11

Light List for the SkyLight List for the SkyJunior NavigationJunior Navigation

Chapter 6Chapter 6

Celestial CoordinatesCelestial CoordinatesJunior NavigationJunior Navigation

Chapter 5Chapter 5

22

Selecting DIP CorrectionSelecting DIP CorrectionHE 14.1ftHE 14.1ft

corr -3.6’corr -3.6’

HE 14.4 ftHE 14.4 ftcorr -3.7’corr -3.7’

HE 14.9ftHE 14.9ftcorr -3.7’ corr -3.7’

1414..44

If an entry falls on an exact number in If an entry falls on an exact number in these tables, use the upper correction these tables, use the upper correction (“upper” means the correction that is (“upper” means the correction that is physically higher on the page).physically higher on the page).

33

Learning ObjectivesLearning 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

44

Defining PositionsDefining Positions To obtain a celestial LOP you need:

Ho, Ho, altitude of celestial body you altitude of celestial body you observedobserved Hc,Hc, altitude you altitude you calculatedcalculated from your DR from your DR

To calculate Hc, you need to know LHA & Dec

55

Terrestrial PositionsTerrestrial PositionsLatitude – 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

GP

Coordinates?

66

Celestial PositionsCelestial PositionsCelestial EquatorGreenwich Celestial MeridianHour CircleParallel of DeclinationGreenwich Hour AngleDeclinationLocal Hour Angle

(latitude) measured along hour circle from equator, N or S, to maximum of 90º

(longitude) measured along the celestial equator West to maximum of 360º

Dec GHA

GP

LHAGr

eat C

ircle

sGr

eat C

ircle

sSt

artin

g Po

ints

Star

ting

Poin

tsCo

ordi

nate

sCo

ordi

nate

s

77

Computing LHAComputing LHA LHA - need to compute local hour angle of body

Relationship between LHA and GHA is defined as:

LHA = GHA – West Longitude

orLHA = GHA + East

Longitude

(cos LHA x cos Lat x cos Dec) + (sin Lat x sin Dec) = sin Hc

88

LHA = GHA – West LHA = GHA – West LongitudeLongitude

LHAGHA

Lo W

M

m

G

g

Lo WGHA

LHA

LHA = GHA 120º – Lo 45º W

LHA = 75º

15º30º

45º

60º

75º

45º

120º

99

LHA = GHA + East LHA = GHA + East LongitudeLongitude

M

m

G

g

Lo E

LHAGHA

Lo E

15º30º

45º

60º

75º

90º

105º

120º

135º150º

165º180º 195º210º

225º

240º

255º

270º

285º

300º

315º45º

270ºGHA

LHA

LHA = GHA 270º + Lo 45º E

LHA = 315º

LHA = GHA 90º – Lo 150º W

LHA = 300º

+ 360ºGHA 450º – Lo 150º W

1010

LHA = GHA – West LHA = GHA – West LongitudeLongitude

M

mG

g

GHALHA

?

Lo W150º

90º

1111

Meridian TransitMeridian TransitWhen sun directly over Observer’s Meridian:When sun directly over Observer’s Meridian: Details in Chapter 9Details in Chapter 9 Sun reaches its maximum altitudeSun reaches its maximum altitude Body is

due North or South Lo = GHA

LHA = 000º

M

m

G

g

Lo WGHA

1212

Sun Overhead Sun Overhead An observer sees the sun directly overhead, An observer sees the sun directly overhead,

Ho 90Ho 90º º 00.0’ 00.0’ Nautical Almanac lists Sun GHA as 298° Nautical Almanac lists Sun GHA as 298° and Sun’s Dec is 20° N and Sun’s Dec is 20° N

What is your latitude and longitude?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 LoGHA of the sun 360° – 298° = 62° E

Published annually by the Nautical Almanac Office of the U.S. Naval Observatory.

2013

NAUTICAL ALMANAC2013 CO

MM

ERCIAL EDITIO

N

JAN 1 2013 THROUGH JAN 1 20142013 N

AU

TICAL A

LMA

NA

C COM

MER

CIAL

EDITIO

N

1313

The AlmanacThe Almanac

1414

The Daily PagesThe Daily Pages2013 JANUARY 10, 11, 12 (THU., FRI., SAT.) 2013 JANUARY 10, 11, 12 (THU., FRI., SAT.)

THURSDAY

FRIDAY

THURSDAY

FRIDAY

LEFT PAGE GHA for Aries, and the GHA & Dec plus Magnitude, SHA, & Mer. Pass. for the four Navigational Planets, and the SHA & Dec for the 57 Navigational Stars

RIGHT PAGE GHA & Dec for Sun and Moon plus times for nautical and civil twilight, sunrise, moonrise, sunset, moonset, and time of meridian passage for sun and moon.

Sun or moon symbols: continuous above horizon continuous below horizon twilight lasts all night

1515

Increments and Increments and CorrectionsCorrectionsTwo minutes per page

UsedUsed 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 Navigation

‘d’ correction needed for sun

1616

Other Almanac PagesOther Almanac Pages Calendars – Public holidays by country; Calendars – Public holidays by country;

religious holidays for United States; moon religious holidays for United States; moon phase calendar, Julian calendarphase calendar, Julian calendar

EclipsesEclipses Standard times through-out the worldStandard times through-out the world Star chartsStar charts Polaris tablesPolaris tables Sight reduction proceduresSight reduction procedures Sight reduction tables (NASR method)Sight reduction tables (NASR method) Conversions of arc to timeConversions of arc to time Altitude correction tables for the moonAltitude correction tables for the moon

1717

Sight Reduction FormSight Reduction Form

1818

Find UT and LHA and DecFind UT and LHA and DecOn 10 May you make an observation of the sun from St. Paul, at 17 – 34 – 37 WT and your WE is 8 sec slow10 May 2012

17 – 34 – 3700 – 08

517 – 34 – 45

22 – 34 – 45 10 May 2012

+

+

1919

Find UT and LHA and DecFind UT and LHA and DecUT is 22 – 34 – 45 and longitude is 92º 14.5’ W

2234 45

92 14 5

–

22

150 55 0

17 49 80 6+

+

8 41 3

0 3159 36 3

67 21 8 17 50 1

1

23

FIRST PAGESECOND PAGE

5

4CALCULATE

???

? ?

MOONARIESSUN PLANETS

m 34

4948474645

444342

8 16.58 41.78 40.3418 40.58 40.88 41.0

8 41.38 41.58 41.88 42.08 42.3

8 41.98 42.38 42.4

8 42.78 42.98 43.28 43.48 43.7

8 16.88 17.08 17.3

8 17.58 17.78 18.08 18.28 18.5

Find UT and LHA and DecFind UT and LHA and DecM

m

Gg

zm 2020

Lo W92.2º159.5º

GHA

UT 2235

ZT 17

35

LHA67.3º

2121

Extract LHA & Dec DataExtract LHA & Dec Data Your DR Lo is

34°33.3´W when you take a sight on the sun at UT 10–38–12 on 19 March.10

38 12

34 33 3

–

10

328 03 0

0 26 01 0–

–

9 33 0

0 6337 36 0

303 02 7

0 25 4

?

??

?

??

? ? ??

2222

Extract LHA & Dec DataExtract LHA & Dec Data Your DR Lo is

34°33.3´W when you take a sight on the sun at UT 12–38–10 on 20 March.12

38 10

34 33 3

–

12

358 07 8

0 00 31 0–

–

9 32 5

0 6367 40 3

333 07 0

0 00 3

?

??

?

??

? ? ??

2323

LHA, Dec & HoLHA, Dec & Ho On 17 August, from the point at Bayport Marina,

you observe the LL of the sun at WT 08-57-12 DST; WEWE is 1 is 1minmin 08 08secsec slow; slow; recording a sextant height of 27°35.2’; °35.2’; IEIE reading is 53.4’ off the arc; reading is 53.4’ off the arc; HEHE is 22.0 is 22.0ftft and and distancedistance to far shore is 0.5 to far shore is 0.5nmnm

GPSGPS reads N45°00.170' W092°46.534' 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.

20 18 16 14 12 10 8 6 4 2READY FOR YOUR ANSWERS?

2424

USPS SR96USPS SR96Sun

LL

1

45 00 292 46 5

1-0808-58-20

17 August

+

17 August08-57-12

+

513-58-20

Gg

zm

25 118 527 16

7

14 2

14 2 0 0 14

227 30 9

-

+

6 6

22 027 35 2

25 1

6 6

13

14 00 55

820 14 35

0

28 35 592 46

5 295 49 0-

13 13 17 40 8

0 816 6

13

--

Ds = (0.4156 x d) + [0.5658 x (h/d)] Ds = (0.4156 x 0.5) + [0.5658 x (22/0.5)] Ds = 0.2078 + (0.5658 x 44) Ds = 0.2078 + 24.8952 Ds = 25.103

NEXT WEEK bring

calculatorHc 27 31.3’ Ho 27 30.9’

2525

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]

QuizQuiz

2626

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°

QuizQuiz

2727

3. All meridians of longitude and parallels of latitude are great circles.

a. True

b. False

QuizQuiz

2828

4. Fill in the blanks in the following statements about celestial coordinates:

a. __________is the angular distance of the GP of a body north or south of the equator.

b. ___________________is the angular distance from the Greenwich meridian westward to the hour circle of a body.

c. ______________ is the angular distance from an observer's local meridian westward to the hour circle of a body.

Declination

Greenwich Hour Angle

Local Hour Angle

QuizQuiz

5. When finding declination of the sun from the Nautical Almanac, a d correction must be determined.

a. True

b. False.

QuizQuiz

2929

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

QuizQuiz

3030

7. Using the Excerpts from the Nautical Almanac, what is the declination of the sun for 1400 UT on March 30?

Declination of the sun = _________ 3° 57.0' N

QuizQuiz

3131

8. Declination of the Sun is equal to the Hour Declination _____________ the d correction.

a. plus

b. minus

c. plus or minus

plus or minus

QuizQuiz

3232

9. The local hour angle (LHA) is found by __________ DR Lo(W) from the GHA of the Sun.

a. adding

b. subtracting

subtracting

QuizQuiz

3333

Celestial CoordinatesCelestial Coordinates

End ofEnd ofJunior NavigationJunior NavigationChapters 5 & 6Chapters 5 & 6

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