Celestial Coordinates
Junior Navigation
Chapter 5
Light List for the Sky
Junior Navigation
Chapter 6
1
Selecting DIP Correction
HE 14.1ft
corr -3.6’
14.4
If an entry falls on an exact number in
these tables, use the upper correction
(“upper” means the correction that is
physically higher on the page).
HE 14.4 ft
corr -3.7’
HE 14.9ft
corr -3.7’
2
Learning Objectives



Define declination, hour circle, GHA, and LHA
Understand how the GP of a body is located by
celestial coordinates, and relationships among
hour angles
Obtain GHA and declination of the sun from the
Nautical Almanac

Calculate LHA and declination from Nautical
Almanac data
3
Defining Positions


To obtain a celestial LOP you need:
 Ho, altitude of celestial body you observed
 Hc, altitude you calculated from your DR
To calculate Hc, you need to know LHA & Dec
4
Terrestrial Positions
Coordinates?
GP
Latitude – measured
from equator along a
meridian of longitude,
N or S, to maximum
of 90º
Longitude – measured
from prime meridian
along a parallel of
latitude, E or W, to a
maximum of 180º
5
GHA
GP
LHA
Circles
Points
Starting
Coordinates Great
Celestial Positions
Celestial Equator
Greenwich Celestial
Meridian
Hour Circle
(longitude) measured
Parallel of Declination
along the celestial
(latitude) measured
equator
West
toAngle
Greenwich
Hour
along hour circle from
maximum of 360º
equator,
N or S, to
Declination
maximum of 90º
Local Hour Angle
6
Computing LHA

LHA - need to compute local hour angle of body
(cos LHA x cos Lat x cos Dec) + (sin Lat x sin Dec) = sin Hc

Relationship between LHA and GHA is defined as:
LHA = GHA – West Longitude
or
LHA = GHA + East Longitude
7
LHA = GHA – West Longitude
M
30º
45º
LHA
GHA
15º
G
45º
120º
60º
75º
LHA = GHA 120º – Lo 45º W
LHA = 75º
g
m
8
LHA = GHA + East Longitude
M
30º
G
45º
15º
45º
315º
60º
300º
75º
90º
285º
LHA = GHA 270º + Lo 45º E
LHA = 315º
105º
LHA
270º
255º
240º
120º
GHA
225º
135º
270º
g
150º
210º
165º 180º 195º
m
9
LHA = GHA – West Longitude
M
LHA = GHA 90º – Lo 150º W
+ 360º
GHA 450º – Lo 150º W
g
LHA = 300º
GHA
LHA
?
90º
G
m
10
Meridian Transit
When sun directly over Observer’s Meridian:

Details in Chapter 9

Sun reaches its maximum altitude
M

Body is
g
 due North or South

Lo = GHA
LHA = 000º
G
m
11
Sun Overhead

An observer sees the sun directly overhead,

Ho 90º 00.0’

Nautical Almanac lists Sun GHA as 298°

and Sun’s Dec is 20° N
What is your latitude and longitude?
Since Dec = 20°N, then Lat = 20°N
GHA of the sun > 180°, so GP of sun is East Lo
GHA of the sun 360° – 298° = 62° E
12
The Almanac

Published annually by
the Nautical Almanac
Office of the U.S.
Naval Observatory.
13
The Daily Pages
2013 JANUARY 10, 11, 12
2013 JANUARY 10, 11, 12
(THU., FRI., SAT.)
LEFT PAGE
RIGHT PAGE
GHA for Aries, and the GHA &
GHAor
& moon
Dec for
Sun and Moon
Sun
symbols:
Dec plus Magnitude, SHA, & Mer.
plus
times for
nautical
and civil
continuous
above
horizon
Pass. for the four Navigational
twilight,
sunrise,
moonrise,
continuous
below
horizon
Planets,
sunset,
moonset,
and time of
twilight
lasts all night
and the SHA
& Dec for
the 57for sun and
meridian
passage
Navigational
Stars
moon.
T
H
U
R
S
D
A
Y
T
H
U
R
S
D
A
Y
F
R
I
D
A
Y
F
R
I
D
A
Y
14
(TH
Increments and Corrections
Two minutes per page



Used to interpolate between whole-hour values of
GHA & Dec
Tables for each minute of the hour
‘v’ (variable motion) & ‘d’ (declination) corrections
 ‘v’ correction for sun included in hourly values of

GHA; other ‘v’ corrections in
‘d’ correction needed for sun
Navigation
15
Other Almanac Pages









Calendars – Public holidays by country; religious
holidays for United States; moon phase calendar,
Julian calendar
Eclipses
Standard times through-out the world
Star charts
Polaris tables
Sight reduction procedures
Sight reduction tables (NASR method)
Conversions of arc to time
Altitude correction tables for the moon
16
Sight Reduction Form
17
Find UT and LHA and Dec
10 May 2012
17 – 34 – 37
On 10 May you make an
observation of the sun
from St. Paul, at 17 –
34 – 37 WT and your
WE is 8 sec slow
00 – 08
+
17 – 34 – 45
+
5
22 – 34 – 45
10 May 2012
18
Find UT and LHA and Dec
UT is 22 – 34 – 45 and
longitude is
92ºARIES
14.5’MOON
W
SUN
m
34
22
34
155
8 441
150
45
0
3
SECOND
FIRST
CALCULATE
PAGE
PAGE
42 8 40 5 8 41 9 8 16 8
41 8 40.3 8 41.7
.
22
?–
159
?36 3
92
14 5
67
?21 8
PLANETS
+
?
8 16.5
.
.
43 8 40.8 8 42.3
8 17.0
44 8 41.0 8 42.4
8 17.3
3
17
45 8
8
249
8 42 7 8 17 5
41.3
0 46 68 41.5
.
5
8 17.7
49 8 42.3 8 43.7
8 18.5
+
47
8 42.9
.
8 41.8 8 043.23 8 18.0
48 817
42.0 ?
8 43.41 8 18.2
50
19
Find UT and LHA and Dec
M
g
G
UT 2235
zm m
20
Extract LHA & Dec Data

10
38
?
?9
328
12
?–
03 0
33 0
10
337
?
36 0
34
33 3
303
02 7
?
Your DR Lo is
34°33.3´W when you
take a sight on the
sun at UT 10–38–12
on 19 March.
?– 1?0
–
?0
?0
26 0
?
0 6
25 4
21
Extract LHA & Dec Data

12
38
?
?9
358
10
?–
07 8
32 5
12
367
?
40 3
34
33 3
333
07 0
?
Your DR Lo is
34°33.3´W when you
take a sight on the
sun at UT 12–38–10
on 20 March.
?– 1?0
–
?0
?0
00 3
?
0 6
00 3
22
LHA, Dec & Ho
20 18 16FOR
14 YOUR
12 10 ANSWERS?
8
6
4
2
READY



On 17 August, from the point at Bayport Marina,
you observe the LL of the sun at WT 08-57-12 DST;
WE is 1min 08sec slow; recording a sextant height of
27°35.2’; IE reading is 53.4’ off the arc; HE is 22.0ft
and distance to far shore is 0.5nm
GPS reads N45°00.170' W092°46.534'
Complete the upper part of the SR96 (USPS Sight
Reduction Form), calculating LHA, Dec, Ho, and draw
time diagram.
23
USPS SR96
1
Sun LL
45 00 2
92 46 5
17 August
08-57-12
1-08
+
08-58-20
5
+
22 0
27 35 2
66
25 1
NEXT
(0.4156 x d)WEEK
+ [0.5658 x (h/d)]
Ds = (0.4156 x 0.5) + [0.5658 x (22/0.5)]
bring
Ds = 0.2078
+ (0.5658 x 44)
Ds = 0.2078 + 24.8952
Ds calculator
= 25.103
6 6 25 1
13-58-20
Ds =
17 August
18 5
27 16 7
g
13Hc
Ho
G
14 2
14 00 5
27 31.3’
27 30.9’
58 20 14 35 0
zm
13
28 35 5
- 92 46 5
295 49 0
-
13
17 4
14 2 0 0
+ 14 2
0 8
16 6
27 30 9
0 8
13
24
Quiz
1. The coordinates of the GP of the sun are:
Lat 7° 09.5' S, Lo 150° 04.2' E.
a. What are the GHA and declination of the sun at
this time?
GHA = 209° 55.8' [GHA = 360° - Lo E]
Dec =
7° 09.5'S
b. If the LHA of the sun at the same time is
48°32.1' what is the observer's Lo?
Lo = 161°23.7' W [Lo W = GHA - LHA]
25
Quiz
2. You have determined your position by GPS to be
Lat 23° 01.8' N, Lo 76° 56.3'. You look up and
see the sun directly overhead.
What are the Declination, GHA, and LHA of the
sun at this time?
Declination of the sun: 23° 01.8'N
GHA of the sun: 76°56.3'
LHA of the sun: 000°
26
Quiz
3. All meridians of longitude and parallels of
latitude are great circles.
a. True
b. False
27
Quiz
4. Fill in the blanks in the following statements
about celestial coordinates:
Declination
a. __________is
the angular distance of the GP
of a body north or south of the equator.
Greenwich Hour Angle
b. ___________________is
the angular distance
from the Greenwich meridian westward to the
hour circle of a body.
Local Hour Angle is the angular distance from
c. ______________
an observer's local meridian westward to the
hour circle of a body.
28
Quiz
5. When finding declination of the sun from
the Nautical Almanac, a d correction must
be determined.
a. True
b. False.
29
Quiz
6. Using the Excerpts from the Nautical Almanac
for August 24, will the d value be entered on the
Sight Reduction form as positive or negative?
a. positive
b. negative
30
Quiz
7. Using the Excerpts from the Nautical Almanac,
what is the declination of the sun for 1400 UT
on March 30?
57.0' N
Declination of the sun = 3°
_________
31
Quiz
8. Declination of the Sun is equal to the Hour
Declination _____________
plus or minus the d correction.
a. plus
b. minus
c. plus or minus
32
Quiz
9. The local hour angle (LHA) is found by
subtracting
__________ DR Lo(W) from the GHA of the Sun.
a. adding
b. subtracting
33
Celestial Coordinates
End of
Junior Navigation
Chapters 5 & 6
34