Celestial navigation

Celestial navigation, also known as astronavigation, is a position fixing technique that was devised to help sailors cross the featureless oceans without having to rely on dead reckoning to enable them to strike land. Celestial navigation uses angular measurements (sights) between the horizon and a common celestial object. The Sun is most often measured. Skilled navigators can use the Moon, planets or one of 57 navigational stars whose coordinates are tabulated in nautical almanacs.

How it works

Celestial navigation is the process whereby angles between objects in the sky (celestial objects) and the horizon are used to locate one's position on the globe. At any given instant of time, any celestial object (e.g. the Moon, Jupiter, navigational star Spica) will be located directly over a particular geographic position on the Earth. This geographic position is known as the celestial object’s subpoint, and its location (e.g. its latitude and longitude) can be determined by referring to tables in a nautical or air almanac.

The measured angle between the celestial object and the horizon is directly related to the distance between the subpoint and the observer, and this measurement is used to define a circle on the surface of the Earth called a celestial line of position (LOP). The size and location of this circular line of position can be determined using mathematical or graphical methods (discussed below). The LOP is significant because the celestial object would be observed to be at the same angle above the horizon from any point along its circumference at that instant.

An example illustrating the concept behind the intercept method for determining one’s position is shown in the Figure below. (Two other common methods for determining one’s position using celestial navigation are the longitude by chronometer and ex-meridian methods.) In the image below, the two circles on the map represent lines of position for the Sun and Moon at 1200 GMT on October 29 2005. At this time, a navigator on a ship at sea measured the Moon to be 56 degrees above the horizon using a sextant. Ten minutes later, the Sun was observed to be 40 degrees above the horizon. Lines of position were then calculated and plotted for each of these observations. Since both the Sun and Moon were observed at their respective angles from the same location, the navigator would have to be located at one of the two locations where the circles cross.

In this case the navigator is either located on the Atlantic Ocean, about convert|350|nmi|km west of Madeira, or in South America, about convert|90|nmi|km southwest of Asunción, Paraguay. In most cases, determining which of the two intersections is the correct one is obvious to the observer because they are often thousands of miles apart. As it is unlikely that the ship is sailing across the Pampas, the position in the Atlantic is the correct one. Note that the lines of position in the figure are distorted because of the map’s projection; they would be circular if plotted on a globe.

Angular measurement

[
sextant to measure the altitude of the sun above the horizon] Accurate angle measurement evolved over the years. One simple method is to hold the hand above the horizon with your arm stretched out. The width of a finger is an angle just over 1.5 degrees. The need for more accurate measurements led to the development of a number of increasingly accurate instruments, including the kamal, astrolabe, octant and sextant. The sextant and octant are most accurate because they measure angles from the horizon, eliminating errors caused by the placement of an instrument's pointers, and because their dual mirror system cancels relative motions of the instrument, showing a steady view of the object and horizon.

Navigators measure distance on the globe in degrees, arcminutes and arcseconds. A nautical mile is defined as 1852 meters, but is also (not accidentally) one minute of angle along a meridian on the Earth. Sextants can be read accurately to within 0.2 arcminutes. So the observer's position can be determined within (theoretically) 0.2 miles, about 400 yards (370 m). Most ocean navigators, shooting from a moving platform, can achieve a practical accuracy of 1.5 miles (2.8 km), enough to navigate safely when out of sight of land.

Practical navigation

Practical celestial navigation usually requires a marine chronometer to measure time, a sextant to measure the angles, an almanac giving schedules of the coordinates of celestial objects, a set of sight reduction tables to help perform the height and azimuth computations, and a chart of the region. With sight reduction tables, the only math required is addition and subtraction. Small handheld computers, laptops and even scientific calculators enable modern navigators to "reduce" sextant sights in minutes, by automating all the calculation and/or data lookup steps. Most people can master simpler celestial navigation procedures after a day or two of instruction and practice, even using manual calculation methods.

Modern practical navigators usually use celestial navigation in combination with satellite navigation to correct a dead reckoning track, that is, a course estimated from a vessel's position, angle and speed. Using multiple methods helps the navigator detect errors, and simplifies procedures. When used this way, a navigator will from time to time measure the sun's altitude with a sextant, then compare that with a precalculated altitude based on the exact time and estimated position of the observation. On the chart, one will use the straight edge of a plotter to mark each position line. If the position line shows one to be more than a few miles from the estimated position, one may take more observations to restart the dead-reckoning track.

In the event of equipment or electrical failure, one can get to a port by simply taking sun lines a few times a day and advancing them by dead reckoning to get a crude running fix.

Latitude

Latitude was measured in the past either at noon (the "noon sight") or from Polaris, the north star. Polaris always stays within 1 degree of celestial north pole. If a navigator measures the angle to Polaris and finds it to be 10 degrees from the horizon, then he is on a circle at about North 10 degrees of geographic latitude. Angles are measured from the horizon because locating the point directly overhead, the zenith, is difficult. When haze obscures the horizon, navigators use artificial horizons, which are bubble levels reflected into a sextant.

Latitude can also be determined by the direction in which the stars travel over time. If the stars rise out of the east and travel straight up you are at the equator, but if they drift south you are to the north of the equator. The same is true of the day-to-day drift of the stars due to the movement of the Earth in orbit around the Sun; each day a star will drift approximately one degree. In either case if the drift can be measured accurately, simple trigonometry will reveal the latitude.

Longitude

Longitude can be measured in the same way. If one can accurately measure the angle to Polaris, a similar measurement to a star near the eastern or western horizons will provide the longitude. The problem is that the Earth turns about 15 degrees per hour, making such measurements dependent on time. A measure only a few minutes before or after the same measure the day before creates serious navigation errors. Before good chronometers were available, longitude measurements were based on the transit of the moon, or the positions of the moons of Jupiter. For the most part, these were too difficult to be used by anyone except professional astronomers.

The longitude problem took centuries to solve. Two useful methods evolved during the 1700s, and are still practiced today: lunar distance, which does not involve the use of a chronometer, and use of an accurate timepiece, or chronometer.

Lunar distance

The older method, called "lunar distances", was refined in the 18th century. It is only used today by sextant hobbyists and historians, but the method is sound, and can be used when a timepiece is not available or its accuracy is suspect during a long sea voyage. The navigator precisely measures the angle between the moon and a body like the sun or a selected group of stars lying along the ecliptic. That angle, after it is corrected for various errors, is the same at any place on the surface of the earth facing the moon at a unique instant of time. Old almanacs used to list angles in tables. The navigator could thumb through the almanac to find the angle he or she measured, and thus know the time at Greenwich. Modern handheld and laptop calculators can perform the calculation in minutes, allowing the navigator to use other acceptable celestial bodies than the old nine. Knowing Greenwich time, the navigator can work out longitude.

Use of time

The considerably more popular method was (and still is) to use an accurate timepiece to directly measure the time of a sextant sight. The need for accurate navigation led to the development of progressively more accurate chronometers in the 18th century. Today, time is measured with a chronometer, a quartz watch, a shortwave radio time signal broadcast from an atomic clock, or the time displayed on a GPS. A quartz wristwatch normally keeps time within a half-second per day. If it is worn constantly, keeping it near body heat, its rate of drift can be measured with the radio, and by compensating for this drift, a navigator can keep time to better than a second per month. Traditionally, a navigator checked his chronometer from his sextant, at a geographic marker surveyed by a professional astronomer. This is now a rare skill, and most harbor masters cannot locate their harbor's marker. Traditionally, three chronometers were kept in gimbals in a dry room near the center of the ship. They were used to set a watch for the actual sight, so that no chronometers were ever risked to the wind and salt water on deck. Winding the chronometers was a crucial duty of the navigator, logged as "chron. wound." for checking by line officers. Navigators also set the ship's clocks and calendar.

Modern celestial navigation

The celestial line of position concept was discovered in 1837 by Thomas Hubbard Sumner when, after one observation he computed and plotted his longitude at more than one trial latitude in his vicinity – and noticed that the positions lay along a line. Using this method with two bodies, navigators were finally able cross two position lines and obtain their position – in effect determining both latitude and longitude. Later in the 19th century came the development of the modern (Marcq St. Hilaire) intercept method; with this method the body height and azimuth are calculated for a convenient trial position, and compared with the observed height. The difference in arcminutes is the nautical mile "intercept" distance that the position line needs to be shifted toward or away from the direction of the body's subpoint. (The intercept method uses the concept illustrated in the example in the “How it works” section above.) Two other methods of reducing sights are the longitude by chronometer and the ex-meridian method.

While celestial navigation is becoming increasingly redundant with the advent of inexpensive and highly accurate satellite navigation receivers (GPS), it was used extensively in aviation until 1960s, and marine navigation until quite recently. But since a prudent mariner never relies on any sole means of fixing his/her position, many national maritime authorities still require deck officers to show knowledge of celestial navigation in examinations, primarily as a back up for electronic navigation. One of the most common current usages of celestial navigation aboard large merchant vessels is for compass calibration and error checking at sea when no terrestrial references are available.

The U.S. Air Force and U.S. Navy continued instructing military aviators on its use until 1997, because:
*it can be used independently of ground aids
*has global coverage
*cannot be jammed (except by clouds)
*does not give off any signals that could be detected by an enemy [U.S. Air Force Pamphlet (AFPAM) 11-216, Chapters 8-13]

The US Naval Academy announced that it was discontinuing its course on celestial navigation, considered to be one of its most demanding courses, from the formal curriculum in the spring of 1998 stating that a sextant is accurate to a three-mile (5 km) radius, while a satellite-linked computer can pinpoint a ship within convert|60|ft|m. Presently, midshipmen continue to learn to use the sextant, but instead of performing a tedious 22-step mathematical calculation to plot a ship's course, midshipmen feed the raw data into a computer. [ [http://query.nytimes.com/gst/fullpage.html?res=9504EED61038F93AA15756C0A96E958260&n=Top%2fReference%2fTimes%20Topics%2fOrganizations%2fU%2fUnited%20States%20Naval%20Academy Navy Cadets Won't Discard Their Sextants] , The New York Times By DAVID W. CHENPublished: May 29, 1998]

Likewise, celestial navigation was used in commercial aviation up until the early part of the jet age; it was only phased out in the 1960s with the advent of inertial navigation systems.

Celestial navigation continues to be taught to cadets during their training in the British Merchant Navy and remains as a requirement for their certificate of competency.

A variation on terrestrial celestial navigation was used to help orient the Apollo spacecraft enroute to and from the Moon. To this day, space missions, such as the Mars Exploration Rover use star trackers to determine the attitude of the spacecraft.

As early as the mid-1960s, advanced electronic and computer systems had evolved enabling navigators to obtain automated celestial sight fixes. These systems were used aboard both ships as well as US Air Force aircraft, and were highly accurate, able to lock onto up to 11 stars (even in daytime) and resolve the craft's position to less than convert|300|ft|m. The SR-71 high-speed reconnaissance aircraft was one example of an aircraft that used automated celestial navigation. These rare systems were expensive, however, and the few that remain in use today are regarded as backups to more reliable satellite positioning systems.

Celestial navigation continues to be used by private yachtsmen, and particularly by long-distance cruising yachts around the world. For small cruising boat crews, celestial navigation is generally considered an essential skill when venturing beyond visual range of land. Although GPS (Global Positioning System) technology is reliable, offshore yachtsmen use celestial navigation as either a primary navigational tool or as a backup.

Celestial navigation trainer

Celestial navigation trainers combine a simple flight simulator with a planetarium in order to train aircraft crews in celestial navigation.

An early example is the Link Celestial Navigation Trainer, used of the Second World War. [cite web|title=World War II|work=A Brief History of Aircraft Flight Simulation|url=http://homepage.ntlworld.com/bleep/SimHist4.html|accessmonthday=January 27 |accessyear=2005] [cite web|title=Corporal Tomisita "Tommye" Flemming-Kelly-U.S.M.C.-Celestial Navigation Trainer -1943/45|work=World War II Memories|url=http://www.geocities.com/CapeCanaveral/Runway/9601/kelly.html|accessmonthday=January 27 |accessyear=2005] Housed in a convert|45|ft|m high building, it featured a cockpit which accommodated a whole bomber crew (pilot, navigator and bomber). The cockpit offered a full array of instruments which the pilot used to fly the simulated aeroplane. Fixed to a dome above the cockpit was an arrangement of lights, some collimated, simulating constellations from which the navigator determined the plane's position. The dome's movement simulated the changing positions of the stars with the passage of time and the movement of the plane around the earth. The navigator also received simulated radio signals from various positions on the ground.

Below the cockpit moved "terrain plates" – large, movable aerial photographs of the land below, which gave the crew the impression of flight and enabled the bomber to practise lining up bombing targets.

A team of operators sat at a control booth on the ground below the machine, from which they could simulate weather conditions such as wind or cloud. This team also tracked the aeroplane's position by moving a "crab" (a marker) on a paper map.

The Link Celestial Navigation Trainer was developed in response to a request made by the British Royal Air Force (RAF) in 1939. The RAF ordered 60 of these machines, and the first one was built in 1941. The RAF used only a few of these, leasing the rest back to the U.S., where eventually hundreds were in use.

ee also

*Air navigation
*American Practical Navigator
*Navigation
*Sextant
*Radio navigation
*Satellite navigation
*Spherical geometry
*Nautical almanac
*Navigational stars
*Ephemeris
*Star clock
*Longitude by chronometer
*History of longitude
*Meridian altitude
*John Harrison
*SIGI

References

External links

* [http://www.celestialnavigation.net Celestial Navigation Net]
* [http://www.angelfire.com/nt/navtrig/F1.html Table of the 57 navigational stars with apparent magnitudes and celestial coordinates]
* [http://www.nmm.ac.uk/server/show/conWebDoc.355 John Harrison and the Longitude problem] at the National Maritime Museum, Greenwich, England
* [http://www.clockwk.com/lunars/easylun.html Calculating Lunar Distances]
* [http://www.geocities.com/andresruizgonzalez Navigational Algorithms]