Navigation

The art of finding the way from one place to another is called navigation. Until the 20th century, the term referred mainly to guiding ships across the seas. Indeed, the word navigate comes from the Latin navis, meaning “ship,” and agere, meaning “to move or direct.” Today, however, the word also encompasses the guidance of travel on land, in the air, and in inner and outer space. (For a discussion of navigation in the air, 

Marine Navigation

There are four basic methods of navigation at sea—piloting, dead reckoning, electronic navigation, and celestial navigation.
In piloting, the navigator directs a vessel from one place to another by observing such landmarks on the Earth's surface as lighthouses, beacons, buoys, and prominent rocks and cliffs, and by measurements, called soundings, of water depths. In dead reckoning, the navigator determines a ship's position by keeping a careful account, or reckoning, of the distance and direction of travel from a known position called the point of departure.
In electronic navigation, the navigator determines a ship's position with the aid of such devices as radar . These instruments variously make use of the directional properties of radio waves, of differences in the times of arrival of radio signals sent simultaneously from different locations, or—occasionally—of the difference in speed between radio waves and sound waves. In celestial navigation, the navigator finds a ship's position by observing the sun, moon, planets, and stars.

General Concepts

Course, heading, and track

The terms course, heading, and track are often loosely used. They should, however, be considered to have the meanings that follow. The course is the intended direction of the ship's travel. The heading is the direction in which the ship is pointed at any given time. The track, or course made good, is the direction of a straight line between a point of departure and a present position.
The factors that together result in failure to make good an intended course are termed drift. The flow of ocean water, however, is only one of the factors involved.

Direction and distance

On the Earth's surface each meridian, or line of longitude, is half of a great circle that passes through the geographical poles of the Earth and lies in a true north-and-south direction  The center of a great circle on the Earth's surface lies at the center of the Earth. The shortest distance between two points on the Earth's surface is the shorter arc of a great circle passing through the points.
The track of a ship that sails along a great circle will cross each meridian at a different angle—unless the ship is sailing directly along a meridian or the equator. The ship's direction, then, would usually have to be altered constantly in order to maintain a perfect great-circle course.
In practice, however, a ship's course is changed at regular intervals—of perhaps several hours—so that the ship follows a series of rhumb lines that approximates a great circle. A rhumb line is a line on the Earth's surface that crosses all meridians at the same angle. A ship sailing a steady, true course is usually following a rhumb line, and the distance it covers is greater than that of a great-circle course.

The instruments of navigation

One of the basic tools of the marine navigator is the nautical chart. This is a representation, drawn to scale, of the water and land areas of a particular region of the Earth's surface.
On the chart the navigator keeps a graphic record of the ship's progress. Such a record is kept regardless of the method—or combination of methods—of navigation that is being used. Lines drawn between successive positions marked on the chart indicate at a glance the courses that the ship has followed. From scales on the chart the navigator can measure directly, without computation, the distance that the ship has traveled.
Traditionally, Mercator charts have been used at sea  Lambert charts may also be used for long sea voyages, though they were designed for air navigation.
A navigator needs other basic instruments to determine a course and plot it on a chart. A compass indicates direction . Dividers are useful in measuring distances on charts. Parallel rulers—usually two straightedges connected by pivoted arms—are used to transfer lines of direction from one portion of a chart to another. A transparent plotter is a combination protractor and straightedge employed in the measurement of angles and distances and in drawing course lines on a chart.
In directing a course by dead reckoning, a device that measures distance traveled is also essential to the navigator. These distance-measuring devices include taffrail logs, or patent logs, and engine-revolution counters

Piloting

In piloting, the navigator guides a ship largely by the bearings of landmarks. A bearing is the horizontal angle between an object and a reference point—for example, true north is the reference point for true bearings. Bearings are usually measured clockwise from 0° at the reference point through 360° and expressed in three digits, as 028°.
Bearings are used to determine, or fix, a ship's position. Drawn on a chart, a bearing forms a line of position—a line on which some point must represent the ship's location. Therefore, when two or more bearings intersect (cross-bearings), the intersection must represent the ship's position.
Bearings of visible objects may be measured with such instruments as the alidade, pelorus, or azimuth circle. These devices usually have sighting vanes and reference circles graduated in degrees. Bearings referred to a magnetic compass must be corrected for compass errors—deviation and magnetic variation
When only one landmark is visible, a ship's position can be fixed by determining the bearing of the object then measuring the distance to it with a range finder or a stadimeter. The range finder is an optical instrument for measuring the distance to any clearly defined object. If the height of the object is known, the stadimeter may be used. It operates on the principle that the closer an object is, the bigger it appears to be.
In shallow water, soundings help fix a ship's position. Sonic, or echo, depth finders make use of the known speed of sound in water. Sound transmitted from the ship is reflected from the ocean floor to a receiver, which measures elapsed time and calculates distance. Some devices produce fathograms—continuous profiles, or graphs, of the ocean bottom. An older depth-finding device is the hand lead and line—a marked cord with a weight on the end.
Light stations and lightships are maintained along coastlines to warn approaching ships of potential dangers such as off-lying rocks. Most lights operate in on-and-off cycles. The length of time required for a light to complete a full cycle of changes is called the period of the light. Lights that are “off” longer than they are “on” are called flashing lights. Occulting lights are “on” as long as, or longer than, they are “off.”
Floating navigational aids (other than lightships and weather ships) which are anchored or moored are called buoys. United States waters are marked for safe navigation by the lateral system of buoyage. Simple arrangements of colors, shapes, numbers, and lights are employed to indicate the side of a buoy on which a ship should pass when moving in a given direction.

Dead Reckoning

In dead reckoning, the navigator estimates a ship's position by keeping a careful record of its movement. The initial point of departure for dead reckoning is usually the last fix the navigator obtains from objects on land at the start of a voyage. From this point, true courses steered and distances traveled (as recorded by log) are plotted on a chart
Points along the dead-reckoning line, representing successive positions of the ship, are labeled with the appropriate time and the notation “D.R.” Dead reckoning commonly begins anew each time bearings, celestial observations, or electronic aids provide an accurate fix. The dead-reckoning line on his chart is important to the navigator because it indicates at a glance the theoretical position of the ship, the track the ship should have followed, and the direction in which the ship is traveling.

Electronic Navigation

Modern electronic devices are important aids in finding position at sea. For example, the navigator whose ship is equipped with a radio direction finder can determine the bearings of radio transmitting stations on shore. Special radio beacons for navigation are established at lighthouses, lightships, and prominent points along coasts. Radio bearings may be plotted on a chart to obtain a fix.
A variety of other electronic aids to navigation are in use or under development. Loran (long-range navigation) and shoran (short-range navigation) are among the most widely known. Radar is also of value, especially for a ship near the shore. Consol, by contrast, is designed for operation over relatively long ranges. A ship at sea can obtain a fix on its position from Consol shore stations with the use of an ordinary radio receiver.

Celestial Navigation

For centuries sailors have guided their ships across the oceans by celestial navigation, or nautical astronomy. This is the art of finding position by observing the sun, moon, stars, and planets.
As they journey for some distance, travelers observe that the celestial bodies appear to change their paths across the sky and to rise and set at new points along the horizon. Since the apparent positions of celestial bodies thus change with time and with changes in an observer's position on the nearly spherical Earth, the location of a ship or other craft may be determined by careful observations of celestial bodies.

The celestial sphere

Celestial bodies, such as the stars, are so far from the Earth that they appear to be located on the inside surface of an imaginary hollow sphere. This sphere, which has an infinite radius, is called the celestial sphere. Its center coincides with the center of the Earth. All points on the Earth's surface are considered to be projected onto the celestial sphere, as are the equator, the parallels of latitude, and the meridians.
For the purpose of navigation, a system of coordinates is required on the celestial sphere in order that the position of a celestial body at any time may be accurately described. One such system is the celestial equator, or equinoctial, system.
In this system the celestial equator, or equinoctial, is the base, or primary, circle. It corresponds to the Earth's equator. At right angles to the celestial equator are the hour circles. An hour circle is a great circle on the celestial sphere that passes through the poles and through a celestial body or point. Each meridian of the celestial sphere is identical with an hour circle.
The declination (dec.) of any point on the celestial sphere is its angular distance north or south from the celestial equator, measured along the hour circle that passes through the point. Declination on the celestial sphere corresponds to latitude on the Earth's surface.
The Greenwich hour angle (GHA) of any point or body is the angle, measured at the pole of the celestial sphere, between the celestial meridian of Greenwich and the hour circle of the point. The angle is measured along the celestial equator westward from the Greenwich celestial meridian, from 0° through 360°. The GHA differs from longitude on the Earth's surface in that longitude is measured east or west, from 0° through 180°, and remains constant. The GHA of a body, however, increases through each day as the Earth rotates.

The theory of celestial navigation

At any instant of time every celestial body is directly above—or in the zenith of—some point on the Earth's surface. This point lies on a line connecting the body and the center of the Earth. It is called the geographical position, or GP, of the body. Sometimes the GP of the sun is called the subsolar point; that of the moon, the sublunar point; and that of a star, its substellar point.
A line from the center of the Earth through the GP of an observer would extend to a point on the celestial sphere. This point is called the zenith of the observer; the line is his local vertical.
The altitude of a celestial body is the angle, measured by an observer on Earth, between the body and the horizon. Were a celestial body—say, a star—directly above, or in the zenith of, an observer, its altitude would be 90°. The observer would be at the GP of the star.
Were the observer a distance away from the GP of a star, however, the altitude of the star would be less than 90° by an amount proportional to the distance. On the celestial sphere, the observer's zenith would be apart from the star by a distance called the zenith distance, or ZD.
All points a given ZD from a star would form around the star a circle of radius equal to the ZD. Were lines from all points on the circle extended to the center of the Earth, a similar circle would be formed on the Earth's surface. From any point on this circle, the observed altitude of the star would be the same; hence, it is called a circle of equal altitude. Its center is the GP of the star. A second circle of equal altitude would exist around the GP of a second star. Ordinarily, the circles would intersect in two widely separated points. One of these points, of course, would be the position of the observer on the surface of the Earth.

Celestial navigation at sea

To put this theory into practice, a navigator measures with a sextant the altitudes of two or more celestial bodies. He carefully notes—to the second—the time at which he made his observations. He obtains the time from radio signals or from accurate clocks called chronometers . These are kept set to Greenwich mean time, or GMT, for this is the time the navigator must know as he turns next to the Nautical Almanac .
The Nautical Almanac is a book of astronomical tables from which may be found, for every second of every day, the positions on the celestial sphere of the sun, the stars, the moon, and the planets used in navigation. The positions are given in declination and GHA. From them, of course, the latitude and longitude of the bodies' GPs may be found.
Knowing the altitudes of the bodies he observed and their GPs at the time, the navigator has the information necessary to construct the circles of equal altitude that define his position. Actually, the navigator does not plot on his chart the full circles. From dead reckoning or other means, he knows his approximate latitude and longitude. All he needs, then, are segments of the circles so short that, without practical loss of accuracy, they may be drawn as straight lines. Like the lines obtained from bearings in piloting, they are called lines of position.

Underwater Navigation

The areas below the Earth's surface, which include the ocean depths and ocean floors, are a new frontier in navigation. These submarine territories harbor an abundant supply of minerals, food, petroleum, and other resources. In recent years, nations have made greater efforts to exploit these resources
The development of such devices as the pressure demand valve has enabled sea divers to descend to depths of several hundred feet. Special mixtures of gases for breathing, which reduce the effects of the bends, have also been developed Undersea explorers have made dives in submersible vehicles to depths in excess of 6 miles (9.6 kilometers). Some have lived for weeks on end in undersea “houses,” emerging as they wish to explore the ocean floor. Ocean navigators may eventually be called upon to locate mineral deposits and to establish “farms” on the ocean floor.
Two incidents in the late 20th and early 21st centuries pointed out both the progress that has been made and the continuing limitations in navigating the ocean depths. Researchers from France and the United States combined their navigational skills and technology in an effort to find the wreck of the luxury ocean liner Titanic, which sank in 1912 off the coast of Newfoundland. They finally succeeded on Sept. 1, 1985. One of the new devices they used was a remotely controlled search vehicle from which they were able to take underwater video images of the ship. Although technology exists to locate objects, there are still limitations in the ability to function underwater. In August 2000 an accident aboard a Russian nuclear-powered submarine led to tragedy when the ship sank and rescue efforts failed to save the 118 crewmembers on board.

The Challenge of Underwater Navigation

Operations within the ocean depths, like those at sea, in the air, and in space, are governed by natural physical laws. Unique problems, however, are encountered below the ocean surface. An example is the great pressure of the water in the depths of the ocean—just the reverse of the near vacuum, or lack of pressure, in outer space.
The flow of ocean currents, temperature gradients, and lack of visibility without the use of artificial lights also makes oceanographic navigation a difficult procedure. The methods of celestial navigation, such visual aids to navigation as buoys, and most electronic methods are not usable.

The Continental Shelf

Around each continent is an area, of varying distance from shore, that lies in water of relatively shallow depth. It is called the continental shelf. In some of these areas, submerged river channels can be traced well out to sea. Mariners and ocean navigators use those submerged channels that have been charted as aids in navigation.
The ocean currents of the world have also been charted. The ocean floor is being charted in greater detail and at greater depths than ever before. This is being done partly to meet the requirements of antisubmarine defenses. Electronic depth-finding instruments have produced much data for charts of the ocean floor. In recent years major advances have been made in underwater archaeology, in oceanography, and in meteorology

The Use of Very-Low-Frequency Radiation

Current methods of ocean navigation and communication involve very-low-frequency radiation, or hydronic radiation, the name given to electromagnetic waves having frequencies of 14 to 30 kilohertz, which travel through water much as radio waves travel through the atmosphere. These waves and methods of transmitting and receiving are especially useful in on-land communication with submarines.
When transmitted from appropriate antennas, very-low-frequency waves appear to have directional properties. Thus “homing” or bearing-taking devices, similar to radio direction finders, are used to receive them. Such equipment can also be an aid to underwater surveying.
Hydronic radiation can carry signals through water for surface distances of at least 30 miles (48 kilometers). The equipment used for this is similar to conventional radio. Scuba divers carrying underwater walkie-talkies, for instance, can talk with people over 300 yards (274 meters) away on the water's surface.
Since signals from land reach depths of only 33 to 49 feet (10 to 15 meters), a project known as ELF, an extremely low-frequency communications system, was proposed in the 1960s. This system would use an enormous antenna buried in the ground, with arms originally reaching 6,000 miles (9,600 kilometers), and would send 72- to 80-hertz signals to submarines at great depths. After much debate the United States Navy abandoned the ELF project in 1981.

Outer-Space Navigation

Space navigation, or astrogation, is the evolving art and science by which space navigators direct the courses of spacecraft. The moon is the nearest to Earth of all the heavenly bodies that astronauts may land on and explore. As scientists have learned how to navigate safely through cislunar space—the space between the Earth and moon—the possibilities for space exploration have expanded. It may even become possible to plan extended trips to such nearby planets in the solar system as Mars and Venus.
As astronauts pilot spacecraft through different areas of cislunar space they use a variety of navigational methods. This section discusses navigation through the area that lies beyond about 500 miles (800 kilometers) from the surface of the Earth. This applies mostly to spacecraft traveling to the moon or other planets. Astronauts aboard the space shuttle and the international space station operate below that level.

Principles of Space Navigation

Many of the principles and tools of celestial navigation at sea will be of equal use to the space navigator. However, the astronaut's local vertical—the line from the center of the Earth to his spacecraft, passing through his GP on the Earth's surface—will assume a new role. It will become a valuable line of position—and an unusual one, in that the space navigator will be able to look down it, toward the Earth, and see his GP.
Due to the rotation of the Earth from west to east, an observer on Earth sees the sun, moon, stars, and planets apparently revolving around the Earth from east to west. However, to an observer in space the Earth would appear as a spinning globe, moving through space and apparently revolving in an orbit around him. In reality, he is moving in relation to the Earth.
The observer assumes that he is at the center of the universe, fixed in space. The stars also appear to be fixed, provided that the observer's spacecraft is stabilized and not tumbling in its orbit. The Earth and moon will appear as large, rapidly moving spheres in space, their speed depending upon the observer's relative distances from them. The sun and planets will appear to move slowly if they are observed over a long period of time.
For close-in orbits around the Earth, the space navigator will be mainly interested in his position and motion relative to the Earth. The Earth itself may be used to fix positions of a vehicle in space.

Positioning the Spacecraft

Astronomers can compute the path of a spacecraft and record this information in the form of a space almanac. Such an almanac would be similar to the Nautical Almanac used by marine navigators and the Air Almanac used by air navigators. These almanacs give the positions of selected celestial bodies for given times. From these the navigators compute their positions on the surface of the Earth. Since a space almanac would in effect give the positions of the spacecraft at intervals as it moved through space, the space navigator would be given in advance his selected path, orbit, or trajectory.
However, because the space navigator cannot see his own position in space relative to fixed stars, astronomers will tabulate the Earth's apparent path, or orbit. Then, as long as the Earth remains “on schedule”—as observed by the space navigator—the spacecraft is also on its correct schedule. The smallest observable deviation from the planned orbit would be corrected by firing a rocket motor for a sufficient interval of time to place and keep the space vehicle and its navigator on course.
Spacecraft must be positioned in three dimensions, while the astronaut's line of sight to the Earth's center is in two dimensions. These two dimensions, expressed in relation to the stars on the celestial sphere, would be given in a space almanac or other publication concerning space navigation as the sidereal hour angle (SHA) and declination (dec.) of the Earth.
The sidereal hour angle of a body is its angular distance on the celestial sphere from the vernal equinox, measured westward from 0° through 360°. It is similar to longitude on Earth.
Declination is angular distance north (+) or south (–) from the celestial equator. It corresponds to latitude on the Earth. The third dimension tabulated in a space almanac would be the distance of the observer from his GP, or from the surface of the Earth, measured along his local vertical.
A space navigator, therefore, would look down his local vertical and see the Earth on the celestial sphere. With the aid of instruments, he would determine—from the apparent position of the Earth among the stars—that the position of his GP on the celestial sphere was, say, SHA 82°30′, dec. 35° north. The navigator would see the Earth, but of course the celestial coordinates would not be visible.With a sextant, the navigator would then measure the angle subtended by the Earth's sphere. If the measured angle were 13° 54′, he would be about 25,000 nautical miles from the Earth's surface. Astronomers have compiled tables of the angles subtended by the Earth and moon at various distances to help with this computation.

The Nature of a Space Almanac

While a space almanac will be similar in principle to the Nautical Almanac, it may differ greatly in form. It may, for instance, not be a book at all; it could as well be a form of computer. Actually, any computation of the path of a spacecraft may be thought of as a space almanac. Whatever its form, a space almanac will give the space navigator the information he needs to determine his position.
The tables in the Nautical Almanac give the ephemerides, or periodic apparent positions, of the celestial bodies used in navigation. The apparent motions of these bodies, of course, are due primarily to the rotation of the Earth about its axis.
A space almanac, on the other hand, may include only a single ephemeris—that of the Earth as seen from a spacecraft following a desired course. The apparent motion of the Earth will, in this case, be due for the most part to the motion of the spacecraft. In effect, the Earth's ephemeris will be the reverse of the spacecraft's path; consequently, the Earth's ephemeris will be of great significance to the space navigator.
The same principles may be applied to the problems of rendezvous in space. For instance, if an astronaut is to dock alongside an artificial satellite, the satellite's ephemeris is also the orbit that the astronaut's spacecraft must follow. A space almanac might well provide the data an astronaut would need to compute any required path for this spacecraft.

The Instruments of Space Navigation

In space navigation a sextant and a timepiece will be used in observing celestial bodies. These will be employed in conjunction with a space almanac.
Lunar charts of the LAC series show details of the moon at a scale of about 14 nautical miles to the inch on a Mercator projection, a type of map that readily allows a navigator to plot a straight-line course. The charts are published by the Aeronautical Chart and Information Center of the United States Air Force. They are used by the Air Force and by the National Aeronautics and Space Administration.
Other instruments for space navigation may include plotting sheets and transparent plotters, similar to those of the seagoing navigator. The space navigator will also, of course, make use of any available electronic aids to navigation.

Lunar Approach Navigation

The problems involving speed, distance, and direction that a space navigator will encounter as he approaches the moon can be visualized by plotting his positions on a scaled diagram. The illustration shows two views of an approach to the moon along a tangent to its surface: a side view in the upper part of the drawing, and a plan (or top) view. The observer's position is plotted to scale, so the height of the observer above the moon's surface may be measured along a line from the observer to the center of the moon. These distances are plotted at intervals of 100 nautical miles, beginning at a distance of 1,000 miles. An artificial satellite 600 miles beyond the observer's horizon is also plotted in the side view, at the upper left.

History of Navigation

The navigation of rivers, lakes, and oceans began before recorded history. Navigation, due to its relationship and importance to transportation, has played a leading part in the advancement of civilization. People learned early that travel by water was a convenient means of transporting their goods of trade to other lands The people living near the Mediterranean Sea—the Sumerians, Cretans, Egyptians, Phoenicians, and Greeks—became able mariners, as did the Scandinavians in northern Europe.
The early mariners did not venture very far from the coasts. Skirting the coastlines, they could identify objects on land and thereby know the positions of their ships. Usually they traveled by day and went ashore at night. They did not have nautical charts, but sometimes they found their way by a list of directions. The Romans called such a list a periplus. It gave details of landmarks, good anchorages, and such hazards as shoals and reefs.

Early Developments in Navigation

The Phoenicians and Greeks were the first of the Mediterranean sailors to navigate far from land and to sail at night. They made primitive charts and knew a crude form of dead reckoning. They used observations of the sun and the North Star, or polestar, to determine directions. They estimated distances from the time it took to cover them.
Advances in seamanship—the art of handling a ship—kept pace with advances in navigation. The Egyptians used rowers, and the Phoenicians and Greeks increased the number of tiers of rowers. The Greeks added a second mast, in the bow, and the Romans a third mast, in the stern.

The First Navigational Aids

One great aid to navigation was the development of the magnetic compass. Although the magnetic properties of the lodestone were known since ancient times, the first use of the magnetic compass by navigators appears to have been in the 12th century. In the next century the Italians learned to make a chart called a portolano. It showed an outline of the coast and had crosslines to aid in finding directions.
Navigators at this time also used the cross-staff and the astrolabe, two devices that the Greeks had invented to measure the altitudes of celestial bodies. From these measurements it was possible to determine the approximate latitude of the vessel as well as approximate local time. The simplest version of the cross-staff was a stick, or staff, about one yard (0.9 meter) long with a shorter sliding stick set at right angles to the staff. The navigator pointed the staff at a spot about halfway between the horizon and the sun or a star. The crosspiece was then moved until the sights at its ends were in line with both the observed body and the horizon. A scale along the staff showed the altitude, or angle above the horizon, of the body.
The astrolabe was a disk of brass or bronze, from 4 to 20 inches (10 to 50 centimeters) in diameter. A pointer, called an alidade, was pivoted at the center of the disk. One person held the astrolabe by a small ring at the top while another person knelt facing the rim of the instrument. The person kneeling pointed the alidade at the sun or a star and read the angle from the markings on the disk.
Such great explorers as Christopher Columbus and Ferdinand Magellan made their voyages with these aids to navigation. The instruments, however, were not satisfactory, and for some two centuries after Columbus, no clock could keep time well enough to aid in fixing longitude

From the 17th Century to the Present

In the 17th century, Britain, France, and other maritime countries actively began to aid the development of navigation. Astronomical observatories were established to provide almanacs. Mapmaking and the invention of required navigational instruments were also encouraged.
In 1731 John Hadley, an Englishman, and Thomas Godfrey, an American, simultaneously invented a quadrant that made it possible to obtain accurate observations of celestial bodies. The instrument was similar to the sextant in common use today. The problem of fixing longitude was solved when John Harrison in England produced several chronometers between 1730 and 1763. Pierre LeRoy in France built an improved chronometer in 1766 . Captain James Cook's voyages of discovery in the Pacific Ocean at this time proved the accuracy and reliability of navigational instruments and techniques
Early in the 19th century, Nathaniel Bowditch of Salem, Mass., devised many improved methods of navigation. In 1837 Capt. Thomas Sumner devised a trigonometric method of obtaining from celestial observations the lines known as Sumner lines of position. In 1875 Frenchman Marcq St. Hilaire improved upon Sumner's trigonometric calculations. These calculations were later used to supplement dead reckoning, a more precise method of correcting for drift using triangular calculations of velocity. Dead reckoning allows a navigator to plot where a craft will be at any time, making it possible to plan a journey in its entirety before the start of the journey. Matthew Fontaine Maury made famous studies of wind and weather and helped in the development of government aids to navigation
Today, electronic devices such as radar and loran are widely used in navigation. Most vessels use an automatic pilot. Since 1978 a satellite system managed by the United States Air Force, called Global Positioning System, has been providing continuous worldwide coverage adequate for determining latitude and longitude to within about 30 feet (10 meters) and, in many places, altitude, with the same accuracy. The digital computer, another tool, works so fast that it can provide continuous information. It also has a memory to store information for use when needed. The Navstar Global Positioning System was implemented in the 1980s. This system allows spacecraft crews to store their course in a computer system, which can then verify the location of the spacecraft to within a few feet and the speed of the spacecraft to within a few feet per second. The human navigator is becoming more and more a manager of computer systems; however, there is no substitute for human judgment to deal with the occasional unexpected situation.