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CELESTIAL SPHERE CELESTIAL SPHERE
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CELESTIAL NAVIGATION.Z
Z’
HE HW
Q
PS
PN
Q’
CELESTIAL SPHERE
CELESTIAL SPHERE
RELATION BETWEENDECLINATION
&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 MERIDIANNORTH & SOUTH POLE. STARTING FROM THE QQ’ 90 N & 90 S
• THE CELESTIAL SPHERE HAS90⁰ DECLINATION N90⁰ DECLINATION S
• EQUINOTIAL IS A GREAT CIRCLE
•Q’ Q
PN
PS
DECLINATION
N
DECLINATION S
N
POLAR DIST.
S
DECLINATION + POLAR DISTANCE = 90
POLAR DISTANCE IS THE DISTANCE FROM VISIBLE POLE TO H.B
MERIDIAN
VERTICAL CIRCLE• 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 CIRCLEJOINNING ZZ’ PASSING BY PN PS&NS ALSO CALLED THE OBSERVERMERIDIAN
Z
Z’
’
S’N
E VIEW
PN
PS
E
W
Q
Q
RELATION BETWEENZENITH 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
NADIR
’
SH’NH
ZENITH DIST
ALTITUDE
ALTITUDE
ZENITH DIST
PRIMEVERTICAL CIRCLE
ALT + Z.D = 90
PN
PS
E
W
THE AZIMUTH
• Ѳ AZIMUTHIS THE ANGLE ATZENITH BETWEENPRINCIPAL VERTICAL CIRCLE`TOVERTICAL CIRCLE OF H,B
X = S60E QOR X = N120E SEMIOR X = 120⁰ T•
Y = N70W OR Y = N070W OR Y = 29O ⁰ T
Z
Z’
SN
VERTICAL CIRCLE
PN
PS
W
E PRINCIPAL VERTICAL CIRCLE
Ѳ Ѳ
60
70
X
Y
•
POLAR &DECLINATIONZENITH DISTANCE & ALLTITUDE
• .
’
ZENITH
NADIR
PN
PS
Q Q’
ALTITUDE
ZENITH DISTANCE
SN
PN
PS
POLAR DISTANCE
DECLINATION
ZENITH
NADIR
EQUATORIAL PROJECTION HORIZON PROJECTION
W
E
LATTITUDE OF THE OBSERVER&
ALTITUDE OF THE POLE
• . QZ = NPNLAT OBSERVER = ALTITUDE OF POLE
PROVING Q PN = 90 Z N = 90
Q Q’
PN
PS
Z
Z’
EQUATORIAL PROJECTION
N
S
LAT
LAT
60
30 60
CELESTIAL COORDINATES
CELESTIAL COORDINATES
GREENWICH HOUR ANGLEGHA
• GHA GREENWICH HOUR ANGLE• IS THE ANGLE AT THE POLES THAT LIES BETWEEN THE GREENWICH UPPER MERIDIAN & THE H.B MERIDIANMEASURED IN W DIRECTION. GHA RANGE 360⁰. GHA IS ALLOCATED ACCORDING TO THE TIME.
PN
PS
G GHA
Q’
Z
Z’
QW
E
GREENWICH HOUR ANGLEGHA (ARIS )
• 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
PS
GGHA
QWQE
λ
λ
λ
Z
Z’
GREENWICH HOUR ANGLEGHA
• 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.
PN
PS
G
GHA
QWQE
MERADIAN OF STARZ
Z’
SIDERIAL HOUR ANGLESHA FOR STARS
• SIDERIAL HOUR ANGLE 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
PS
W E
GHA λ
λGHA = GHA + SHA
SH A λ G
ARISSTAR
GHA
RIGHT ASCENSIONR.A FOR STARS
• RIGHT ASCENSION 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
PS
E W
R.A
S.H.A + R.A = 360⁰.
λ
LOCAL HOUR ANGLELHA (LONG E)
LHA LOCAL HOUR ANGLE IS THE ANGLE AT THE POLETHAT LIES BETWEEN THE H.B UPPER MERIDIAN& OBSER. UPPER MERIDIAN.MEASURED WESTERLY
PN
PS
GOBS.LONG
LONG E
GHA
LHA
QE QW
LHA = GHA + LONG (E)
LOCAL HOUR ANGLE
LHA (LONG W)
LHA IS THE ANGLE AT THE POLETHAT LIES BETWEEN THE H.B UPPER MERIDIAN& OBS. UPP. MERIDIAN.MEASURED WESTERLY
PN
PS
G OBS.LONG
GHA
QE QW
LHA
Z
Z’
LHA = GHA – LONG(W)
LONG
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)CIRCUMPOLAR2)RISE & SET
.
’
Z
Z’
PN
PS
N S
Q’
Q
DEC+LAT ≥ 90⁰
N S
Z
Z’
PN
PS
Q
Q’
DEC +LAT < 90
CIRCUMPOLAR RISE & SET
LAT
DEC
1- 2-
DEC
LAT
4) DECL < LAT
. DEC < LAT
Q
PN Z
N
Q’
Z’
S
DEC
LAT
PS
PASS PRIME MERIDIAN
5) DECL > LAT
.
Q
PN
Z
N
Q’
Z’
S
DEC > LAT
MAXIMUM AZIMUTH DURING DURINAL MOTION
DEC.
PS
LAT.
3) DECL = LAT
.
Q
PN Z
N
Q’
Z’
S
DEC = LAT
PASS BY ZENITH
6) DECL = 0
. DEC = O
Q
PN Z
N
Q’
Z’
S
DEC = 0
RISE & SET EQUALS RISE & SET at E& W POINTS
PS
7) DECL = 90
. DEC = 9O
Q
PN Z
N
Q’
Z’
S
DEC = 90
PASSES BY THE POLES
PS
8) LAT = 90
.
Q
PN /Z
N/Q’
PS/ Z’
\S
LAT= 90
DECL = ALTITUDE
APPARENT ANNUAL PATH OF SUN
APPARENT ANNUAL PATH OF SUN
APPARENT ANNUAL PATH &DECLINATION OF SUN
•Q Q’
PN
PS
.
λ 1ST POINT OF ARIESSUN
ECLIPTIC
DECLINATION 23⁰ 26.5’ N
DECLINATION 23⁰ 26.5’ S
21 MAR.Vernal equinox
22 JUNE 69 CANCERSummer solistic
23 SEPT.Autumn equinox
22 DECWinter solistic.CAPRICORN
Ω
λ
Ω 1ST POINT OF LIBRA
DEC.
23⁰ 27’N
23⁰ 27’S
21 MARCH
λ
23 DEC
23 SEPT. Ω
21 MARCH λ
•Q Q’
PN
PS
.
λ 1ST POINT OF ARIESSUN
ECLIPTIC
DECLINATION 23⁰ 27’ N
DECLINATION 23⁰ 27 S
21 MAR.Vernal equinox
22 JUNE 69 CANCERSummer solistic
23 SEPT.Autumn equinox
22 DECWinter solistic.CAPRICORN
Ω
λ
Ω 1ST POINT OF LIBRA
MAX DECLINATION OF THE SUN = 23⁰ 27’N OR 23⁰ 27’S
DAY & NIGHT PHENOMENA FOR OBS. LAT 30⁰ N
THE CONDITION FOR RISING & SETTING ISTHE RISE & SETTING WILL BE EQUAL WHEN DECL = 0
21 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
.
21 MAR
22 JUNE
23 SEPT
22 DEC.
DECL23 27N
DECL23 27S
DAY>NIGHTLAT +DEC<90
DAY<NIGHTLAT +DEC<90
21 MAR.
DAY=NIGHTDEC=0
DAY=NIGHTDEC= 0
LAT 30 N⁰
DAY & NIGHT PHENOMENA FOR OBS. LAT 69 S
THE CONDITION FOR RISING & SETTING IS
21 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
.
21 MAR
22 JUNE
23 SEPT
22 DEC.
DECL23 27N
DECL23 27S
DAY<NIGHTLAT +DEC<90
DAY<NIGHTLAT +DEC<90
21 MAR.
DAY=NIGHTDEC=0
DAY=NIGHTDEC= 0
LAT 69 S⁰DECL=21N 69 -90 = 21
POLAR NIGHTLAT+DEC≥90
POLAR DAYLAT+DEC≥90
DECL=21S
DAY & NIGHT PHENOMENA FOR OBS. LAT 90 S
THE CONDITION FOR RISING & SETTING IS
21 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
.
21 MAR
22 JUNE
23 SEPT
22 DEC.
DECL23 27N
DECL23 27S
POLAR NIGHTLAT +DEC ≥ 90
POLAR DAYLAT +DEC ≥ 90
21 MAR.
DAY=NIGHTDEC=0
DAY=NIGHTDEC= 0
LAT 90 S⁰
DAY & NIGHT PHENOMENA FOR OBS. LAT
00 (EQUATOR)
21 MARCH DECL = 0 LAT = 0 DEC = LAT DAY=NIGHTSUN PASS Z
22 JUNE DECL = 23⁰ 27’N LAT =00 DAY=NIGHT
DEC = LAT DAY=NIGHT23 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
21 MARCH DECL = 0 LAT = 90SUN 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 POLAR22 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 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 JULYPREHELION AT JAN
T² ∞ d³
KEPLER’S 3RD LAWPRACTICE 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) = 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
ab
Earth
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 PLANETIS 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
E
W
G.M.T (UT) & L . M . T
.G
G’
WE
P
G.M.T
G.H.A
ANGLE AT POLE BETWEEN GREENWICH’ LOWER MERIDIAN&MERIDIAN OF THE MEAN SUN
WE
L.H.AL.M
.T
M.SUN M.SUN
OBS.
OBS.’
ANGLE AT POLE BETWEEN OBS. LOWER MERIDIAN & MERIDIAN OF THE MEAN SUN
G.M.T = GHA (T) +/- 12H L.M.T = LHA (T) +/- 12H
RELATIONL.M.T & G.M.T (UT)
. G
G’
P
E W
M.S
OBS
OBS’
GMT
LONGL .M.T
LMT = GMT +/- LONG E / W
LONG
G.A.T & L . A . T
.G
G’
WE
P
G.A.T
G.H.A
ANGLE AT POLE BETWEEN GREENWICH’ LOWER MERIDIAN&MERIDIAN OF THE TRUE SUN
WE
L.H.AL.A.T
T.SUN T.SUN
OBS.
OBS.’
ANGLE AT POLE BETWEEN OBS. LOWER MERIDIAN & MERIDIAN OF THE TRUE SUN
G.A.T = GHA (T) +/- 12H L.A.T = LHA (T) +/- 12H
RELATIONL.A.T & G.A.T
. G
G’
P
E W
M.S
OBS
OBS’
GAT
LONGL .A.T
LAT = GAT +/- LONG E / W IN TIME (/ 15)
LONG
EQUATUION OF TIME
• EQUATUION OF TIMEIS 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.TEQ. TIME = GHA - GHAEQ. TIME = LHA - LHAEQ. 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
TRUE SUN
MEAN SUN
EQUATUION OF TIME&
RELATIONS BETWEEN TIME
EXERCISE
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