Sail Away
Cover  <<  Sail Away  <<  Celestial Navigation  <<  .

## Terms and Conventions

Astronomy is the framework for Celestial Navigation and it has been developed over the last 5000 years. However, as most marine navigators had no real astronomical background and were only interested in the practical use of astronomical observations, they developed their own system, which was good enough to solve their navigational problems, but differs to some extend from the scientific astronomical models.

In the next sections, the basic terms and conventions used in the system of Celestial Navigation are summarized.

### The Celestial Sphere

When discussing the position and motion of objects in the sky, navigators like to pretend them to be attached to an imaginary sphere surrounding the Earth. This fictitious construction is called the Celestial Sphere. It is centred around the Earth and depicts all celestial objects as if they were at the same distance away from the Earth. Although this ancient geocentric model is not correct, it is a simple and convenient way to describe the motions of the stars and planets for an earth-bound observer. We know today that a star's apparent brightness is determined by its distance, as well as its physical size and temperature. We also know that the stars' apparent motion through the sky is due to the Earth rotation. This rotational motion makes all celestial objects appear to move together from East to West for any earth-bound observer. And since the celestial objects are so far away from us, the distance to them cannot be simply estimated so that they can be imagined to be pinned to an imaginary sphere centred around the Earth. The Ecliptic is the apparent path of the Sun through the year, plotted on the Celestial Sphere. The plane of the Ecliptic is tilted about 23.5° against the plane of the Equator. This is because the rotation axis of the Earth is tilted 23.5° against the orbital plane of the Earth around the Sun. Twice a year - on the equinoxes - the Ecliptic crosses the celestial equator. The point on the Celestial Sphere at which the Ecliptic crosses the celestial equator from south to north is called the vernal equinox.

#### Coordinate System of the Celestial Sphere

Like the Longitude and Latitude system on Earth, the Celestial Sphere can be provided with a coordinate system to uniquely describe locations of stars and planets. Note that there exists more than one coordinate system for the Celestial Sphere. The system described here is traditionally used for Celestial Navigation and differs from the one used by astronomers in the reference (the "celestial Prime Meridian") used for defining the East-West coordinate.

 The coordinate system of the celestial sphere consists of the following components: The celestial poles - the North Celestial Pole and South Celestial Pole - are aligned with the poles of the Earth (coinciding axis of rotation). The Celestial Equator lies in the same plane that includes the Earth's Equator. And like the Earth's Equator, the Celestial Equator divides the celestial sphere in a northern and southern celestial hemisphere. Similar to the Meridians and Parallels of the Earth's coordinate system, the coordinate system of the celestial sphere consists of Hour Circles and Circles of constant Declination. An hour circle is a great circle on the celestial sphere that passes through the poles and intersects at right angles with the circles of constant Declination. Hour Circles are the meridians on the celestial sphere. The Hour Circle passing through the Zenith of a Location on the Prime Meridian of Greenwich is called Greenwich Hour Circle. The angle between two arbitrary Hour Circles (measured e.g. at one of the celestial poles) is called Hour Angle. The Hour Angle is similar to a Longitude difference on the Earth. The Hour Angle is called Local Hour Angle if the Hour Circle passing through the Zenith of the observer is involved and it is called Greenwich Hour Angle if the Greenwich Hour Circle is involved.

The Declination (Dec) of a point on the celestial sphere is the angular distance North or South of the celestial equator, measured along the Hour Circle that passes through the point. Declination on the celestial sphere corresponds to Latitude on the Earth.

The Greenwich Hour Angle (GHA) of a point on the celestial sphere is the angle between the Greenwich Hour Circle and the Hour Circle of the point. The angle is measured westward along the Celestial Equator starting from the Greenwich celestial meridian - from 0° through 360°. The GHA differs from Longitude on the Earth in two aspects:

• Longitude is measured East or West - from 0° through 180° - whereas GHA is measured West from 0° through 360°
• and in contrast to Longitude of a fixed location, the GHA of a fixed star increases by about 15°/h due to the rotation of the Earth.

The following Table summarizes the equivalent terms of both coordinate systems:

 Terms of the Earth's coordinate system Terms of the Celestial Sphere Equator Celestial Equator Latitude Declination Longitude (referring to Greenwich Meridian) Greenwich Hour Angle Longitude (referring to observer's Meridian) Local Hour Angle Longitude (angular E-W distance) Hour Angle Parallels Circles of constant Declination Meridians Hour Circles North Pole North Celestial Pole South Pole South Celestial Pole Location of the Observer Zenith of the Observer

The stars, pinned to the celestial sphere, turn around the Earth keeping their relative position to each other. This apparent fixed constellation is due to the fact, that the stars are so far away from the Earth, that their relative motion as seen from the Earth is very small (order of magnitude: milliarcsec per year). For the Sun, Moon and the planets, which are much closer to the Earth, this is different: the Moon "moves" over the celestial sphere (against the celestial background of stars) with about 0.5° per hour.

The Celestial Poles, being in the axis of rotation, remain fixed in the sky. Also stars located near a celestial pole will appear to be stationary in the sky. That's the case for Polaris, a star that is near the North Celestial Pole (its Declination is 89° 05' N). Polaris is always in the North direction, a fact known by every navigator in the northern hemisphere. Near the South Celestial Pole there's no corresponding bright star.

### The Zenith

The line connecting the center of the Earth with a location on the surface of the Earth is called local vertical. The local vertical of an earthbound observer, will eventually extend to a point on the celestial sphere. This point is called the Zenith of the observer. So the Zenith is the point directly "overhead" of the observer. The term "overhead" is defined by the direction of the local vertical.

### The Geographical Position of a Celestial Object Like the Zenith links the position of an earthbound observer to a point directly overhead on the celestial sphere, the Geographical Position links the location of celestial object on the celestial sphere to a point on the surface of the Earth. The Geographical Position (GP) of a celestial object is the location on Earth for which the particular object is in the Zenith. For each celestial object, the Geographical Position is a single and unique location on the Earth, which can be found by drawing an - imaginary - line from the center of the Earth to the center of the particular object in the sky. The location where this imaginary line passes through the surface of the Earth is the Geographical Position of the celestial object. An observer positioned in the Geographic Position of a star will see this star directly in the vertical, above his head (his Zenith).

The Geographic Position of the Sun is also called the sub-solar point. The Geographic Position of the Moon is the sub-lunar point and that of a star its sub-stellar point.

Since the GP of a celestial object is located on the Earth, it is expressed in Latitude and Longitude. The GP can be easily calculated from the ephemerides (celestial coordinates) of the celestial objects compiled in the Nautical Almanac for each integral hour of the year.

Since the planes of the Equator and the Celestial Equator are the same, the Latitude of the GP is equal to the Declination of the celestial object. The Longitude can be directly calculated from the GHA.

```  GP_Latitude  = Declination
GP_Longitude = -GHA            if GHA < 180°
= 360° - GHA      if GHA > 180°   ```

For understanding the principle of celestial navigation, it is fundamental to recognize, that the Altitude of an object measured with a sextant, is directly related to the distance between the observer and the GP of the observed celestial object:

`  Distance_from_Observer_to_GP = 90° - Measured_Altitude`

Each Altitude measurement yields a distance to the GP of the observed body and the resulting Line-of-Position is a Circle-of-equal-Altitude centred on the GP.

This will be further elaborated in the next sections.

 Cover  <<  Sail Away  <<  Celestial Navigation  <<  . .  >>  Instruments last updated: 17-Dec-2004