Celestial Coordinates
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Celestial Coordinates. Junior Navigation Chapter 5. Light List for the Sky. Junior Navigation Chapter 6. Selecting DIP Correction. HE 14.1ft corr -3.6’ HE 14.4 ft corr -3.7’ HE 14.9ft corr -3.7’. 14 . 4.

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Light List for the Sky

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Light list for the sky

Celestial Coordinates

Junior Navigation

Chapter 5

Light List for the Sky

Junior Navigation

Chapter 6


Light list for the sky

Selecting DIP Correction

HE 14.1ft

corr -3.6’

HE 14.4 ft

corr -3.7’

HE 14.9ft

corr -3.7’

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).

2


Learning objectives

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 Almanacdata

3


Defining positions

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

Terrestrial Positions

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

Coordinates?

GP

5


Celestial positions

Celestial Positions

Coordinates

Starting Points

Great Circles

GHA

Dec

LHA

Celestial Equator

Greenwich Celestial Meridian

Hour Circle

Parallel of Declination

Greenwich Hour Angle

Declination

Local Hour Angle

GP

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

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

6


Computing lha

Computing LHA

LHA - need to compute local hour angle of body

Relationship between LHA and GHA is defined as:

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

LHA = GHA – West Longitude

or

LHA = GHA + East Longitude

7


Lha gha west longitude

LHA = GHA – West Longitude

M

Lo W

GHA

LHA

LHA

GHA

Lo W

m

15º

30º

G

45º

45º

120º

60º

75º

LHA = GHA 120º – Lo 45º W

LHA = 75º

g

8


Lha gha east longitude

LHA = GHA + East Longitude

M

Lo E

LHA

GHA

Lo E

m

15º

30º

G

45º

45º

315º

60º

300º

75º

285º

LHA = GHA 270º + Lo 45º E

LHA = 315º

270º

90º

255º

105º

LHA

240º

120º

GHA

225º

135º

270º

150º

210º

g

165º

195º

180º

9


Lha gha west longitude1

LHA = GHA – West Longitude

M

LHA = GHA 90º – Lo 150º W

LHA = 300º

+ 360º

GHA 450º– Lo 150º W

m

g

Lo W

150º

GHA

90º

LHA ?

G

10


Meridian transit

Meridian Transit

When sun directly over Observer’s Meridian:

Details in Chapter 9

Sun reaches its maximum altitude

Body is

due North or South

Lo = GHA LHA = 000º

Lo W

GHA

M

g

G

11

m


Sun overhead

Sun Overhead

An observer sees the sun directly overhead,

Ho 90º00.0’

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.

The Almanac

2013

2013 NAUTICAL ALMANAC COMMERCIAL EDITION

NAUTICAL ALMANAC

2013 COMMERCIAL EDITION

JAN 1 2013 THROUGH JAN 1 2014

13


Light list for the sky

2013 JANUARY 10, 11, 12 (THU., FRI., SAT.)

THURSDAY

THURSDAY

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

FRIDAY

FRIDAY

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

SATURDAY

SATURDAY

The Daily Pages

2013 JANUARY 10, 11, 12 (THU., FRI., SAT.)

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.

14


Increments and corrections

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 Navigation

    • ‘d’ correction needed for sun

15


Other almanac pages

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

Sight Reduction Form

IGNORE

IGNORE

IGNORE

17


Find ut and lha and dec

Find UT and LHA and Dec

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

10 May 2012

17 – 34 – 37

00 – 08

+

17 – 34 – 45

5

+

22 – 34 – 45

10 May 2012

18


Find ut and lha and dec1

Find UT and LHA and Dec

IGNORE

m 34

SUN PLANETS

ARIES

MOON

22

8 41.9

8 40.5

8 16.8

41

8 40.3

8 41.7

8 16.5

8 17.0

8 40.8

8 42.3

34 45

42

8 41.0

8 42.4

8 17.3

43

44

8 41.3

8 42.7

8 17.5

8 17.7

8 41.5

8 42.9

45

92 14 5

8 18.0

8 41.8

8 43.2

46

8 42.0

8 18.2

8 43.4

47

8 43.7

8 42.3

8 18.5

48

49

UT is 22 – 34 – 45 and longitude is 92º 14.5’ W

CALCULATE

SECOND PAGE

FIRST PAGE

1

150 55 0

4

8 41 3

IGNORE

2

22

17 49 8

IGNORE

3

?

159 36 3

?

0 6

+

5

?

0 3

+

?

67 21 8

?

17 50 1

19


Find ut and lha and dec2

Find UT and LHA and Dec

M

LHA67.3º

Lo W

92.2º

GHA

159.5º

ZT 1735

UT 2235

m

g

G

20

zm


Extract lha dec data

Extract LHA & Dec Data

IGNORE

  • 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

328 03 0

?

9 33 0

38 12

IGNORE

?

10

0 26 0

IGNORE

?

?

?

337 36 0

1 0

?

?

34 33 3

0 6

?

?

303 02 7

0 25 4

21


Extract lha dec data1

Extract LHA & Dec Data

IGNORE

  • 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

358 07 8

?

9 32 5

38 10

IGNORE

?

12

0 00 3

IGNORE

?

?

?

367 40 3

1 0

?

?

34 33 3

0 6

?

?

333 07 0

0 00 3

22


Lha dec ho

LHA, Dec & Ho

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.

20

18

16

14

12

10

8

6

4

2

READY FOR YOUR ANSWERS?

23


Usps sr96

USPS SR96

1

17 August

22 0

Sun LL

08-57-12

27 35 2

45 00 2

1-08

+

92 46 5

6 6

08-58-20

25 1

5

+

6 6

25 1

13-58-20

18 5

-

17 August

27 16 7

g

G

14 2

14 00 5

13

20

14 35 0

58

zm

13

13 17 4

14 2 0 0

28 35 5

14 2

0 8

+

-

92 46 5

0 8

-

-

27 30 9

295 49 0

13

16 6

NEXT WEEK bring calculator

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

Hc 27 31.3’ Ho 27 30.9’

24


Light list for the sky

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


Light list for the sky

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


Light list for the sky

Quiz

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

  • True

  • b. False

27


Light list for the sky

Quiz

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

28


Light list for the sky

Quiz

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

a. Trueb. False.

29


Light list for the sky

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. positiveb. negative

30


Light list for the sky

Quiz

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

31


Light list for the sky

Quiz

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

a. plusb. minusc. plus or minus

plus or minus

32


Light list for the sky

Quiz

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

a. addingb. subtracting

subtracting

33


Celestial coordinates

Celestial Coordinates

End of

Junior Navigation

Chapters 5 & 6

34


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