Transcript Celestial

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