Ex-meridian
Encyclopedia
Ex- Meridian is an astronomical 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.
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 heavenly 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
MZD = Meridian Zenith Distance
TZD = True Zenith Distance
H = Local Hour Angle
L = DR Latitude
D = Declination
Once the figure for the Meridian
Zenith Distance is obtained the sum or the difference is obtained between it and the declination of the object to obtain the latitude. This is the latitude where the position line crosses the 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.
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.
Navigation
Navigation is the process of monitoring and controlling the movement of a craft or vehicle from one place to another. It is also the term of art used for the specialized knowledge used by navigators to perform navigation tasks...
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
Noon
Noon is usually defined as 12 o'clock in the daytime. The word noon is also used informally to mean midday regarding the location of the sun not the middle of a persons day. Although this is a time around the middle of the day when people in many countries take a lunch break...
and as a result a meridian altitude
Meridian altitude
Meridian Altitude is an astronomical navigation method of calculating an observer's latitude.- Principle :This is the simplest calculation of astronomical navigation and is when an observer determines his latitude by measuring the altitude of a heavenly object at the time of its meridian passage....
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.
Methodology
This method uses an assumed longitudeLongitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....
and calculates the latitude
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...
that a position line crosses it. The position line obtained is actually part of a small circle
Small circle
A circle of a sphere is a circle defined as the intersection of a sphere and a plane. If the plane contains the center of the sphere then the circle is called a great circle, otherwise it is a small circle...
, as opposed to great circle
Great circle
A great circle, also known as a Riemannian circle, of a sphere is the intersection of the sphere and a plane which passes through the center point of the sphere, as opposed to a general circle of a sphere where the plane is not required to pass through the center...
, where any observer can stand and the heavenly 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
Sextant
A sextant is an instrument used to measure the angle between any two visible objects. Its primary use is to determine the angle between a celestial object and the horizon which is known as the altitude. Making this measurement is known as sighting the object, shooting the object, or taking a sight...
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
Nautical almanac
A nautical almanac is a publication describing the positions of a selection of celestial bodies for the purpose of enabling navigators to use celestial navigation to determine the position of their ship while at sea...
, the declination
Declination
In astronomy, declination is one of the two coordinates of the equatorial coordinate system, the other being either right ascension or hour angle. Declination in astronomy is comparable to geographic latitude, but projected onto the celestial sphere. Declination is measured in degrees north and...
(celestial latitude), and the Greenwich
Greenwich
Greenwich is a district of south London, England, located in the London Borough of Greenwich.Greenwich is best known for its maritime history and for giving its name to the Greenwich Meridian and Greenwich Mean Time...
hour angle
Hour angle
In astronomy and celestial navigation, the hour angle is one of the coordinates used in the equatorial coordinate system to give the position of a point on the celestial sphere....
(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
MZD = Meridian Zenith Distance
TZD = True Zenith Distance
H = Local Hour Angle
L = DR Latitude
D = Declination
Once the figure for the Meridian
Meridian (astronomy)
This article is about the astronomical concept. For other uses of the word, see Meridian.In the sky, a meridian is an imaginary great circle on the celestial sphere. It passes through the north point on the horizon, through the celestial pole, up to the zenith, through the south point on the...
Zenith Distance is obtained the sum or the difference is obtained between it and the declination of the object to obtain the latitude. This is the latitude where the position line crosses the 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.
Ex-Meridian Tables
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.Accuracy and Versatility
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 methodIntercept method
The "Intercept Method", or "Marcq St Hilaire method", as it is also rather inaccurately known, is an astronomical navigation method of calculating an observer's position on earth. It was originally called the azimuth intercept method because the process involves drawing a line which intercepts the...
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.
See also
- Celestial navigationCelestial navigationCelestial navigation, also known as astronavigation, is a position fixing technique that has evolved over several thousand years to help sailors cross oceans without having to rely on estimated calculations, or dead reckoning, to know their position...
- NavigationNavigationNavigation is the process of monitoring and controlling the movement of a craft or vehicle from one place to another. It is also the term of art used for the specialized knowledge used by navigators to perform navigation tasks...
- LatitudeLatitudeIn geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...
- LongitudeLongitudeLongitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....
- Haversine formulaHaversine formulaThe haversine formula is an equation important in navigation, giving great-circle distances between two points on a sphere from their longitudes and latitudes...
- Intercept methodIntercept methodThe "Intercept Method", or "Marcq St Hilaire method", as it is also rather inaccurately known, is an astronomical navigation method of calculating an observer's position on earth. It was originally called the azimuth intercept method because the process involves drawing a line which intercepts the...
- Longitude by chronometerLongitude by chronometerLongitude by chronometer, is an astronomical navigation method of calculating the longitude of an observer's position on Earth. The longitude derived by this method must be combined with the latitude of the observer's position to resolve a "fix" or exact position of the observer on the...