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 west of Madeira, or in South America, about 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.
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.
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 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.
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.
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.
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 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 . 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.
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 . 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.
An early example is the Link Celestial Navigation Trainer, used of the Second World War. Housed in a 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.