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CELESTIAL NAVIGATION Z PN HW . Q HE Q’ PS 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 PN NORTH & SOUTH POLE. STARTING FROM THE QQ’ 90 N & 90 S N THE CELESTIAL SPHERE HAS 90⁰ DECLINATION N MERIDIAN 90⁰ DECLINATION S POLAR DIST. Q’ • DECLINATION DECLINATION • EQUINOTIAL IS A GREAT CIRCLE S PS POLAR DISTANCE IS THE DISTANCE FROM VISIBLE POLE TO H.B DECLINATION + POLAR DISTANCE = 90 S N Q VERTICAL CIRCLE • PRIME VERTICAL CIRCLE WHICH JOINS Z TO Z’ PASSING BY E & W Z OVER HORIZON PN Q VERTICAL CIRCLE IS A GREAT CIRCLE JOINNING ZZ’ TO THE HORIZON E’ N PRINCIPAL VERTICAL CIRCLE Q JOINNING ZZ’ PASSING BY PN PS &NS ALSO CALLED THE OBSERVER MERIDIAN S’ W PS Z’ E VIEW RELATION BETWEEN ZENITH DISTANCE & ALTITUDE • ZENITH & NADIR ARE THE VERTICAL POINTS OVER THE OBSERVER ZENITH HH’ TO ZENITH = 90⁰ HH’ TO NADIR = 90 PN ZENITH&NADIR IS A GREAT CIRCLE JOINS THE ZENITH WITH NADIR. ZENITH DIST PRIME VERTICAL CIRCLE ZENITH & NADIR MERIDIAN TO HORIZON HH’ W ’ ALTITUDE SH’ NH 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 ALTITUDE E ZENITH DIST NADIR ALT + Z.D = 90 PS THE AZIMUTH • Ѳ AZIMUTH IS THE ANGLE AT ZENITH BETWEEN PRINCIPAL VERTICAL CIRCLE` TO VERTICAL CIRCLE OF H,B N X = S60E Q OR X = N120E SEMI OR X = 120⁰ T• Z PN Ѳ Ѳ X E VERTICAL CIRCLE 60 S 70 • W Y Y = N70W OR Y = N070W OR Y = 29O ⁰ T PS Z’ PRINCIPAL VERTICAL CIRCLE POLAR &DECLINATION ZENITH DISTANCE & ALLTITUDE • . HORIZON PROJECTION EQUATORIAL PROJECTION PN POLAR DISTANCE 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 EQUATORIAL PROJECTION LAT OBSERVER = ALTITUDE OF POLE PN Z N 60 30 60 Q PROVING Q PN = 90 Z N = 90 Q’ Z’ S PS CELESTIAL COORDINATES CELESTIAL COORDINATES GREENWICH HOUR ANGLE GHA • GHA GREENWICH HOUR ANGLE • IS THE ANGLE AT THE POLES THAT LIES BETWEEN THE GREENWICH UPPER MERIDIAN Z & THE H.B MERIDIAN G MEASURED IN W DIRECTION. GHA RANGE 360⁰. GHA IS ALLOCATED ACCORDING TO Q’ THE TIME. PN GHA W Q E PS Z’ GREENWICH HOUR ANGLE GHA (ARIS λ) • GHA GREENWICH HOUR ANGLE λ • IS THE ANGLE AT THE POLES THAT LIES BETWEEN THE GREENWICH PN UPPER MERIDIAN Z & THE MARIDIAN OF ARIS GHA λ G MEASURED. WESTERLY GHA RANGE 360⁰. GHA IS ALLOCATED ACCORDING TO QE THE TIME. λ QW Z’ PS GREENWICH HOUR ANGLE GHA • GHA GREENWICH HOUR ANGLE • IS THE ANGLE AT THE POLES THAT LIES BETWEEN THE GREENWICH UPPER MERIDIAN Z & THE MERADIAN OF MEASURED WESTERLY MERADIAN OF STAR PN GHA . GHA RANGE 360⁰. GHA IS ALLOCATED ACCORDING TO THE TIME. QE QW G PS Z’ SIDERIAL HOUR ANGLE SHA FOR STARS PN • SIDERIAL HOUR ANGLE IS THE ANGLE AT THE POLES THAT LIES BETWEEN THE GHA λ & THE HEAVINLY BODY MERIDIAN. MEASURED WESTERLY SH A W GHA ITS RANGE FROM 0⁰ TO 360⁰, GHA = GHA STAR λ + SHA PS ARIS λ GHA λ G E RIGHT ASCENSION R.A FOR STARS • RIGHT ASCENSION IS THE ANGLE AT THE POLES THAT LIES BETWEEN THE GHA λ & THE HEAVINLY BODY MERIDIAN. MEASURED EASTERLY PN λ R.A W E ITS RANGE FROM 0⁰ TO 360⁰, S.H.A + R.A = 360⁰ . PS LOCAL HOUR ANGLE LHA (LONG E) PN LHA LOCAL HOUR ANGLE IS THE ANGLE AT THE POLE THAT LIES BETWEEN THE H.B UPPER MERIDIAN & OBSER. UPPER MERIDIAN. MEASURED WESTERLY LHA QE QW OBS. LONG LHA = GHA + LONG (E) LONG E G GHA PS LOCAL HOUR ANGLE LHA (LONG W) PN LHA IS THE ANGLE AT THE POLE THAT LIES BETWEEN THE H.B UPPER MERIDIAN & OBS. UPP. MERIDIAN. Z LONG MEASURED WESTERLY QW QE OBS. LONG G GHA Z’ PS LHA = GHA – LONG(W) LHA BASIC PRACTISE • EXERCISE CELESTIAL CONDITIONS CELESTIAL CONDITIONS CIRCUMPOLAR • CIRCUMPOLAR • MEANS THAT THE HEAVENLY BODY ALWAYS RISING NEVER SETS , OR MEANS THAT HEAVENLY BODY ALWAYS ABOVE THE HORIZEN. OR MEANS THAT H.B ALWAYS SETTING NEVER RISES, OR MEANS THAT H.B ALWAYS BELOW THE HORIZON. 1)CIRCUMPOLAR 2)RISE & SET . Z Z Q PN N S N S PS Q’ DEC+LAT ≥ 90⁰ PS Q’ Z’ 1- Q PN Z’ 2- DEC +LAT < 90 ’ CIRCUMPOLAR RISE & SET 4) DECL < LAT . DEC < LAT PN Z LAT N DEC Q Q’ S Z’ PS PASS PRIME MERIDIAN 5) DECL > LAT . DEC > LAT PN N Z DEC. LAT. 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 EQUALS RISE & SET at E& W POINTS 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 OF SUN DEC. APPARENT ANNUAL PATH &DECLINATION OF SUN 23⁰ 27’N ECLIPTIC PN 21 MARCH 23 SEPT. λ Ω 21 MARCH . λ 23⁰ 27’S 23 SEPT. Autumn equinox 23 DEC Q 22 DEC Winter solistic. CAPRICORN DECLINATION 23⁰ 26.5’ N Ω • λ DECLINATION 23⁰ 26.5’ S SUN 22 JUNE 69 CANCER Summer solistic Q’ 21 MAR. Vernal equinox PS λ 1ST POINT OF ARIES Ω 1ST POINT OF LIBRA = 23⁰ 27’N MAX DECLINATION OF THE SUN OR ECLIPTIC PN 22 JUNE 69 CANCER Summer solistic . 23 SEPT. Autumn equinox Q DECLINATION 23⁰ 27 S DECLINATION 23⁰ 27’ N Ω • λ 23⁰ 27’S Q’ 21 MAR. Vernal equinox 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 LAT + DECL < 90 THE RISE & SETTING WILL BE EQUAL WHEN DECL = 0 21 MARCH DECL = 0 LAT=30 N 22 JUNE DECL = 23⁰ 27’N 23 SEPT DECL = 0 LAT= 30N DAY = NIGHT DECL = 23⁰ 27’S LAT=30N DAY < NIGHT 22 DEC LAT=30N DAY = NIGHT DAY > NIGHT DAY & NIGHT PHENOMENA FOR OBS. LAT 30⁰ N . DECL 23 27N 21 MAR 22 JUNE DAY>NIGHT LAT +DEC<90 LAT 30⁰ N 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 LAT + DECL ≥ 90 21 MARCH DECL = 0 LAT = 69S DAY = NIGHT 22 JUNE LAT =69S CIRCUM POLAR POLAR NICHT LAT =69S DAY = NIGHT 23 SEPT 22 DEC . DECL = 23⁰ 27’N 69 + 23.4 ≥ 90 DECL = 0 DECL = 23⁰ 27’S 69 + 23.4 ≥ 90 LAT= 69S CIRCUM POLAR POLAR DAY DAY & NIGHT PHENOMENA FOR OBS. LAT 69 S . DECL 23 27N 22 JUNE POLAR NIGHT LAT+DEC≥90 LAT 69⁰ S DECL=21N 69 -90 = 21 DAY<NIGHT LAT +DEC<90 21 MAR 21 MAR. 23 SEPT DAY=NIGHT DEC=0 DAY<NIGHT LAT +DEC<90 DECL=21S POLAR DAY LAT+DEC≥90 DECL 23 27S 22 DEC. DAY=NIGHT DEC= 0 DAY & NIGHT PHENOMENA FOR OBS. LAT 90 S THE CONDITION FOR RISING & SETTING IS LAT + DECL ≥ 90 21 MARCH DECL = 0 LAT = 90S DAY = NIGHT 22 JUNE LAT =90S CIRCUM POLAR POLAR NICHT LAT =90S DAY = NIGHT 23 SEPT 22 DEC . DECL = 23⁰ 27’N 90 + 23.4 ≥ 90 DECL = 0 DECL = 23⁰ 27’S 90 + 23.4 ≥ 90 LAT= 90S CIRCUM POLAR POLAR DAY DAY & NIGHT PHENOMENA FOR OBS. LAT 90 S . DECL 23 27N 22 JUNE LAT 90⁰ S POLAR NIGHT LAT +DEC ≥ 90 21 MAR 23 SEPT DAY=NIGHT DEC=0 DECL 23 27S 21 MAR. POLAR DAY LAT +DEC ≥ 90 22 DEC. DAY=NIGHT DEC= 0 DAY & NIGHT PHENOMENA FOR OBS. LAT 00 (EQUATOR) LAT = DECL PASS BY ZENITH 21 MARCH DECL = 0 LAT = 0 22 LAT =00 23 JUNE SEPT 22 DEC . DECL = 23⁰ 27’N DECL = 0 DECL = 23⁰ 27’S LAT =00 LAT=00 DEC = LAT DAY=NIGHT SUN PASS Z DAY=NIGHT DEC = LAT DAY=NIGHT SUN PASS Z DAY=NIGHT DAY & NIGHT PHENOMENA FOR OBS. LAT 90 ⁰ N/S 6 MONTH POLAR DAY 21 MARCH DECL = 0 , 6 MONTH POLAR NIGHT LAT = 90 22 JUNE DECL = 23⁰ 27’N LAT =90 23 SEPT DECL = 0 LAT =90 22 DEC . DECL = 23⁰ 27’S LAT=90 SUN MOVES ON HH LAT =90N LAT =90S POLAR POLAR DAY NIGHT SUN MOVES ON HH POLAR POLAR NIGHT DAY LAT=90N LAT= 90 S KEPLER’S LAWS • KEPLER 1ST LAW THE PLANET REVOLVING AROUND THE SUN IN AN ECLIPS WITH THE SUN IN COMMON FOCUS . APHELION AT JULY PREHELION AT JAN • 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 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 T² (PLANET) = d ³ ( planet) (EARTH ) = d ³ (EARTH) T ( PLANET) = ²√ T ( PLANET) = ²√ T² (EARTH) = d ³ ( planet) d ³ ( EARTH) 1 ² X 777.8 ³ 149.5 ³ T (PLANET ) = 11.9 IN EARTH YEARS ECCENTRICITY • Eccentricity Earth a e = a - b a e : eccentricity a : ½ major axis b : ½ minor axis b TIME TIME DEFINITION OF DAY • APPARENT SOLAR 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 W ONE DATE IS ADDED E ONE DATE IS SUBTRACT G.M.T (UT) & L . M . T OBS. G . E W W E P M.SUN L.H.A M.SUN G’ OBS.’ 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) . E G W OBS P M.S OBS’ G’ LMT = GMT +/- LONG E / W G.A.T & L . A . T OBS. G . E W W E P T.SUN L.H.A T.SUN G’ OBS.’ 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 . E G W OBS P M.S 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 EQ . T = APPARENT TIME - MEAN TIME EQ . T (+VE) WHEN APP. TIME > MEAN TIME EQ . T (- VE) WHEN APP. TIME < MEAN TIME & MEAN SUN EQUATUION OF TIME EQ . T = APPARENT TIME - MEAN TIME EQ . T (+VE) WHEN APP. TIME > MEAN TIME EQ. EQ. EQ. EQ. EQ. TIME = G.A.T TIME = L.A.T TIME = GHA TIME = LHA TIME = SHA EQ .T ( - VE) WHEN APP. TIME < MEAN TIME - G.M.T (UT) - L.M.T - GHA - LHA - SHA MEAN SUN TRUE SUN EQUATUION OF TIME & RELATIONS BETWEEN TIME EXERCISE
