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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

**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 21^{st}. 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 28^{th},
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 22^{nd}, 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 21^{st} 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 21^{st}
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 21^{st}, 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°.