correction (Section 10.21) used to correct UT to UTl time should be determined. It is recommended that a pocket calculator equipped with a time module and stopwatch be used as a timing device. In this way, the instantaneous time of centering on the
This operation reduces the total time required to complete the set of angles and yields the timing accuracy necessary for hour-angle method. Next, the theodolite or total station system is set up and leveled very carefully over the station at one end of the line. Use of an instrument with a vertical circle compensator is recommended, in which case the flnal leveling should be performed using the vertical circle compensator (Section 6.40). Sight along the given line with the telescope direct and the horizontal circle set to 0 or, if a direction instrument is being used, observe the horizontal circle. At this stage, before sighting on the srrr, be absolutely certain the obiective or eyepiece sun filter is in place or severe damage to the operator' s eye may result. Loosen the horizontal clamp (upper clamp if a repeating instrument is being used) and take a series of sights to the sun, first with the telescope direct and then reversed, according to the directions given in Section 10.24. Record time and horizontal circle readings for each observation, using either a data collector or field notebook. When the center tangent method is utilized, at least four pointings on the sun, as illustrated in Figure 10.16a, should be made for morning observations. In the afternoon, the pointings would correspond to Figure 10.16c. No zenith or vertical angle is being measured, so it is essential only that the trailing edge of the sun be tangent to the vertical cross hair at a point near the cross-hair intersection. At this instant, the key on the timing device is pressed to record time for the measurement. Next, the telescope is reversed, and the entire group of pointings is repeated. When observations are completed, the telescope, now in ieversed position, again is sighted along the line and the circle reading is observed for
checking. When the instrument is equipped with a solar circle, the required number of repetitions with the telescope direct and reversed are taken, centering directly on the sun. As in the other methods, the horizontal angle and time are recorded for each pointing.
lestial down
use
ion
of of
trther interkage, gin et meris
run.un be recorded and stored by the instrument operator simply by pressing a single key.
10ur-
:h or
:ulty
nals,
llcuLngle
so is
nbe
592
*
fU, Survey Operations
of obserr
FIGURE 10.19
Field notes for a direct solar observation, hour-angle method'
tabulated and usin!
G
consist of at least two people: eyepiece of the telescope (Section \0.24),the party should
Ifsightingonthesunisperformedindirectly'usingawhitecard.heldbehindthe
so that u
one holding the white
"uid key on the timing device' In this and manipilating the horizontal tangent screw and the the image
case, motions of the sun are the
b"hind the relescope and the other operating the theodolite
G.H.A.o
."u"rr" of those shown in Figure 10'16, with ofthesunmovingdownandtotherightinthemorningandupandtotherightinthe
afternoon.
which
cc
next are
an instrument Figure 10.19 shows notes for a solar observation made from a backsight on station campanile. The instrument used station Mclaughlin (McL.) with of the horizontal circle are was a direction theodolite, so ttte recorded measurements in a hand calculator set directions. Recorded times were determined with a time module correction applied (Section 10'21)' BeJi."ctty ro UTl time from WWV with the DUT a solar reticule or objective filter' cause the theodolite used was not equipped with either
setup at
latitude, is east o
sun:z
the
sun.
The angle fr<
of the sun reflected on a pointing on the trailing limb of the sun-was done using the image of the sun, B, found by Equacard (Section 10.26). A correction for the semidiameter the altitude of the sun is not tion ( 1 0.1 6), must be added to the horizontal angles. Because be calculated using Equation (10'la)', observed in this method, it must the line McL' to Campanile' Reduction of the daia and computation of the azimuth of .10' 1 to illustrate are shown in Table using the second observation with the telescope direct, triangle is shown in Figure 10.20' First, the procedure. The geometry of the spheriial from the directions and listed along UT1 with times of observation'
Examini
deviates are in gc
for the
i
Nol observe
horizon of this I or
a the
ungl", u." computed
(scaled from a U:l;G'S' topographic The latitude and longitude are known for the point l'7
most ob
of 0h, May l6 and quadrangle map) and values for the equation of time and declination
'
fromtheephemerispermitdeterminingtheG.H.A.(UTltime)anddeclinationattheinstant
593
CHAPTER
1O:
ffi
Introduction to Astronomy
+
il
t
il
il
--L:---,+1---_:-)-- -l |
,'r"r'f1
Equatorl
-/ it1,
I I I
-l -_ --l*.- - - - r:.:_ _ _ _ . \A.r'-{i -z'^--'r \.t," \-'' /
Greenwich G.H.A. sun
I I I
I
il
do\'r'
I
\l
FIGURE
1.0.20
f
Spherical triangle for solar observation in Table 10.1. of observation. Note that the G.H.A. also could be determined by interpolation between tabulated values for G.H.A. of the sun at 0h on May 16 and l7 , as given in the ephemeris and using the following equation:
the
rle:
so
G.H.A.ob.
:
G.H.A.or,
+
(G.H.A.24h
-
G.H.A.Oh
+ 360")(UTl/24)
(
10.20)
that using the given data
tite
G.H.A.ob,:180"55'02.3"+(180'54'48.2'-180'55'02.3'+360')(17.309444t'/24r)
his
rge
:
80"33'22.2"
lhe
at
ied
which corresponds to the value calculated in Table 10.1. The G.H.A.ob, and west longitude next.are used in Equation (10.1c) to get the angle r and the L.H.A. Then, the declination, latitude, and / are substituted into Equation (10.13) to yield the angle Z. Because the sun is east of the meridian, the L.H.A. is between 180' and 360", and Z is negative, A" of the
ile
set
le-
ef, 1a
larot
rte
cf
)n.
tic
'7
180'. The azimuth of line McL. to Campanile is found by applying the observed horizontal angle from the mark to the sun, corrected for the semidiameter of the sun to the azimuth of the sun. The azimuths for the remaining measurements then are calculated and listed. Examination of these azimuths reveals no blunders. However, the sixth value,151"27'32.3", deviates from the mean by 17", so this value and D1 are deleted. The remaining azimuths are in good agreement with o : 3.1" and a mean of 751'21'45.1 " is taken as the final value for the azimuth. Note that, prior to examining these calculated azimuths, no check on the quality of observed data had been performed. To check for blunders in the observed times and horizontal angles, the angles could have been plotted versus time, as done in Procedure 2 of this section, on azimuth by the altitude method. However, for the hour-angle method, most observations are made with either a total station system equipped with data collector or a theodolite and hand calculator containing a stored program for astronomical reduction
sun: Z +
rnt
594
TABLE 10.1
TABLE
1O.I
**t
fff,
Survey Operations
method Computation of azimuth by solar observations, hour-angle !sq$$w$Fii$si#iss8!*d!swl*l;!rd!ffiFs:4*!e;ffiq$tls*Piqffids4$e&ffiss6wryi65&#Fq9S[69S&l$la!*r!:4*$qf;$$54$P;$i UTI time Horizontal angle
Telescope
D1
312"59'35.0'
313"45'5'1 .0" 314"13',41.5',
fir14^54.1',
17"
D2
D3
18-34.0"
43.'7"
l'7h20
D4
R5 R6 R7 R8
Notes:
314'3'7'08.8',
1'1^22 31.3"
17h26^50.2"
3r5'34',22.z',
3t6"11'55.5"
316"53',O1.0'
17h29 35.4 17h32 35.2"
17h35-04.6"
Similarly, tt
317"27'55.5"
Azlr
Date: May 16, 1995;Instrument at Station
McL (Mclaughlin)
Forthesecondobservation,D2'thehorizontalclockwiseanglefromMcL.tosyl^;3'|4"45'51.0,,andUTl : 17h18*34 .o' : 17 '309444h' 6 : 37'52'21 z"' and i : 122"15'32'8'' ii-"
"i "Lr"i""ion From the ePhemeris,
: apparent - mean : 00h03'40 16' :00h03'39'21" Equation oftime24h, 5-16-95 : -0 95" Difference in equation of time : (-0'95) (11 '3/24) : -0 68' Correction to time of observuliotl : 00b03'39 48" Equation of time at 17 '309444h: 00h03'40 16" - 0'68' : 17h18'34'0' uTl atobservation - 17h22'13 48' G.A.T. aL observation - 12h
Equation of time
0h'
5-16-95
of the dat
needs onl
G.H.A. of sun at instant of observatlon G.H.A. converted to degrees
West longitude
r
:
G.H.A.
L.H.A.
From ephemeris,
:
-
west longitude (Equation
(10'lc))
360' + t (Equation (10 1a))
Declination of sun 0h Declination of sun 24h
- 5h22^13.48" : 80"33'22.2" : -122"15'32.8" : -41"42'10.6" -- 3 18" 11 49 .4',
'
ter of sun
generate as soon repeated both a di
number
<
: :
6on
:
18"56'17 0"
6zqn: 19'10'l 1'0'
Proced
Finding
Declinatronob"
:
50h
+
(624h
-
A.h)
(UT1/24) + (0 0000395(60J sin [(7 5)(UTl)]
1
Declinationoo. Then, by Equation (10.13)'
: 19'o6'2o'4": 19 105665'
{tan 5 + Z:
sin
and shou time by In tl
Z: tan-r[-(sin
r)/(cos
f
cos
r)]
:
-'74'466'7O0"
altitude
measure
and Zis negatrve' so The L.H.A. is 180-360', the sun is east of the meridian'
with
th
Azimuth of sun :
From the ePhemerts,
180"
105'53330
=
105'31'59 8"
as descri
Semidiameter of sun at 0b UT Semidiameter of sun at
24h
: :
15'50'1" 15'50'5'
UT
correction at 17h18-34.0'
By Equation (10.16)'
:
15'50.'7"
+ (15'50.5" -
15',50.7',) (17.3094/24)
=
15',50'6"
in whicl
azimuth
line thet
B = (5'50.6")/ ft : sin r(sin
cos h
{sin 5 +
cos @cos Scos
t:
49'273095"
(Equation (10.14)) (continued)
TABLE 10.1 (concluded\
595
Horizonral angle to center of sun :
F
(15'50.6)/cos 49.273095
313.45,5j .0,
:
CHAPTER 0.4041112.
1O:
-
0"24,16.9,,
Introduction to
Astronomy
+
0.24'16.9,,
=
Azimurh of line McL. ro Campanile
314'10'13.9" [360"
- A, =
_
(314"10'13...