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