Ex-meridian is a celestial navigation method of calculating an observer's position on Earth. The method gives the observer a position line on which the observer is situated. It is usually used when the Sun is obscured at noon, and as a result, a meridian altitude is not possible. The navigator measures the altitude of the Sun as close to noon as possible and then calculates where the position line lies.
This method uses an assumed longitude and calculates the latitude that a position line crosses it. The position line obtained is actually part of a small circle, as opposed to great circle, where any observer can stand and the celestial object would have the same altitude in the sky. When plotting the small segment of this circle on a chart it is drawn as a straight line, the resulting tiny errors are too small to be significant.
The assumed longitude is usually obtained from the DR or Dead Reckoning position run up from a morning sight taken at around 9.00 am. This is worked out by applying the distance from that position either by log or by the estimated speed over time with the course steered. A sight is taken, that is the distance above the horizon of a heavenly object, in this case nearly always the sun, is measured with a sextant and the exact time noted in UTC. The sextant angle obtained is corrected for dip (the error caused by the observers height above the sea) and refraction to obtain the true altitude of the object above the horizon. This is then subtracted from 90° to obtain the angular distance from the position directly above, the zenith. This is referred to as the True Zenith Distance. The true zenith distance of the object is also the distance (in arc) on the Earth's surface from the observer to where that object is overhead, the geographical position of the object.
Using a nautical almanac, the declination (celestial latitude), and the Greenwich hour angle (celestial longitude) are obtained of the observed object for the time of observation. The assumed longitude is now added or subtracted to the Greenwich Hour Angle of the object to obtain the local hour angle, that is the difference in longitude between the DR position and the geographical position of the object.
With this information it is possible using the haversine formula to calculate the latitude where the position line crosses the assumed longitude. The formula is:
Where
= Meridian Zenith Distance
= True Zenith Distance
= Local Hour Angle
= DR Latitude
= Declination
Once the value of the Meridian Zenith Distance is obtained the algebraic sum of it with the declination of the object gives the latitude of a point where the position line crosses the meridian of DR longitude.
To draw the position line on a chart the azimuth or bearing of the heavenly object must be known. It is usually calculated but could have been observed. A line at right angles to the azimuth is drawn through the calculated position which is where the calculated latitude and the DR longitude cross. The observer is somewhere on this line.
To obtain a fix (a position) this line must be crossed with another position line either from another sight or from elsewhere. In the case of ex-meridian the position line is usually crossed with the position line obtained earlier which has been run up.
The first of these tables applies corrections to the altitude taken with the argument of Change of Altitude in one minute from Meridian Passage. Two other tables apply more corrections until the correct latitude is arrived at.
The Ex-Meridian method of calculating sights is at its most accurate when the azimuth of the object is near to south or north. As the azimuth changes towards the east or west the cross of the position line with the assumed longitude becomes more and more oblique and the position obtained is therefore less accurate. For this reason it is a less versatile method of calculating sights than the intercept method which can be used for all azimuths. The tables are a quick and easy way to correct the altitude when the object is fairly low in the sky and the observer has only missed noon by a few minutes but if noon has been missed by more than that or the sun is high in the sky it is better to work out a sight by the intercept method.
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In astronomy and celestial navigation, the hour angle is the angle between two planes: one containing Earth's axis and the zenith, and the other containing Earth's axis and a given point of interest.
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 of the Earth without relying solely on estimated positional calculations, commonly known as "dead reckoning." Celestial navigation is performed without using satellite navigation or other similar modern electronic or digital positioning means.
In observational astronomy, culmination is the passage of a celestial object across the observer's local meridian. These events were also known as meridian transits, used in timekeeping and navigation, and measured precisely using a transit telescope.
The great-circle distance, orthodromic distance, or spherical distance is the distance along a great circle.
In geography and geodesy, a meridian is the locus connecting points of equal longitude, which is the angle east or west of a given prime meridian. In other words, it is a line of longitude. The position of a point along the meridian is given by that longitude and its latitude, measured in angular degrees north or south of the Equator. On a Mercator projection or on a Gall-Peters projection, each meridian is perpendicular to all circles of latitude. A meridian is half of a great circle on Earth's surface. The length of a meridian on a modern ellipsoid model of Earth has been estimated as 20,003.93 km (12,429.87 mi).
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In astronomical navigation, the intercept method, also known as Marcq St. Hilaire method, is a method of calculating an observer's position on Earth (geopositioning). It was originally called the azimuth intercept method because the process involves drawing a line which intercepts the azimuth line. This name was shortened to intercept method and the intercept distance was shortened to 'intercept'.
Longitude by chronometer is a method, in navigation, of determining longitude using a marine chronometer, which was developed by John Harrison during the first half of the eighteenth century. It is an astronomical method of calculating the longitude at which a position line, drawn from a sight by sextant of any celestial body, crosses the observer's assumed latitude. In order to calculate the position line, the time of the sight must be known so that the celestial position i.e. the Greenwich Hour Angle and Declination, of the observed celestial body is known. All that can be derived from a single sight is a single position line, which can be achieved at any time during daylight when both the sea horizon and the sun are visible. To achieve a fix, more than one celestial body and the sea horizon must be visible. This is usually only possible at dawn and dusk.
Meridian altitude is a method of celestial navigation to calculate an observer's latitude. It notes the altitude angle of an astronomical object above the horizon at culmination.
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The navigational triangle or PZX triangle is a spherical triangle used in astronavigation to determine the observer's position on the globe. It is composed of three reference points on the celestial sphere:
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The position of the Sun in the sky is a function of both the time and the geographic location of observation on Earth's surface. As Earth orbits the Sun over the course of a year, the Sun appears to move with respect to the fixed stars on the celestial sphere, along a circular path called the ecliptic.
An azimuth compass is a nautical instrument used to measure the magnetic azimuth, the angle of the arc on the horizon between the direction of the Sun or some other celestial object and the magnetic north. This can be compared to the true azimuth obtained by astronomical observation to determine the magnetic declination, the amount by which the reading of a ship's compass must be adjusted to obtain an accurate reading. Azimuth compasses were important in the period before development of the reliable chronometers needed to determine a vessel's exact position from astronomical observations.
The circle of equal altitude, also called circle of position (CoP), is defined as the locus of points on Earth on which an observer sees a celestial object such as the sun or a star, at a given time, with the same observed altitude. 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.
In astronavigation, sight reduction is the process of deriving from a sight the information needed for establishing a line of position, generally by intercept method.
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