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

2. CELESTIAL SPHERE
CELESTIAL SPHERE

3. 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

4. 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

5. 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

6. 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’

7. 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

8. 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

9. CELESTIAL COORDINATES

10. 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 ⁰.
GHA IS ALLOCATED ACCORDING TO
THE TIME. PN Z G
GHA W Q’ Q E Z’ PS

11. 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 ⁰.
GHA IS ALLOCATED ACCORDING TO
THE TIME. PN Z λ
GHA λ G QE QW Z’ PS

12. 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 ⁰.
GHA IS ALLOCATED ACCORDING TO
THE TIME.
MERADIAN OF
STAR PN Z
GHA QE G QW Z’ PS

13. 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

14. 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

15. 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

16. 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)

17. BASIC PRACTISE
EXERCISE

18. CELESTIAL CONDITIONS
CELESTIAL CONDITIONS

19. 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.

20. 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

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

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

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

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

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

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

27. APPARENT ANNUAL PATH OF SUN

28. 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

29. 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 S
21 MAR.
Vernal equinox λ
22 DEC
Winter solistic.
CAPRICORN PS
SUN
λ 1ST POINT OF ARIES
Ω 1ST POINT OF LIBRA

30. 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 = LAT=30 N DAY = NIGHT
JUNE DECL = 23⁰ 27’N LAT=30N DAY > NIGHT
SEPT DECL = LAT= 30N DAY = NIGHT
22 DEC DECL = 23⁰ 27’S LAT=30N DAY < NIGHT
LAT + DECL < 90

31. 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.

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

33. DAY & NIGHT PHENOMENA FOR OBS. LAT 69 S
DECL N 22
JUNE
LAT 69⁰ S
POLAR NIGHT
LAT+DEC≥90
DECL=21N = 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.

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

35. 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.

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

37. DAY & NIGHT PHENOMENA FOR OBS. LAT 90 ⁰ N/S
MARCH DECL = LAT = 90
SUN MOVES ON HH
LAT =90N LAT =90S
JUNE DECL = 23⁰ 27’N LAT =90 POLAR POLAR
DAY NIGHT
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

38. 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

39. KEPLER’S 3RD LAW PRACTICE EXAMPLE
THE MEAN DISTANCE OF THE PLANT EARTH FROM THE SUN MILLION KM,AND THAT OF THE PLANET JUPITER 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 ) = IN EARTH YEARS
T² (EARTH) = d ³ ( planet)
d ³ ( EARTH)
1 ² X ³
149.5 ³

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

41. TIME
TIME

42. 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

43. 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 )

44. 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

45. 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

46. 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 .
ONE DATE IS ADDED
ONE DATE IS SUBTRACT W E

47. 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

48. 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

49. 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

50. 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)

51. 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

52. 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

53. EQUATUION OF TIME & RELATIONS BETWEEN TIME
EXERCISE