MODULE IIIFIELD ASTRONOMY

ByAbdul MujeebAsst ProfessorDept Civil EngineeringKVGCE

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THE CELESTIAL SPHERE

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To observe the positions

/direction and movement

of the celestial bodies, an

imaginary sphere of

infinite radius is

conceptualized having its

centre at the centre of the

earth.

The stars are studded

over the inner surface of

the sphere and the earth

is represented as a point

at the centre.

The important terms and

definitions are as follows:6

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Point of view of the observer

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(11) Latitude• It is the angular distance of any place on

the earths surface north or south of

equator and measured on the meridian of

the place.

• Marked as +, - or N or S

• Defined as angle between zenith and

celestial equator.

• It varies from zero degree to 90° N and 0°

to 90° S.30

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(12) Co-latitude• It angular distance from zenith to the pole.

• It is complement of latitude and equal to

(90-ɵ).

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(13) Longitude• It is the angle between fixed reference

meridian (prime meridian) and meridian of

the place.

• Universally adopted meridian- Greenwich.

• Varies between 0° to 180°.

• Represented as Φ° east or west of

Greenwich.

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(14) Altitude (α)• Altitude of celestial or heavenly bodies is

its angular distance above the horizon,

measured on the vertical circle passing

through the body.

(15) Co-altitude or zenith distance

(z)• It is angular distance of heavenly body

from zenith.

• It is complement of altitude i.e z=(90-α)35

(16) Azimuth(A)• It is the angle between observers meridian

and vertical circle passing through that body.36

(17) Declination (δ)• It is the angular distance from plane of

equator measured along the stars meridian

called declination circle

• Varies from 0° to 90° and marked as + or

– according to north or south.

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(18) Co-declination or Polar

distance.• It is angular distance of heavenly body

from nearer pole.

• Compliment of declination i.e p=(90°- δ)

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(19) Hour Circle.• Are great circles passing through north and

south celestial poles. Ex: Declination circle

of heavenly body39

(20) Hour angle.• Angle between observers meridian ad

declination circle passing through the

body.

(21) Right Ascension (R.A)• It is equatorial angular distance measured

eastward from the first point of aries to

hour circle passing through heavenly body.

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(22) Equinoctial points• The points of intersection of the ecliptic with

the equator are known as equinoctial points.

Declination os sun is zero at this point

• Vernal Equinox or First point of Aries is the

point in which sun’s declination changes

from south to north. Marks arrival of spring.

• Autumnal Equinox or first point of Libra is

point in which sun’s declination changes

from north to south, marks arrival of autumn.

They are six months apart in time. 41

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(23) Ecliptic• The great circle along which the sun

appears to move round the earth in a year

is called the ecliptic.

• The plane of ecliptic is inclined to plane of

equator at angle about 23° 27ꞌ.

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(24) Solastices• Are the points at which

north and south

declination of the sun is

maximum.• Point at which north

declination is maximum

- summer solastice

• Point at which south

declination is maximum

- winter solastice. 44

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THE CELESTIAL CO-ORDINATE

SYSTEM

• The position of heavenly body can be

specified by 2 spherical co-ordinates, i.e by

two angular distance measured along arcs

of two great circles which cut each other at

right angles.

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• In practical astronomy celestial body can

be specified by following system of

co-ordinates.

1. Horizon system

2. Independent equatorial system

3. Dependent equatorial system

4. The celestial latitude and longitude system

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1. Horizon system (Altitude and Azimuth

system)

• Dependent on position of observer

• Horizon is plane of reference & co-

ordinates of heavenly body are azimuth and

altitude

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• M is the heavenly body in eastern part of

Celestial sphere, Z-zenith & P- celestial pole

• Pass a vertical circle through M to intersect

Mꞌ.

• First co-ordinate of M is azimuth- angle

between observers meridian and vertical circle.

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• It can be either angular distance along

horizon measured from meridian to foot of

vertical circle.

• It is also equal to zenith distance between

meridian and vertical circle through M.

• Another co-ordinate of M is altitude (α)-

angular distance above horizon on vertical

through the body.

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2. Independent Equatorial system (The

declination and Right Ascension system)

• Independent on position of observer.

• Great circle of references are equatorial

circle and declination circle.

• First co-ordinate of body is right ascension-

angular distance along equator from first

point of aries towards east to declination

circle passing through the body.

• It is also angle measured at eastward

celestial pole hour circle through RA and

declination circle through M.

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• RA is measured in direction to opposite to

motion of heavenly body, measured in

degrees, minutes and seconds on in terms of

time.

• Another co-ordinate system is declination- it

is angular distance of body from equator

measured along arc of declination circle.

• Declination is positive if body is north and

negative if body is south of equator.

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3. Dependent Equatorial system (The

declination and Hour angle system)

• One co-ordinate is independent and other

co-ordinate is dependent on position of

observer.

• Great circle of references are horizon and

declination circle.

• First co-ordinate of M is hour angle-

angular distance along arc of horizon

measured from observers meridian to

declination circle. 55

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• It is also measured as angle subtended at

pole between observers meridian and

declination circle.

• Hour angle is measured from south towards

east up to declination circle. Varies from 0°

to 360°.

• Other co-ordinate is declination.

• In Fig SMꞌ is hour angle M1M is

declination.

• Mꞌ and M1 are projections of M on horizon

and equator57

4. Celestial latitude and longitude system

• Prime plane of reference- ecliptic and

secondary plane- great circle passing through

first point of aries and perpendicular to plane

of ecliptic.

• Two co-ordinates are (i) Celestial latitude

(ii) Celestial longitude

• Celestial latitude is arc of great circle

perpendicular to ecliptic. May be +ve or –ve

• Celestial longitude is arc of ecliptic

intercepted between great circle first point of

aries and celestial latitude

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• It is measured eastwards from 0° to 360°.

• M1M is celestial latitude and M1 is celestial

longitude for heavenly body

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Comparison of systems.

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Horizon system Independent

Equatorial

system

Dependent

Equatorial

system

Celestial latitude

and longitude

system

Coordinate

dependency

Depends on

position of

observer

Both coordinates

does not depends

on position of

observer

One coordinate

depends and

another does

not depends on

position of

observer

Does not depends

on position of

observer

Reference

plane

Altitude and

azimuth

Declination and

right ascension

Declination and

hour angle

Celestial latitude

and longitude

Great circle Horizon Equatorial circle

and declination

circle.

Horizon and

declination

circle.

Ecliptic and great

circle passing

through first point

of aries

Example:

Position of

star

Altitude-45º

Azimuth-140º

Declination-70º

Right ascension-

4h

Declination- 70º

Hour angle-50º

Celestial lat-40º

Celestial long-170º

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Example for Horizon system

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Example for latitude and longitude system

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Example for Independent Equatorial system

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Spherical trigonometry and spherical

triangle

• It is triangle which is formed upon surface

of the sphere by intersection of three arcs of

great circle.

• Angles formed by arcs at vertices of

triangle- spherical angles

• In Fig AB, BC and CA are 3 angles of great

circles and intersect each other at A, B & C.

• Angles at A, B, C are denoted by sides

opposite to them (a, b & c) 74

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• The sides of spherical triangle are

proportional to the angle subtended by them

at centre of sphere and are expressed in

angular measure.

• Sine b means sine of angle subtended at

centre of arc AC.

• A spherical angle is angle between 2 great

circles and is defined by plane angle between

tangents to their circles at point of

intersection.

• Angle A is angle between A1AA2 between

tangents AA1 and AA2

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Formulae in spherical trigonometry

For computation purpose

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Napier’s rule

• Relationship of right angled triangle are

obtained from Napier’s rule.

• In Fig ABC is spherical right angled triangle.

• Napier defines circular part as follows.

• These parts arranged around circle in order as

they are in triangle

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• Starting with side a, orders are b,90°-A,

90°-c, 90°-B.

• If any part is considered as ‘middle part’,

adjacent 2 parts are ‘adjacent parts’ and

remaining 2 sides are ‘opposite parts’.

• From Napier rule

sine of middle part=product of tangents of

adjacent parts

sine of middle part= product of cosines of

opposite parts

sin b= tan a tan (90°-A)

sin b= (cos 90°-A) cos (90°-c)82

Astronomical Triangle

• Astronomical triangle is obtained by joining

pole, zenith and any star M on the sphere by

arcs of great circle.

• From this triangle, relation existing amongst

spherical co-ordinates may be obtained.

Let

α-altitude of celestial body (M)

δ-declination of celestial body (M)

ɵ- latitude of observer83

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ZP= co-latitude of observer

PM= co-declination or polar distance of

M=(90-δ)=p

ZM= zenith distance = co-altitude of body=

(90- α)=z

The angle at Z=MZP= The azimuth(A) of body

The angle at P=ZPM=The hour angle(H)of body

The angle at M=ZMP= parallactic angle

If three sides MZ, ZP and PM are known angle

A and H can be computed from formulae of

spherical trignometry85

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Important Questions

1. Introduction and purpose of field

astronomy

2. Definitions

3. The Celestial co-ordinate system

4. Comparison of system

5. Spherical triangle and properties

6. Napier's rule

7. Astronomical triangle

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