Amp8.xls

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Compute Sun Azimuth using Sin amplitude only sun/moon at horizon

Date 8-Dec-04

Time (UTC) 17:45

Sun Azimuth (Obs.) 100.0 Gryo Formula:

Sun Azimuth (Calc.) 240.5 Sin Amp = Sin Dec. Sec Lat

C-O 140.5 GyroInput Position

Lat 38 7.3 S 38.121667

Long 148 18 S 148.3

Sun Declination 22 48.2 S 22.803333

True Gyro 84 applied to gyro

Magnetic 61

Magnetic error 23 (-ve W, +ve E) or 14.1/2W means is more to West

Variation at location 13 Formula:

Deviation 10 Deviation = Error +/ - Variation

if diff. Name error and variation, minus, else plus

Date 8-Dec-04

Time (UTC) 17:45

Sun Azimuth (Obs.) 92.0

Sun Azimuth (Calc.) 119.5C-O 27.5

Input Position

Lat 38 7.3 S 38.121667

Long 148 18 S 148.3

Sun Declination 22 48.2 S 22.803333

True Gyro 86

Magnetic 63

Magnetic error 23 (-ve W, +ve E)

Variation at location 13 Formula:

Deviation 10 Deviation = Error - Variation

Note : If North hemisphere, Sun rise, 90 - Sin(Amp), Sun set, 270 + Sin(Amp)

If South hemispere, Sun rise, 90 + Sin(Amp), Sun set, 270 - Sin(Amp)

W E

0

90

180

270

360

3W

2E

4E

1W

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Sun

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Compute Sun Azimuth

Formula Cot_Azimuth

cot Az =((cosecLHA Tan Dec) + - (cot LHA Tan Lat)) cos lat

If Dec, Lat same name, minus else plus or use ABC Nobies table

When using nobies table to determine AZ. eg. S85W is 180+85,

N85W is 360-85, N85E is 85, S85E is 180-85cot H.A. tan lat as A, cosec H.A tan dec. as B. A +/- B = C

If LHA, Lat same name, plus else minus

A is named opposite to Lat depend on hour angle, see table.

B has same name as dec.

C is S or N (A +/- B) W or E.

Also LHA is 0-180, sun on West (value W), if 180-360, sun East

Morning Sun

Lat (d m) 38 7.5 S Lat (dd) 38.125

Long (d m) 148 20 E

LHA = GHA (+ -) Longitude * East plus, West minus

GHA

22hr 153 7.1 from Almanac

30m 7 30 + from AlmanacLong 148 20 +

LHA (d m) 309 -2.9

LHA (dd) 308.9517

Dec (d m) 5 59.8

Dec (dd) 5.997

If Lat and Dec are same name, minus (-), else plus

Cot Az 0.392822

Az 68.55399

180 + Az

Az 248.554 (Calculated Azimuth)

Afternoon Sun

Lat (d m) 21 12.95 S Lat (dd) 21.21583

Long (d m) 114 39.4 E

LHA = GHA (+ -) Longitude

GHA

10hr 333 9.2

0m 0 0

Long 114 39.4

LHA (d m) 447 48.6

LHA (dd) 87.81

Dec (d m) 6 10.8

Dec (dd) 6.180


Cot Az 0.087178

Az 85.01769180 + Az


Example

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Lat (d m) 21 13.4 S Lat (dd) 21.22333

Long (d m) 114 38.7 E


GHA

22hr 153 11.2

0m 1 15

Long 114 38.7

LHA (d m) 268 4.9

LHA (dd) 268.0817

Dec (d m) 6 22.1

Dec (dd) 6.368


Cot Az -0.11622

Az -83.3707

180 + Az

Az 96.62928

To find out moon Az, Alt.

Lat (d m) 21 31.88 S Lat (dd) 21.53133

Long (d m) 114 46.99 E


GHA

13hr 184 47.7

40m 9 32.7

Long 114 46.99

LHA (d m) 308 67.39

LHA (dd) 309.1232

Dec (d m) 10 22.2 N

Dec (dd) 10.370


Cot Az -0.51793

Az -62.6192

360 - Az


Lat (d m) 21 12.46 S Lat (dd) 21.20767

Long (d m) 114 41.5 E


GHA

23hr 330 34

00m 0 0

Long 114 41.5

LHA (d m) 445 15.5

LHA (dd) 85.25833

Dec (d m) 12 27.4 NDec (dd) 12.457


Cot Az 0.236654

Az 76.68566

360 - Az


Lat (d m) 21 12.46 S Lat (dd) 21.20767

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Long (d m) 114 41.5 E


GHA

22hr 315 59.5

44m 10 41.5

Long 114 41.5

LHA (d m) 441 22.5

LHA (dd) 81.375

Dec (d m) 12 24.2 N

Dec (dd) 12.403


Cot Az 0.262247

Az 75.30526

360 - Az


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Meridian Pass for Sun

11 47 0 UTC from Nautical Almanac

7 38 48 (-ve) from longitude divide 15 to get hms

4 8 12 UTC

8 0 0 GMT +8

12 8 12 Time LocalSun at Zenith.

Formula

LHA = GHA +/- Long If W, minus, E, plus

GHA star = GHA Aries + SHA star.

Local mean times (LMT)

UT = LMT +/- Long If W, plus, E, minus

Longitude need to be converted to time, Long/15=Hr.

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Sin_Az formula

Sin Az = Sin LHA * Cos Dec * Sec Alt Formula 1

or

Sin Az = Sin LHA * Cos Dec * Cosec Zd. Formula 2

Cos Zd = ((cos LHA * cos Lat * Cos Dec)+/- (Sin Lat * Sin Dec)) Formula 3

or Sin Alt if Lat & Dec same name, plus else minus

True Alt. Is the sextant observe altitude angle

Lat (d m) 21 12.95 S Lat (dd) 21.21583

Long (d m) 114 39.4 E


GHA

10hr 333 9.2

0m 0 0

Long 114 39.4

LHA (d m) 447 48.6

LHA (dd) 87.81

Dec (d m) 6 10.8

Dec (dd) 6.180

Cos Zd 0.074374

Zd 85.73475

Alt 4.265248 or 4.265248

Sextant Alt

S.Alt 74 44 d m

Index Error (+)

Obs. Alt 74 44

Hgt. Eye 5.6 (-) from Almanac

App.Alt 74 38.4

Total Corr. 15.9 (+) from Almanac

True Alt. 74 54.3

If true altitude is larger than cal. Alt, then the actual position intercept toward (diff true &cal=min or mile)

else is away.

Azimuth from sun

calc.

away towards

position is along the line, need to observe a few others star for confirmation

Calculate is assumption position as good as it can be.

True is actual position.

Thus using sin Az

Azimuth 85.01769 Azimuth from sun Formula 1

Azimuth 85.01769 Formula 2

So Az = 265.0177

Note: for N latitude, LHA >180, Az= Az

True

Sun

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LHA 180, Az=180-Az

LHA

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Calculating Lat using sun

Meridian Pass for Sun

11 47 0 UTC from Nautical Almanac

7 38 48 (-ve) from longitude divide 15 to get hms

4 8 12 UTC8 0 0 GMT +8

12 8 12 Time Local

Sun at Zenith.

Sextant Alt 74 44 d m

Index Error (-)

Obs. Alt 74 44

Hgt. Eye 5.6 (-) from Almanac

App.Alt 74 38.4

Total Corr. 15.9 (+) from Almanac

True Alt. 74 54.3Mer.True ZD 15 5.7 90-True Alt.

Declination 6 5.1 (+) from Almanac

Latitude 21 10.8 d m

Declination (S), Latitude (S)

Same name, plus, different name, minus Formula :

Lat = Zd +/- Dec.

Dec + Zd = Lat

Dec_s

Zd_s

Dec_n

Zd_s

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