Geographical Position

The position of this point when expressed in latitude

And longitude is known as the Geographical Position.

Sub-solar point-when the body observed is the sun the corresponding part of the earth.

Sub-astral point or Sub- stellar point - when the body is a star.

Sub-lunar point-when the body is the moon.

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THE EQUINOCTIAL SYSTEM

Celestial Poles ( Pn ,Ps )-are those points where the axis of the earth when the directions for an infinite distance pierces the celestial sphere.

Equinoctial (QQ 1 ) or Celestial Equator -is the great circle on the celestial sphere.

Celestial Meridian-is a great circle of the celestial sphere which corresponds to a terrestrial meridian.

Hour Circle-is a great circle of the celestial sphere similar to the celestial meridian.

-it is considered to rotate with the celestial body.

Diurnal Circle or Circle of Declination-is a projection of the parallel of the latitude into celestial sphere.

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Polar Distance ( Px ) - is the angular distance of any celestial body from the elevated pole.

Hour Angle - is the angle between the planes of the meridian passing through any selected reference point.

Local Hour Angle (LH) - is the angular distance between the plane of the observer’s meridian to the plane of the circle passing thru the body.

Meridian Angle (t) – is the angular distance of the body (minor arc) from the plane of the observer’s to the plane of the hour circle passing through the body.

Sidereal Angle (SHA) – is the angular distance of the celestial body measured westward along the equinoctial from the hour circle of vernal equinox.

Right Ascension (RA) – is the angular distance measured eastward from the hour circle of the first point of the Aries to the hour circle passing through the celestial body.

Greenwich Hour Angle (GHA) – is the angle between the plane of the celestial meridian of Greenwich and the plane of an hour circle passing through the body.

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THE ECLIPTIC

Ecliptic – the complete annual path is a great circle.

-the sun appears to move across the celestial sphere along a path which is in the same plane as the earth’s orbit.

Obliquity of the Ecliptic – the plane of the ecliptic is inclined to the plane of the equinoctial at an angle of about 231/2 °   ,or more accurately 23 27’.

-the earth’s axis is not perpendicular to the plane of its orbit.

– the suns annual path cuts the equinoctial at two points.

Equinoxex- the suns annual path cuts the equinoctial at two points.

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Vernal Equinox or Spring Equinox – the sun appears to cross the equinoctial from the southern celestial hemisphere into northern.

Summer Solstice - the sun will be at the position in its apparent annual path or orbit which remote from the equinoctial in the northern celestial hemisphere. Appear between June 21 and 23.

Winter Solstice – the sun will be at the position in its apparent path which is farthest to the southwards of the equinoctial .Occurs between December21 and 23.

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THE HORIZON COORDINATES SYSTEM

The horizon system of coordinates comprises those coordinates which are measured by the navigator himself with primary visible plane such as horizon.

Visible Horizon – is the apparent boundary between the sea and the sky or the line where the sky and sea appear to meet which to an observer when not in sight of land appears to each encircle him.

Sensible Horizon – is a small circle on the celestial sphere whose plane is parallel to the rational horizon, and which passes through the observer’s eye.

Geoidal Horizon – is an imaginary plane parallel to the sensible horizon.

Geometrical Horizon – is below the visible horizon by the amount of terrestrial refraction.

Celestial Horizon or Rational Horizon – is a plane passing through the center of the earth and parallel to the sensible horizon.

Zenith (Z) –is the point in the celestial sphere directly overhead of the observer.

Nadir (Na) – is the point in the celestial sphere directly underneath the observer.

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Azimuth (Zn) –is the angle at the observer’s zenith between the plane of the observer’s meridian and the plane of the vertical circle passing through the body.

Azimuth Angle (Z) – is the angle between the same two planes but it is reckoned from either the north or the south point of the horizon towards either the east or west point.

Amplitude – of a heavenly body is the arc of the horizon contained between the East or West point of the horizon, and the position of the body when rising or setting.

Altitude – of a celestial body is the angular distance of the body above the celestial horizon measured along the vertical circle passing through the body

Zenith Distance (Zx) – of a body is its angular distance from the zenith of the observer measured along the vertical circle passing through the body.

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THE EARTH’S ROTATION

Rotation is turning on an axis .The Earth rotates daily from west to east on an axis joining its north and south poles. This rotation causes the phenomena of day and night and form the basis on which our measure of time is founded

- Causes the heavenly bodies to appear to move around the earth in the opposition direction, that is form east to west.

THE THREE EFFECT OF EARTH ROTATION

1. The direction of the prevailing winds.2. The spinning of cyclones.3. The oblateness of the earth.

13Deflection on the surface winds

-cooled at the higher altitudes, the currents descends,

- Easterly trade winds of the tropics and the westerlies of the temperate zone as these currents are deflected by the earth’s eastward rotation.

-are easterly surface winds in the polar regions, when the colder air moves toward the equator.

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Cyclones or hurricanes- are deflected like projectiles by the earth rotation so that they spiral inward in the counterclockwise direction in the northern hemisphere and clockwise in the southern hemisphere .

Coriolis effect- deflection of moving objects relative to the surface of the rotating Earth.

Three Coriolis Effect

1. The CF causes objects to deflect to the right of their intended path in the northern hemisphere and to the left in the southern hemisphere.

- This is why low pressure system like hurricanes and extra-tropical cyclones circulate CCW in the NH

2. The CF only effects direction of an object not into its speed.

3. The strength of the deflection is proportionate to the speed

- For example the faster an airplane flies the more the pilot must adjust the flight to account for the Coriolis effect periodic in the direction of the star.

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Earth’s revolution

-earth revolves yearly around the sun in an easterly direction.

-inclined to the plane of the equinoctial at an angle of about 23° 27’

- the effect of the earth revolution is imperceptible.

Aberration- of starlight is the apparent displacement of a star in the direction the Earth is moving.

Three displacement factor of aberration

- It is directly proportional to the speed of the Earth.- It is inversely proportional to the speed of the light - The displacement is greatest when earth moves at right angles to the star’s

direction and become zero if the earth moves toward the star’s left direction

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Earths precession- is a low movement of the Earth’s axis around a line joining the ecliptic poles, having a period of about 25,800years

Nutation- the nodding of the pole

- The mean position in the precessional path.- The precessional path of the celestial pole is irregular; it is not exactly circular

and is not precisely the same from one cycle to the next.

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