Navigation ( Part 1 )

 

                 Navigation ( Part 1 ) 

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Geographic Poles

The two points where the axis of rotation cuts the center of earth are called geographic poles.

The upper one is called North pole and lower one is called South pole.

 

Equator

The equator is a great circle which is equidistant from and therefore 90 degree away from the geographic poles . the equator divides the earth into two hemispheres.

The Northern hemisphere and Southern hemisphere

 

Parallels of latitude

Parallels of latitude are small circles parallel to the equator.

 

Meridians of Longitude

Meridians are semi great circle that pass through the geographic poles. Meridians cross the equator and all parallels of latitude at right angles . all meridians run North to South.

 

Latitude (Geocentric)

Latitude of a place is the arc of a meridian or the angle at the center of the earth measured between the equator and the parallel of latitude passing through that place Latitude is expressed in degrees and minutes, North or south of the equator. The latitude of a place can have any value between 0 degree and 90 degree N or S . the latitude of the North pole is 90 degree North and that of south pole is 90 degree South .

 

Prime Meridian

The meridian which passes through Greenwich is called the Prime Meridian and has the value of 0 degree of longitude .

 

 

Longitude

Longitude of a place is the arc of the equator ,or the angle at the geographic pole contained between the Prime Meridian and the Meridian passing through that place . longitude is expressed in degrees and minutes , east or west of Greenwich . Longitude of a place can have any value between 0 degree to 180 degree . longitude 180 degree E and 180 degree W refer to the same Meridian .

 

D’lat – Difference of Latitude

 d’lat between two places is the arc of a Meridian ,or the angle at the center of the earth contained between the Parallel of latitude passing through those two places .

 

D’long  - Difference of Longitude

D’long between two places is the arc of the equator or the angle at the geographic pole contained between the meridians passing through these two points.

 

M’lat  - Mean Latitude

M’lat between places is that Parallel of Latitude which lies midway between the Parallels of Latitude of those two points.

 

The Celestial sphere

For the purpose of Astronomical Navigation , the earth is assumed to be surrounded by a concentric sphere , of infinite radius called the celestial sphere. All astronomical bodies such as the sun ,moon ,stars and planets are assumed to lie on the surface of the celestial sphere. Since all calculations are based on angular measurements . the radius of the celestial sphere is irrelevant . the earth is assumed to be stationary while the celestial bodies are assumed to move on the surface of the celestial sphere.

 

Earth                            -   Celestial Sphere

The geographic poles -   Celestial Poles

Equator                       -   Equinoctial

Meridians                    -   Celestial Meridian

Parallels of Latitude    -   Declination Circles

Position of Observer   -   Zenith of Observer

 

 

Celestial Sphere

The two points where the axis of rotation of the earth cuts the surface of the celestial sphere are called the celestial poles.

 

Equinoctial

The equinoctial is the great circle which is equidistant from and therefore 90 degree away from the celestial poles.

The equinoctial is also referred to as the celestial equator.

 

Declination circles

Declination circles are small circles on the celestial sphere parallel to the equinoctial.

 

Celestial Meridians

Celestial Meridians are semi great circles that pass through the celestial poles. Celestial Meridians cross the equinoctial and all declination circles at right angles.

 

Declination

Declination of a celestial body is the arc of a celestial meridian or the angle at the center of the celestial sphere measured between the equinoctial and the Declination circle passing through that body .  Declination is expressed in degrees and minutes , North or South of the equinoctial . The declination of a celestial body must have a value between 0 degree and 90 degree N or S .

 

 

GHA – Greenwich Hour Angle 

Greenwich hour angle or GHA of a celestial body is the arc of the equinoctial or the angle  at the celestial pole measured westerly from the celestial meridian of Greenwich to the celestial meridian passing through that body. GHA is expressed in degrees and minutes from 0 degree to 360 degree .

GHA would be o degree when the body is on the Greenwich Meridian , increases stadily until it is 360 degree . when it would again be on the Greenwich meridian .

 

LHA – Local Hour angle

Local Hour angle or LHA of a celestial body is the arc of the equinoctial or the angle at the celestial pole ,measured westerly from the observer’s celestial meridian to the celestial meridian passing through that body . like GHA , LHA of a celestial body would increase steadily from 0 degree to 360 degree . LHA would be 0 degree when the body is on the observer’s meridian and steadily increases until it is 360 degree.

LHA = GHA +/- Longitude of observers

 

Note :

Sun’s Orbit is inclined to the equinoctial by about 23 degree 26.5 minutes .

Maximum Northerly declination 23 degree 26.5 minutes N

occurs around june 22nd

Maximum southerly declination 23 degree 26.5 minutes S

Occurs around dec 22nd

There are two specific reference points on the sun’s orbit called the First Point Of Aries and the First Point Of Libra .they are also referred to as the equinoctial points.

 

First Point of Aries

The First Point of Aries is that point on the surface of the celestial sphere where the sun’s path crosses the equinoctial from South to North . The sun’s declination at this point is 0 degree. Occurs around 21 March and is called Vernal Equinox.

 

First Point of Libra

The First Point Of Libra is that point on the surface of the celestial sphere .where the sun’s path crosses the equinoctial from North to South . This occurs around 23^rd sept and is called Autumnal Equinox. The sun’s declination at this point is 0 degree.

 

SHA  - SHA is the arc of the equinoctial or the angle at the celestial pole measured westerly from the First Point Of Aries to the Celestial Meridian passing through the star

GHA * = GHA Aries + SHA *

Right Ascension

Right Ascension of a celestial body is the arc of the equinoctial or the angle at the celestial poles contained between the celestial meridian of the first point of Aries and through that body , measured eastwards from Aries. RA maybalso be expressed in hours , minutes and seconds.

It should be noted that since SHA is measured Westward and RA eastwards from the same point. the SHA and RA of any body will together always add up to 360 degree.

Geographical  Position

The line joining a celestial body and the center of the earth would cut the earth’s surface at a point called the geographical position of that body .

Geographical position is expressed in Latitude and Longitude ,the value of declination is the Latitude of the Geographical position and the value of GHA converted to Longitude would be the Longitude of the Geographical position.

 

Relation between Arc and Time

 

Arc                              Time

360 degree                24 hours

15 degree                  1 hours

  1 degree                  4 minutes

  1 minute                  4 seconds

 

Vertical Circle

Any great circle on the celestial sphere passing through the zenith of the observer is called a vertical circle.

 

Note = the polar distance of the equinoctial is 90 degree .

 

Will revert Navigation Part 2 Shortly

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Good Luck.