Celestial Navigation
, also known as A
stronavigation
, is a position-fixing process that has enabled sailors to cross featureless oceans with certainty and target unsighted land with precision. Astronavigation uses angular measurements or sightings between the horizon and a common celestial object to perform navigational problem-solving. Although the Sun is the most often measured celestial object, more sophisticated navigators are prepared to use our Moon, other planets, or one of 57 "navigational stars" described in nautical almanacs to observe the positions of these celestial objects relative to the observer and a known location. In ancient times, the vessel's home port or home capital was used as the known location. With the rise of the British Navy and merchant marine, the Greenwich Meridian or Prime Meridian at Greenwich, England eventually became the starting location for most celestial almanacs. Astronavigation calculates angles between objects in the sky (celestial objects) and the horizon to locate one's position on the globe. At any given instant of time, any celestial object such as the Earth's Moon, the planet Jupiter, or the navigational star Spica, one of the brightest stars in the nighttime sky, will be located directly over a particular geographic position on the Earth. This geographic position is known as the celestial object's sub-point and its location, defined by latitude and longitude, can be determined from the tables of nautical or air almanacs.
These almanacs describe the positions and movements of celestial bodies, including the sun, moon, planets, and 57 stars chosen for their ease of identification and wide spacing. The Almanac specifies for each whole hour of the year the position on the Earth's surface at which each body is directly overhead. The Sun, Moon and Planets are perceived independently and are therefore specified separately however, only the star Aries is specified, while the other stars are assigned a set angular distance. The navigator can extrapolate by means of navigational tables to acquire the position of each object for each minute of time.
In Great Britain a nautical almanac has been published annually by the HM Nautical Almanac Office, ever since the first edition was published in 1767. Also commercial almanacs were produced that combined other information. A good example would be Brown's - which commenced in 1877 - and is still produced annually, its early twentieth century subtitle being "Harbour and Dock Guide and Advertiser and Daily Tide Tables". This combination of trade advertising, and information "by permission... of the Hydrographic Department of the Admiralty" provided a useful compendium of information. More recent editions have kept up with the changes in technology - the 1924 edition for example had extensive advertisements for coaling stations.
The "Air Almanac" of the United States and Great Britain tabulates celestial coordinates at 10 minute intervals. The Sokkia Corporation's annual "Celestial Observation Handbook and Ephemeris" tabulates daily celestial coordinates (to a tenth of an arc-second) for the Sun and nine stars, Polaris and eight others.
To determine the position of a ship or aircraft by celestial navigation or astronavigation, the navigator uses a sextant to take a "sight" to measure the apparent height of the celestial object above the horizon, and notes the time from a marine chronometer. The object's position is then looked up in the Nautical Almanac for that particular time and after allowance for refraction, instrument error and other errors, a position circle on the Earth's surface is calculated.
Previously,
latitude
was measured either at noon (the "noon sight") or from the angle between Polaris, the North Star or the Pole Star, and the horizon. Polaris always stays within 1 degree of celestial North Pole. At the North Pole, which is 90 degrees latitude, Polaris is directly overhead at an altitude of 90 degrees. At the equator, which is zero degrees latitude, Polaris is on the horizon with zero degrees altitude. Between the equator and the North Pole, the angle of Polaris above the horizon is a direct measure of geographic or terrestrial latitude. 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 or terrestrial latitude. The latitudinal angles are reversed in the Southern hemisphere, where the equator is still zero degrees however; the South Pole is at an altitude of 90 degrees. In the Southern Hemisphere, a constellation called the Southern Cross, or Crux, points to the place the southern stars circle around. The Southern Cross is a key constellation for navigating south of the equator. Navigational 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.
Azimuth 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.
Comparatively,
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 precision 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, as presented in the book
Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time
by Dava Sobel
. As opposed to a degree of latitude, which is always sixty nautical miles or about 111 km (69 statute miles, each of 5280 feet), a degree of longitude varies from 0 to 111 km: it is 111 km times the
cosine
of the latitude, when the distance is laid out on a circle of constant latitude. More precisely, one degree of longitude = (111.320 + 0.373sin²Φ)cosΦ km, where Φ is latitude).
Two useful methods evolved during the 1700s, and both are still practiced today: lunar distance without a chronometer; and lunar distance with a chronometer, or an accurate timepiece.
The first method, called "lunar distances," was refined in the 18th century. Although it is only used today by sextant hobbyists and historians, this method is dependable, and can be used when a timepiece is not available or the accuracy of a timepiece 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 listed angles in tables, from which the navigator could look up the measured angle, and then 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 original nine. After identifying Greenwich Time (GMT), the navigator can calculate longitude. While GMT could refer to either an astronomical day starting at noon or a calendar day starting at midnight, Universal Time (UT) was established in 1928 as more precise. The term Greenwich Mean Time persists however, and is in popular usage to this day in reference to civil timekeeping, whereas there are several versions of Universal Time [see glossary].
The considerably more popular method was, and still is, to use an accurate timepiece to directly measure the time of a sextant sighting. 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 broadcast from an atomic clock, or the time displayed on a GPS display. A quartz wristwatch normally maintains 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. Navigators check chronometers from his sextants, at geographic markers surveyed by professional astronomers. This is now a rare skill, and most harbor masters cannot locate harbor markers.
Historically, three chronometers were kept in gimbals, so that they remained level, 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.
Early navigators on the northern hemisphere could determine their latitude by measuring the angular altitude of the North Star. The earliest sailors simply used measurements of hand or finger widths to determine latitude; later, cross-staffs and astrolabes were developed to increase the precision of the sighting. Eventually quadrants, octants, and sextants were invented, along with the introduction of printed tables of the positions of the sun, moon, and stars for various times and days of the year. Determining latitude by the sun is more complicated, since one has to measure the sun's altitude at noon (or: the sun's highest point in the sky for a given day) which changes during the year for a given location.
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, determining both latitude and longitude. Later in the 19th century came the development of the modern
Marc 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 arc-minutes is the nautical mile "intercept" distance that the position line needs to be shifted toward or away from the direction of the body's sub-point. Two other methods of reducing sights are the longitude by chronometer and the ex-meridian method.
(image available in print form)
Figure 1
,
Source:
[8]
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. 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.
A number of increasingly accurate instruments were developed over many years to measure navigational angles, including the kamal (a rectangle of wood cut to fit the distance from the horizon to the star with a piece of knotted string attached, which could be held in the teeth, guaranteeing that an "arm's length" distance would remain constant), astrolabe (a compact instrument used to observe and calculate the position of celestial bodies before the invention of the sextant), octant (an instrument for observing altitudes of a celestial body from a moving ship or aircraft) and sextant (an instrument for measuring angular distances used especially in navigation to observe altitudes of celestial bodies, as in ascertaining latitude and longitude). The sextant and octant are most accurate, and an improvement over the astrolabe, because they measure angles from the horizon, eliminating errors caused by the placement of an instrument's pointers, and because their dual mirror system neutralizes relative motions of the instrument, showing a steady view of the object and horizon.
(image available in print form)
Figure 2
,
Source: Spinka, 2007. The marine
SEXTANT
measures the altitude of a celestial object above the horizon.
Navigators measure distance on the globe in degrees, arc-minutes and arc-seconds. A nautical mile is defined as 1852 meters or 1.150779 miles, but is also (not accidentally) one minute of angle along a meridian on the Earth. Sextants can be read accurately to within 0.2 arc-minutes. 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), more than close enough to navigate safely when out of sight of land.
The U.S. Air Force and U.S. Navy continued instructing military aviators on the use of astronavigation until 1997 as a redundant method to GPS, because:
-
1 it can be used independently of ground aids
-
2 has global coverage
-
3 cannot be jammed (except by clouds)
-
4 does not give off any signals that could be detected by an enemy[4]
Astronavigation 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.
A variation on terrestrial celestial navigation was used to help orient the Apollo spacecraft traveling to and from the Moon. To this day, space missions, such as the Mars Exploration Rover use celestial navigation to guide spacecraft throughout the solar system.
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 300 feet. 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. Similar systems have been used on spacecraft such as Deep Space 1. As part of NASA's New Millennium program, the primary goal of Deep Space 1 was the testing of technologies to lower the cost and risk of future missions.
Modern practical navigators nearly always use celestial navigation in combination with
satellite navigation
to correct a
dead reckoning track
, or 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 pre-calculated 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.
Dead reckoning is the process of estimating a present position by projecting course and speed from a known past position.
(image available in print form)
Figure 3
,
Source:
Spinka, 2007. Dead reckoning estimates positions by projecting the course and speed from past positions.
Dead reckoning navigation plots the 9am position as illustrated by the triangle; then by extrapolating the course from that position with a known average speed the position at 9:30am and 10am can be estimated respectively, as illustrated by the corresponding semi-circles. While this method of navigation is no longer considered primary, dead reckoning is frequently used as a backup navigation method should the primary navigation system fail. Clearly, the precision of dead reckoning can be compromised by both
set
and
drift
, which are characteristics of the current or the velocity of water over the ground in which a ship is sailing. While drift is the magnitude of the current, typically measured in knots, set is the bearing in the direction the current is flowing, typically measured in degrees clockwise from either magnetic or true (geographical) North.
