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Naut. Almanac    

 

Celestial Navigation

 

 

Celestial Sphere

 

The Celestial sphere

In celestial navigation, the earth is regarded as a sphere. Any circle on the surface of the earth whose plane passes through the center of the earth is called a great circle. Thus, a great circle is a circle with the greatest possible diameter on the surface of the earth.

Any circle on the surface of the earth whose plane does not pass through the earth’s center is called a small circle. The equator is the (only) great circle whose plane is perpendicular to the polar axis, the axis of rotation.

Further, the equator is the only parallel of latitude being a great circle. Any other parallel of latitude is a small circle whose plane is parallel to the plane of the equator.

A meridian is a great circle going through the geographic poles, the points where the polar axis intersects the earth’s surface. The upper branch of a meridian is the half from pole to pole passing through a given point; the lower branch is the opposite half.

The Greenwich meridian, the meridian passing through the center of the transit instrument at the Royal Greenwich Observatory, was adopted as the prime meridian at the International Meridian Conference in October 1884. Its upper branch (0°) is the reference for measuring longitudes, its lower branch (180°) is known as the International Dateline.

The apparent annual motion of the sun and Concept of the Ecliptic

Note the sun does not move, it is the earth, which revolves around the sun in an elliptical path, and again the sun is not exactly at the centre of the ellipse. Also the elliptical path of the earth is inclined at an angle to the plane passing through the centre of the sun due to the axis of the earth being tilted on one side.

However observing from the earth the sun apparently describes the elliptical path, with the observer as stationary.

The sun apparently moves along the ecliptic and on June 21st. is at 23.5˚N declination, the maximum northerly travel the earth experiences summer in the Northern Hemisphere. The sun now begins its travel southward along the ecliptic and on September 28th, arrives at the Autumnal equinox, where the days and the nights are equal and the declination of the sun is 0°. The sun continues its travel southward and on December 22nd, arrives at its most southerly point, the declination being 23.5°S, this is the winter in the northern hemisphere. With this point the sun travels back on the elliptical path and starts its journey northward. It arrives on 21st March at the Vernal Equinox, when again the nights are equal to the days. From here it continues its travel until again it reaches the point of Maximum northerly declination, 23.5°N on the 21st of June.

The reason of a maximum of 23.5°N or S is because the earth traces an elliptical path around the sun, the sun is not however at the ce3ntre of the ellipse. Also the earth’s axis of rotation is not perpendicular to this path but is tilted by 23.5°. Thus the as earth travels around the sun the sun keeps bobbing up and down 23.5° up or below the earths centre line – the equator.

From the earth it seems that the sun is the body, which is moving, up or down from the equator. This path, which never varies, is known as the ecliptic.

‘Celestial poles’, ‘celestial meridians’, ‘equinoctial’ and the ‘obliquity of the ecliptic’

The apparent position of a body in the sky is defined by the horizon system of coordinates. In this system, the observer is located at the center of a fictitious hollow sphere of infinite diameter, the celestial sphere, which is divided into two hemispheres by the plane of the celestial horizon.

Similar to the poles on the earth, this celestial sphere also has imaginary poles. The poles of the earth are at the two extremities of the axis of rotation and if this axis is extended to meet the celestial sphere then the point of intersection become the Poles of the celestial sphere.

Also similar to the earth’s meridians the celestial sphere is divided into vertical celestial great circles, which are known as the celestial meridians.

The plane passing through the centre of the earth and perpendicular to the axis of rotation divides the earth into two halves. The imaginary circle, which passes through the earth at this point, is called the equator, and if the same is projected on the celestial sphere, which will divide the celestial sphere into two equal halves. This imaginary line on the celestial sphere is called the equinoctial.

Note the sun does not move, it is the earth, which revolves around the sun in an elliptical path, and again the sun is not exactly at the centre of the ellipse. Also the elliptical path of the earth is inclined at an angle to the plane passing through the centre of the sun due to the axis of the earth being tilted on one side.

However observing from the earth the sun apparently describes the elliptical path, with the observer as stationary.

The declinations of sun and planets change primarily due, the inclination of the earth’s equator to the plane of the earth’s orbit (ecliptic) this is known as the obliquity of the ecliptic

The equinoctial as a fixed reference plane and the direction of the First Point of Aries as a reference direction (ignoring the effect of precession)

For all navigational calculations the equinoctial is taken to be unchanged and is used as a fixed reference circle. The point where the ecliptic meets the equinoctial on March 21st, Vernal Equinox, that is when the apparent sun is at a declination of 0°, and is travelling towards maximum declination of 23.5°N, is called the First Point of Aries.

This is the main reference point for all navigational calculations.

The equinoctial system of co‑ordinates and sidereal hour angle, declination and polar distance

The geographic position of a celestial body, GP, is defined by the equatorial system of coordinates. The Greenwich hour angle, GHA, is the angular distance of GP westward from the upper branch of the Greenwich meridian (0°), measured from 0° through 360°.

The declination, Dec, is the angular distance of GP from the plane of the equator, measured northward through +90° or southward through -90°. GHA and Dec are geocentric coordinates (measured at the center of the earth).

The great circle going through the poles and GP is called hour circle.

GHA and Dec are equivalent to geocentric longitude and latitude with the exception that the longitude is measured from -(W) 180° through +(E) 180°.