The circle of equal altitude, also called circle of position (CoP), is defined as the locus of points on

Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

on which an observer sees a

celestial object An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists within the observable universe. In astronomy, the terms ''object'' and ''body'' are of ...

such as the

sun The Sun is the star at the centre of the Solar System. It is a massive, nearly perfect sphere of hot plasma, heated to incandescence by nuclear fusion reactions in its core, radiating the energy from its surface mainly as visible light a ...

or a

star A star is a luminous spheroid of plasma (physics), plasma held together by Self-gravitation, self-gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sk ...

, at a given time, with the same observed

altitude Altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum (geodesy), datum and a point or object. The exact definition and reference datum varies according to the context (e.g., aviation, geometr ...

. It was discovered by the American sea-captain Thomas Hubbard Sumner in 1837, published in 1843 and is the basis of an important method in

celestial navigation Celestial navigation, also known as astronavigation, is the practice of position fixing using stars and other celestial bodies that enables a navigator to accurately determine their actual current physical position in space or on the surface ...

Discovery

Sumner discovered the line on a voyage from

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Greenock Greenock (; ; , ) is a town in Inverclyde, Scotland, located in the west central Lowlands of Scotland. The town is the administrative centre of Inverclyde Council. It is a former burgh within the historic county of Renfrewshire, and forms ...

Scotland Scotland is a Countries of the United Kingdom, country that is part of the United Kingdom. It contains nearly one-third of the United Kingdom's land area, consisting of the northern part of the island of Great Britain and more than 790 adjac ...

in 1837. On December 17, as he was nearing the coast of

Wales Wales ( ) is a Countries of the United Kingdom, country that is part of the United Kingdom. It is bordered by the Irish Sea to the north and west, England to the England–Wales border, east, the Bristol Channel to the south, and the Celtic ...

, he was uncertain of his position after several days of cloudy weather and no sights. A momentary opening in the clouds allowed him to determine the altitude of the sun. This, together with the chronometer time and the

latitude In geography, latitude is a geographic coordinate system, geographic coordinate that specifies the north-south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at t ...

enabled him to calculate the

longitude Longitude (, ) is a geographic coordinate that specifies the east- west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lett ...

. But he was not confident of his latitude, which depended on

dead reckoning In navigation, dead reckoning is the process of calculating the current position of a moving object by using a previously determined position, or fix, and incorporating estimates of speed, heading (or direction or course), and elapsed time. T ...

(DR). So he calculated longitude using his DR value and two more values of latitude 10' and 20' to the north. He found that the three positions were on a straight line which happened to pass through Smalls Lighthouse. He realised that he must be located somewhere on that line and that if he set course E.N.E. along the line he should eventually sight the Smalls Light which, in fact he did, in less than an hour. Having found the line empirically, he then worked out the theory, and published this in a book in 1843. The method was quickly recognized as an important development in celestial navigation, and was made available to every ship in the

United States Navy The United States Navy (USN) is the naval warfare, maritime military branch, service branch of the United States Department of Defense. It is the world's most powerful navy with the largest Displacement (ship), displacement, at 4.5 millio ...

Parameters

The center of the CoP, is the geographical position (GP) of the observed body, the substellar point for a star, the

subsolar point The subsolar point on a planet or a moon is the point at which its Sun is perceived to be directly overhead (at the zenith); that is, where the Sun's rays strike the planet exactly perpendicular to its surface. The subsolar point occurs at the ...

for the sun. The radius is the great circle distance equal to the zenith distance of the body. * Center = geographical position (GP) of the body: (''

B_

'', ''

L_

'') = (''Dec'', ''-GHA'') ** If

L_

is defined as ''west'' longitude (+W/-E) then it will be ''+GHA'', since HA (GHA or LHA) is always measured west-ward (+W/-E). * Radius = zenith distance: ''zd'' m= 60 ⋅ (90 - ''Ho'') (aka co-altitude of ''Ho'') As the circles used for navigation generally have a radius of thousands of miles, a segment a few tens of miles long closely approximates a straight line, as described in Sumner's original use of the method.

Equation

The equation links the following variablesVector equation of the Circle of Position
/ref> * The position of the observer: ''B'', ''L''. * The coordinates of the observed star, its geographical position: ''GHA'', ''Dec''. * The true altitude of the body: ''Ho''.

\sin(Ho) = \sin(B) \cdot \sin(Dec) + \cos(B) \cdot \cos(Dec) \cdot \cos(LHA)\,

Being ''B'' the latitude (+N/-S), ''L'' the longitude (+E/-W). ''LHA'' = ''GHA'' + ''L'' is the local hour angle (+W/-E), ''Dec'' and ''GHA'' are the declination and Greenwich hour angle of the star observed. And ''Ho'' is the true or observed altitude, that is, the altitude measured with a

sextant A sextant is a doubly reflecting navigation instrument that measures the angular distance between two visible objects. The primary use of a sextant is to measure the angle between an astronomical object and the horizon for the purposes of cel ...

corrected for dip, refraction and parallax.

Special cases of COPs

* Parallel of latitude by Polaris altitude. * Parallel of latitude by altitude of the sun at noon, or meridian altitude. * Meridian of longitude known the time and latitude. * Circle of illumination or terminator (star = Sun, ''Ho'' = 0 for places at Sunrise/Sunset).

References

{{Reflist

External links