CELESTIAL NAVIGATION . Z Q PN HW HE PS Q’ Z’

CELESTIAL SPHERE CELESTIAL SPHERE

RELATION BETWEEN DECLINATION & POLAR DISTANCE DECLINATION IS PARALLEL TO THE EQUINOTIAL, EITHER N DECLINATION OR S DECLINATION. THE DECLINATION STARTS FROM QQ’ UPTO THE DECLINATION MEASURED ON THE H.B MERIDIAN NORTH & SOUTH POLE. STARTING FROM THE QQ’ 90 N & 90 S THE CELESTIAL SPHERE HAS 90⁰ DECLINATION N 90⁰ DECLINATION S EQUINOTIAL IS A GREAT CIRCLE PN N MERIDIAN POLAR DIST. DECLINATION N Q’ Q • DECLINATION S S PS POLAR DISTANCE IS THE DISTANCE FROM VISIBLE POLE TO H.B DECLINATION + POLAR DISTANCE = 90

VERTICAL CIRCLE Z PN Q E ’ N S’ W Q PS Z’ E VIEW PRIME VERTICAL CIRCLE WHICH JOINS Z TO Z’ PASSING BY E & W OVER HORIZON VERTICAL CIRCLE IS A GREAT CIRCLE JOINNING ZZ’ TO THE HORIZON PRINCIPAL VERTICAL CIRCLE JOINNING ZZ’ PASSING BY PN PS &NS ALSO CALLED THE OBSERVER MERIDIAN Z PN Q E ’ N S’ W Q PS Z’ E VIEW

RELATION BETWEEN ZENITH DISTANCE & ALTITUDE ZENITH & NADIR ARE THE VERTICAL HH’ TO ZENITH = 90⁰ POINTS OVER THE OBSERVER HH’ TO NADIR = 90 ZENITH&NADIR IS A GREAT CIRCLE JOINS THE ZENITH WITH NADIR. ZENITH & NADIR MERIDIAN TO HORIZON HH’ THE HEVINLY BODY ALTITUDE MEASURED ON THE ZZ MERIDIAN STARTING FROM THE HH’. THE REST OF THE MERIDIAN IS THE ZENITH DISTANCE OF THE HEAVINLY BODY ZENITH PN PRIME VERTICAL CIRCLE ZENITH DIST W ’ ALTITUDE SH’ NH E ALTITUDE ZENITH DIST PS NADIR ALT + Z.D = 90

THE AZIMUTH Z PN Ѳ Ѳ X E 60 N S • 70 W Y PS Z’ Ѳ AZIMUTH IS THE ANGLE AT ZENITH BETWEEN PRINCIPAL VERTICAL CIRCLE` TO VERTICAL CIRCLE OF H,B X = S60E Q OR X = N120E SEMI OR X = 120⁰ T• Y = N70W OR Y = N070W OR Y = 29O ⁰ T Z PN Ѳ Ѳ VERTICAL CIRCLE X E 60 PRINCIPAL VERTICAL CIRCLE N S • 70 W Y PS Z’

POLAR &DECLINATION ZENITH DISTANCE & ALLTITUDE . HORIZON PROJECTION EQUATORIAL PROJECTION POLAR DISTANCE PN ZENITH ZENITH DISTANCE PN ZENITH ALTITUDE ’ DECLINATION E Q Q’ N S W PS NADIR PS NADIR

LATTITUDE OF THE OBSERVER & ALTITUDE OF THE POLE . QZ = NPN LAT OBSERVER = ALTITUDE OF POLE PROVING Q PN = 90 Z N = 90 EQUATORIAL PROJECTION PN LAT Z N LAT 60 30 60 Q Q’ S Z’ PS

CELESTIAL COORDINATES

GREENWICH HOUR ANGLE GHA GHA GREENWICH HOUR ANGLE IS THE ANGLE AT THE POLES THAT LIES BETWEEN THE GREENWICH UPPER MERIDIAN & THE H.B MERIDIAN MEASURED IN W DIRECTION. GHA RANGE 360⁰. GHA IS ALLOCATED ACCORDING TO THE TIME. PN Z G GHA W Q’ Q E Z’ PS

GREENWICH HOUR ANGLE GHA (ARIS ) λ GHA GREENWICH HOUR ANGLE λ IS THE ANGLE AT THE POLES THAT LIES BETWEEN THE GREENWICH UPPER MERIDIAN & THE MARIDIAN OF ARIS MEASURED. WESTERLY GHA RANGE 360⁰. GHA IS ALLOCATED ACCORDING TO THE TIME. PN Z λ GHA λ G QE QW Z’ PS

GREENWICH HOUR ANGLE GHA GHA GREENWICH HOUR ANGLE IS THE ANGLE AT THE POLES THAT LIES BETWEEN THE GREENWICH UPPER MERIDIAN & THE MERADIAN OF MEASURED WESTERLY . GHA RANGE 360⁰. GHA IS ALLOCATED ACCORDING TO THE TIME. MERADIAN OF STAR PN Z GHA QE G QW Z’ PS

SIDERIAL HOUR ANGLE SHA FOR STARS IS THE ANGLE AT THE POLES THAT LIES BETWEEN THE GHA λ & THE HEAVINLY BODY MERIDIAN. MEASURED WESTERLY ITS RANGE FROM 0⁰ TO 360⁰, PN GHA λ SH A λ G E W GHA GHA = GHA + SHA λ PS STAR ARIS

RIGHT ASCENSION R.A FOR STARS IS THE ANGLE AT THE POLES THAT LIES BETWEEN THE GHA λ & THE HEAVINLY BODY MERIDIAN. MEASURED EASTERLY ITS RANGE FROM 0⁰ TO 360⁰, PN R.A λ W E S.H.A + R.A = 360⁰ . PS

LOCAL HOUR ANGLE LHA (LONG E) LHA LOCAL HOUR ANGLE IS THE ANGLE AT THE POLE THAT LIES BETWEEN THE H.B UPPER MERIDIAN & OBSER. UPPER MERIDIAN. MEASURED WESTERLY PN LHA QE QW OBS. LONG LONG E G GHA LHA = GHA + LONG (E) PS

LOCAL HOUR ANGLE LHA (LONG W) LHA IS THE ANGLE AT THE POLE THAT LIES BETWEEN THE H.B UPPER MERIDIAN & OBS. UPP. MERIDIAN. MEASURED WESTERLY PN Z LONG QW QE G OBS. LONG GHA LHA Z’ PS LHA = GHA – LONG(W)

BASIC PRACTISE EXERCISE

CELESTIAL CONDITIONS CELESTIAL CONDITIONS

CIRCUMPOLAR CIRCUMPOLAR MEANS THAT H.B ALWAYS SETTING NEVER RISES, MEANS THAT THE HEAVENLY BODY ALWAYS RISING NEVER SETS , OR MEANS THAT HEAVENLY BODY ALWAYS ABOVE THE HORIZEN. MEANS THAT H.B ALWAYS SETTING NEVER RISES, MEANS THAT H.B ALWAYS BELOW THE HORIZON.

1)CIRCUMPOLAR 2)RISE & SET . Z Z Q PN Q PN N S N S DEC DEC PS Q’ PS Q’ LAT Z’ Z’ LAT 1- DEC+LAT ≥ 90⁰ 2- DEC +LAT < 90 ’ RISE & SET CIRCUMPOLAR

4) DECL < LAT . DEC < LAT PN Z LAT N Q Q’ S Z’ PS PASS PRIME MERIDIAN

5) DECL > LAT . DEC > LAT PN N Z Q’ Q Z’ S PS MAXIMUM AZIMUTH DURING DURINAL MOTION

3) DECL = LAT . PASS BY ZENITH PN Z DEC = LAT N Q Q’ S Z’

6) DECL = 0 . DEC = O PN Z DEC = 0 N Q Q’ S Z’ PS RISE & SET at E& W POINTS RISE & SET EQUALS

7) DECL = 90 . DEC = 9O PN Z DEC = 90 N Q Q’ S Z’ PS PASSES BY THE POLES

8) LAT = 90 . PN / Z LAT= 90 Q \S N/ Q’ PS/ Z’ DECL = ALTITUDE

APPARENT ANNUAL PATH OF SUN

APPARENT ANNUAL PATH &DECLINATION OF SUN ECLIPTIC PN 21 MARCH λ 23 SEPT. Ω 21 MARCH λ 22 JUNE 69 CANCER Summer solistic . 23 DEC DECLINATION 23⁰ 26.5’ N Ω 23 SEPT. Autumn equinox 23⁰ 27’S Q Q’ • 21 MAR. Vernal equinox λ DECLINATION 23⁰ 26.5’ S 22 DEC Winter solistic. CAPRICORN PS SUN λ 1ST POINT OF ARIES Ω 1ST POINT OF LIBRA

MAX DECLINATION OF THE SUN = 23⁰ 27’N OR 23⁰ 27’S ECLIPTIC PN 22 JUNE 69 CANCER Summer solistic . 23 SEPT. Autumn equinox DECLINATION 23⁰ 27’ N Ω Q Q’ • DECLINATION 23⁰ 27 S 21 MAR. Vernal equinox λ 22 DEC Winter solistic. CAPRICORN PS SUN λ 1ST POINT OF ARIES Ω 1ST POINT OF LIBRA

DAY & NIGHT PHENOMENA FOR OBS. LAT 30⁰ N THE CONDITION FOR RISING & SETTING IS THE RISE & SETTING WILL BE EQUAL WHEN DECL = 0 MARCH DECL = 0 LAT=30 N DAY = NIGHT 22 JUNE DECL = 23⁰ 27’N LAT=30N DAY > NIGHT 23 SEPT DECL = 0 LAT= 30N DAY = NIGHT 22 DEC DECL = 23⁰ 27’S LAT=30N DAY < NIGHT LAT + DECL < 90

DAY & NIGHT PHENOMENA FOR OBS. LAT 30⁰ N DECL 23 27N 22 JUNE LAT 30⁰ N DAY>NIGHT LAT +DEC<90 21 MAR. 21 MAR 23 SEPT DAY=NIGHT DEC= 0 DAY=NIGHT DEC=0 DAY<NIGHT LAT +DEC<90 DECL 23 27S 22 DEC.

DAY & NIGHT PHENOMENA FOR OBS. LAT 69 S THE CONDITION FOR RISING & SETTING IS MARCH DECL = 0 LAT = 69S DAY = NIGHT 22 JUNE DECL = 23⁰ 27’N LAT =69S CIRCUM POLAR 69 + 23.4 ≥ 90 POLAR NICHT 23 SEPT DECL = 0 LAT =69 S DAY = NIGHT 22 DEC . DECL = 23⁰ 27’S LAT= 69S CIRCUM POLAR 69 + 23.4 ≥ 90 POLAR DAY LAT + DECL ≥ 90

DAY & NIGHT PHENOMENA FOR OBS. LAT 69 S DECL 23 27N 22 JUNE LAT 69⁰ S POLAR NIGHT LAT+DEC≥90 DECL=21N 69 -90 = 21 DAY<NIGHT LAT +DEC<90 21 MAR. 21 MAR 23 SEPT DAY=NIGHT DEC= 0 DAY=NIGHT DEC=0 DAY<NIGHT LAT +DEC<90 DECL=21S POLAR DAY LAT+DEC≥90 DECL 23 27S 22 DEC.

DAY & NIGHT PHENOMENA FOR OBS. LAT 90 S THE CONDITION FOR RISING & SETTING IS MARCH DECL = 0 LAT = 90S DAY = NIGHT 22 JUNE DECL = 23⁰ 27’N LAT =90S CIRCUM POLAR 90 + 23.4 ≥ 90 POLAR NICHT 23 SEPT DECL = 0 LAT =90S DAY = NIGHT 22 DEC . DECL = 23⁰ 27’S LAT= 90S CIRCUM POLAR 90 + 23.4 ≥ 90 POLAR DAY LAT + DECL ≥ 90

DAY & NIGHT PHENOMENA FOR OBS. LAT 90 S DECL 23 27N 22 JUNE LAT 90⁰ S POLAR NIGHT LAT +DEC ≥ 90 21 MAR. 21 MAR 23 SEPT DAY=NIGHT DEC= 0 DAY=NIGHT DEC=0 POLAR DAY LAT +DEC ≥ 90 DECL 23 27S 22 DEC.

DAY & NIGHT PHENOMENA FOR OBS. LAT 00 (EQUATOR) MARCH DECL = 0 LAT = 0 DEC = LAT DAY=NIGHT SUN PASS Z 22 JUNE DECL = 23⁰ 27’N LAT =00 DAY=NIGHT DEC = LAT DAY=NIGHT 23 SEPT DECL = 0 LAT =00 SUN PASS Z 22 DEC . DECL = 23⁰ 27’S LAT=00 DAY=NIGHT LAT = DECL PASS BY ZENITH

DAY & NIGHT PHENOMENA FOR OBS. LAT 90 ⁰ N/S MARCH DECL = 0 LAT = 90 SUN MOVES ON HH LAT =90N LAT =90S 22 JUNE DECL = 23⁰ 27’N LAT =90 POLAR POLAR DAY NIGHT 23 SEPT DECL = 0 LAT =90 SUN MOVES ON HH POLAR POLAR DEC . DECL = 23⁰ 27’S LAT=90 NIGHT DAY LAT=90N LAT= 90 S 6 MONTH POLAR DAY , 6 MONTH POLAR NIGHT

KEPLER’S LAWS KEPLER 1ST LAW KEPLER 2ND LAW THE PLANET REVOLVING AROUND THE SUN IN AN ECLIPS WITH THE SUN IN COMMON FOCUS . KEPLER 2ND LAW THE LINE JOINING THE PLANET & THE SUN SWEAPS OUT EQUAL AREAS IN EQUAL TIME KEPLER 3RD LAW THE SQUAR OF SIDERIAL PERIOD OF PLANET IS DIRECT PROPORTION TO THE CUBE OF ITS MEAN DISTANCE FROM THE SUN APHELION AT JULY PREHELION AT JAN T² ∞ d³

KEPLER’S 3RD LAW PRACTICE EXAMPLE THE MEAN DISTANCE OF THE PLANT EARTH FROM THE SUN 149.5 MILLION KM,AND THAT OF THE PLANET JUPITER 777.8 MILLION KM ,CALCULATE THE SIDERIAL PERIOD OF JUPITER IN EARTH YEARS. T² (PLANET) = d ³ ( planet) T² (EARTH ) = d ³ (EARTH) T ( PLANET) = ² √ T (PLANET ) = 11.9 IN EARTH YEARS T² (EARTH) = d ³ ( planet) d ³ ( EARTH) 1 ² X 777.8 ³ 149.5 ³

ECCENTRICITY Eccentricity e = a - b a e : eccentricity a : ½ major axis b : ½ minor axis Earth a b

TIME TIME

DEFINITION OF DAY APPARENT SOLAR DAY : MEAN SOLAR DAY : LUNAR DAY : IS THE INTERVAL FOR THE TRUE SUN TO TURN 360 ⁰ ,”ECLIPTIC” VARIABLE SPEED MEAN SOLAR DAY : IS THE INTERVAL FOR THE MEAN SUN TO TURN 360 ⁰ “EQUINOTIAL” CONSTANT SPEED LUNAR DAY : IS THE INTERVAL FOR THE MOON TO TURN 360 ⁰ . SIDERIAL DAY : IS THE INTERVAL FOR THE STAR ARIS TO TURN 360 ⁰ SIDEREAL FOR PLANET IS THE INTERVAL FOR THE PLANET TO TURN 360 ⁰AROUND SUN

ZONE NUMBER ZONE NUMBER Z.N EVERY 15 ⁰ LONGITUDE GIVES A ZONE ,SINCE THERE IS 180 ⁰ LONGITUDES ,SO WE HAVE 180/15 12 ZONES EAST GREENWICH ( - VE ) & 12 ZONES WEST GREENWICH ( +VE )

ZONE TIME ZONE TIME IS THE LOCAL MEAN TIME LMT OF THE MIDDLE LONG IN A ZONE G.M.T (UT) = Z.T + Z.N

STANDARD TIME STANDARD TIME IS IT IS THE LOCAL MEAN TIME (L.M.T) OF A CERTAIN LONG IN A COUNTRY ,IT DIFFERS THAN G.MT BY HOURS ,MIN. , SECONDS

DATE LINE DATE LINE IS THE LINE OPPOSITE TO GREENWICH , WHICH MEANS THE 180 ⁰ LONG. WHEN SHIP SAILING EASTWARD , ONE DAY ADDED. WHEN SHIP SAILING WESTWARD , ONE DAY SUBTRACTED . -12 +12 ONE DATE IS ADDED ONE DATE IS SUBTRACT W E

G.M.T (UT) & L . M . T . OBS. G W E G.H.A W E P L.H.A M.SUN M.SUN ANGLE AT POLE BETWEEN GREENWICH’ LOWER MERIDIAN & MERIDIAN OF THE MEAN SUN ANGLE AT POLE BETWEEN OBS. LOWER MERIDIAN & MERIDIAN OF THE MEAN SUN G.M.T = GHA (T) +/- 12H L.M.T = LHA (T) +/- 12H

RELATION L.M.T & G.M.T (UT) . G E W OBS P M.S OBS’ G’ LONG P M.S GMT LONG L .M.T OBS’ G’ LMT = GMT +/- LONG E / W

G.A.T & L . A . T . OBS. G W E G.H.A W E P L.H.A T.SUN T.SUN G.A.T ANGLE AT POLE BETWEEN GREENWICH’ LOWER MERIDIAN & MERIDIAN OF THE TRUE SUN ANGLE AT POLE BETWEEN OBS. LOWER MERIDIAN & MERIDIAN OF THE TRUE SUN G.A.T = GHA (T) +/- 12H L.A.T = LHA (T) +/- 12H

RELATION L.A.T & G.A.T . G E W OBS P M.S OBS’ G’ LONG P M.S GAT LONG L .A.T OBS’ G’ LAT = GAT +/- LONG E / W IN TIME (/ 15)

EQUATUION OF TIME EQUATUION OF TIME IS THE RELATION BETWEEN THE MOTION OF THE TRUE SUN & MEAN SUN EQ . T = APPARENT TIME - MEAN TIME EQ . T (+VE) WHEN APP. TIME > MEAN TIME EQ . T (- VE) WHEN APP. TIME < MEAN TIME

EQUATUION OF TIME EQ. TIME = G.A.T - G.M.T (UT) EQ. TIME = L.A.T - L.M.T EQ. TIME = GHA - GHA EQ. TIME = LHA - LHA EQ. TIME = SHA - SHA EQ . T = APPARENT TIME - MEAN TIME EQ . T (+VE) WHEN APP. TIME > MEAN TIME EQ .T ( - VE) WHEN APP. TIME < MEAN TIME MEAN SUN TRUE SUN

EQUATUION OF TIME & RELATIONS BETWEEN TIME EXERCISE