The document discusses key concepts in field astronomy including: 1. The axis of rotation of Earth and how it intersects the Earth's surface at the North and South poles. 2. Latitude is the angular distance north or south of the equator, measured along a meridian. 3. Longitude is the angular distance east or west of the prime meridian, measured along the equator. 4. The celestial sphere is an imaginary sphere where astronomical objects appear to be projected for analysis of their positions. Key points on the celestial sphere like the celestial poles and equator are discussed in relation to their Earth-based counterparts.

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FIELD ASTRONMY
EARTH
AXIS OF ROTATION
The Axis about which earth rotates is called axis of rotation.This axis intersects earth surface
at two points, known as south pole and north pole or another way we can say that the axis
of rotation of earth is joining the passing from north pole south pole of earth.
LATTITUDE
It is an angular distance of any place on the earth surface north and south point of equator,
and is on the meridian of the place. It marked + or – (or N or S) according as the place is
north or south of the equator. The latitude may also be defined as the angle between Zenith
and celestial equator.

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LONGITUDE (Ø)
The longitude of a place is the angle between fixed refrence meridian called the prime
meridian or the fixed meridian and the meridian of the place .The prime meridian
universally adopted is that of Greenwich .the longitude of any place varies between 0 to 180
degree, and is reckoned as ( Ø ) degree east or west of Greenwich.
CELESTIAL SPHERE
The imaginary sphere on which all stars moon , sun , planets etc are considered to be
projected for analysis of position know as celestial sphere.
The millions of stars that we see on the sky on the cloudless night are all at varying distance
from us .Since we concerned with the relative distance rather than their actual distance
from the observer , it is exceedingly convenient to the picture the stars are distributed on
the surface on The imaginary spherical sphere having its centre at the position of the
observer. The imaginary sphere on which stars appears to lie or to be studded is known as
celestial sphere. The radius of the celestial sphere may be of any value from a few thousand
meters to few thousand kilometers . Since the stars are very distance from us, the cenre of
the earth may be taken as the center of the celestial sphere.
CELESTIAL POLE
The Axis of rotation of Earth intersects celestial sphere at two points called pole points of
the celestial sphere , or we can also say that if we increase the line joining in both direction
then it intersects at the the celestial sphere at the two points ,these points are Celestial
poles
CELESTIAL EQUATER
The great circle perpendicular to axis of rotation on Celestial sphere is known as Celestial
Equator in which it is intersected by the plane of terrestrial equator. It is an special case of a
great circle in which great circle makes complete 90 degree angle with the axis of rotation of
Earth having radius equals to the radius of Celestial sphere of the system.

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GREATCIRCLE
Any circle of celestial sphere, which has center same as celestial center is known as
great circle.
The radius of the great circle is always same as the radius Celestial sphere. In any
celestial sphere there may of of infinite number of great circles.
Celestial sphere is also a type of great circle or we can also say that Celestial sphere is
the subset of set of Great circles.
ZENITH
The Point on celestial sphere vertically above observer’s position on Earth is called
Zenith point.
It may be also can understand as if the line joining the observer position on the Earth
and the the centre of earth cuts the celestial sphere then the upper position of the
observer’s position on the Celestial sphere is Zenith point

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NADIR
The Point vertically below the observers position on earth and Celestial sphere known as
Nadir point.
It may be also can understand as if the line joining the observer position on the Earth
and the the centre of earth cuts the celestial sphere then the lower position of the
observer’s position on the Celestial sphere is known as Nadir point.
VERTICLE CIRCLE
All those great circles perpendicular to passing through Zenith and Nadir called verticle
circle. They all cut the Celestial horizon at the right angle.
There can be infinity number of Great circles are possible which are passing through Zenith
and Nadir point that means there are infinite number of vertical circle are possible in the
any Celestial system.

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OBSERVERS MERIDIAN
The Verticle circle passing through pole points along Zenith and Nadir called Observer
meridian. The meridian of any particular point is that circle which passing through zenith
and Nadir of the point as well as through the poles.
Thus Observer meridian is the subset of set of verticle circle having special case when it
passing also through the poles points of celestial sphere.
PRIMEVERTICLE
The Great circle(verticle circle) perpendicular to Observers meridian called prime verticle.
Prime verticle is the subset of the set of verticle circle where the possibility of having prime
verticle in verticle circle is one with respect to number of verticle circles on celestial
sphere.It is also an special case of verticle circle.

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CELESTIAL HORIZON
The great circle which is perpendicular to zenith and nadir line called celestial horizon. It is
also called as True or rational or Geocentric horizon. It is great circle traced upon the
celestial sphere by that plane which is perpendicular to the Zenith-Nadir line ,and which
passes through the center of the Earth (Great circle is a section of a sphere when the plan
passess through the center of the sphere).
SENSIBLEHORIZON
A circle on celestial sphere parallel to celestial horizon with observer as center is known as
sensible horizon.
It is a circle in which a plane passing through the point of observations and tangential to the
earth surface ( or perpendicular to the Zenith-Nadir Line) intersects with Celestial sphere .
the line of sight of an accurately levelled telescope lies in the plane.
NOTE- The distance between celestial horizon and sensible horizon is always equals to the
radius of the earth.

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ECLIPTIC
The path traverse by Sun on celestial sphere is known as Ecliptic. It as also can be defined as
the great circle of the heavens which the sun appears to describe on the celestial sphere
with the earth as a center in a course of a year . The plane of the Ecliptic is inclined to the
plane of the Equator at an angle( angle of obliquity) of about 23 degree and 27 minutes , but
is subjected to an diminution of about 5 second in a century.
DIRECTION
HORIZONSYSTEM -
The Intersection of the observer meridian to celestial horizon will give N-S point of the
Horizon system. The Intersection of the prime verticle with Celestial horizon will give E-W
point point of the Horizon system.
EQUITERIAL SYSTEM:-
The Intersection of observer meridian with equator give North-South point of the Equitorial
System and the intersection of prime verticle with Equator gives East-West point.

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

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ASTRONOMICAL CO-ORDINATESYSTEM:-
 HORIZONSYSTEM:-
ALTITUDE (α):-
The Angle of star measured above or below horizon towards zenith is called altitude
angle. It can also be defined as the altitude angle of celestial or heavily body is its
angular distance above the horizon , measured on the verticle circle passing through the
body.
CO-ALTITUDE(90-α):-
Angle between the observer meridian and great circle passing from the zenith and star
or projection of star is called Azimuth (A).It is also called as Zenith distance.
Note:- At the sunset and the sunrise position, altitude of sun is zero degree (α = 0).

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EQUTORIAL SYSTEM:-
DECLINATION ANGLE(δ):-
The Angle above and below equator measured along declination circle towards pole is
called the declination angle .It can also be defined as the angular distance from the plane of
Equator, measured along the star’s meridian generally called the declination circle.
It varies between 0 to 90 degree.
CO-DECLINATION ANGLE(90-δ):-
The Angle between the pole and star along the declination circle called co-declinatio also
known as a polar distance.
It can also be define as the angular distance between the heavily body from the nearer pole.

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HOUR ANGLE(H)
The Angle measured along the equator starting from the South point towards the star
position is called the Hour angle.
It may also be define as the angle between the observer’s meridian and the declination
circle passing through the body. Hour angle always measured westwards.
SPHERICAL TRIANGLE:-
Spherical triangle is that triangle which is formed upon the surface of the sphere of the
sphere by intersections of the three arcs of three Great circles and the angle formed by the
arcs at the vertices of the triangle, is called spherical triangle.

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SIDES (a,b,c):-
The Angle made at centre of sphere by any two edge is called side of spherical triangle. The
sides of spherical triangle are propotional to the angle substend by them at the centre of
the sphere .
ANGLES (A, B, C):-
The Angle between any two faces is called spherical angle.
NAPIER’S RULE
This rule is valid for the right angle spherical triangle only.
Steps:-
1) Write all parameters in sequence (Either clock wise or anti clock wise)
[ a C b A c ]
Note-Do not consider the angle which is 90 degree.
2) Keep extreme values as it is and write co-value of all other parameters.

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a C b A C
a (90-C) (90-b) (90-A) C
3) Draw Napier’s circle
4) Now we can write to formula using to given key relations
Example:-
Sin (a) = cos (90-a) x cos (90 –b) = [sin A sin b]
Sin (a) = tan (90-C) x tan c = [cot C tan c]

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ASTRONOMICAL TRIANGLE:-

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Triangle ZPM is Astronomical Triangle.
Sides:-
MZ:- Co-altitude
= 90 – α [ zenith distance]
MP = Co-declination
= ( 90-δ) [polar distance]
ZP = Co-altitude = (90-θ)
Angle:-
A= Azimuth α = Altitude
H= Hour Angle δ – Declination
M= star Angle θ- Latitude

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Relations:-
Cos H = Sinα/(Cos θ Cosδ) – Tan θ Tan δ
Cos A = Sin δ/ (Cos θ cosα) - tan θ tan α
Star at transit position:-
(a) upper transit position (M1)
- When a star is crossing observers meridian near zenith it is known as upper transit
position.
b) Lower transit position (M2)
- When a star is crossing observers meridian opposite to zenith known as lower transit
position.
CIRUM POLAR STAR:-
Any star moving around axis of rotation of celestial which never in intersect horizon called
circum polar star.It may also be say as those star which are always above the Horizon ,and
which don’t ,therefore, set. Such a star appear to the observer to describe the circle above
the pole.

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DISTANCEBETWEEN TWO POINTS ON EARTH SURFACEALONG THEGREAT
CIRCLE:-
ROUTE:-

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The distance between two points along the the Earth surface may be considered as the
Great circle distance or the distance between two points on the surface of earth measured
along the sphere , On the sphere there are no straight lines these replaced by the Geodesics
on the sphere. Geodesics are the circles on the sphere of which having center coincide with
center of sphere.
Cos AB = cos a cos b + sin a sin b cos P
Arc distance (AB) = (2πR/360) x (AB )
Direction:-
Tan ((A+B)/2) = [cos ((a-b)/2)] / [cos ((a+b)/2)] x cot (p/2)
Tan ((A-B)/2) = [sin ((a-b)/2)] / [sin ((a+b)/2)] x cot (p/2)
TIME CONCEPT:-
a) TIME:-
- The Change in hour angle of star with respect to standard meridian (fixed meridian)
is called time .
b) SOLAR TIME:-
- Solar time is the calculation of passage of time based on the position of the sun in
sky. The fundamental unit of time is Day.
- There are two types of solar time
1) Mean solar time
2) Apparent solar time
c) APPARENTSOLAR TIME:-
- Time with respect to actual suns movement on celestial sphere is known as apparent
solar time (along ecliptic).
d) Meansolar time.
- According to actual suns movement, perpendicular day ≠ 24 hours exactly. There is a
we consider a fictitious moving along equator with constant rate. According to which
360 degree = 24 hours

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- A time corresponding to this fictitious sun known as a mean solar time.
e) Equation of time:-
- Difference of apparent and mean solar time is known equation of time.
f) Standard time:-
-In one century, everyone has to follow one time corresponding to the standard
meridian
Example:-
In India we considered a time of standard meridian (passes through Allahabad(82◦ 30’ E)).
g) Local mean time (LMT)
-Local mean time is aform of solar time that correct the variation of local apparent time ,
forming a uniform Time scale at a specified Longitude.
LMT = Standard time ± difference of longitude.
(+) –when place is in east of standard meridian.
(-) – When place is in west of standard meridian.
Conversion
360 degree = 24 hours
Angle Hours/Time
1◦ 1/15 Hrs.
1” 1/15 sec.
1’ 1/15 min.

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