Editing Celestial navigation (section)

===Longitude===
{{see also|Longitude determination}}
[[File:Problem of longitude.svg|thumb|350px|The relative longitude to a position (for example [[Greenwich]]) can be calculated with the position of the Sun and the reference time (for example, [[Coordinated Universal Time|UTC]]/GMT).]]

If the angle to Polaris can be accurately measured, a similar measurement of a star near the eastern or western horizons would provide the [[longitude]]. The problem is that the Earth turns 15&nbsp;degrees per hour, making such measurements dependent on time. A measure a few minutes before or after the same measure the day before creates serious navigation errors. Before good [[Marine chronometer|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 invention of the modern chronometer by [[John Harrison]] in 1761 vastly simplified longitudinal calculation.

The [[longitude problem]] took centuries to solve and was dependent on the construction of a non-pendulum clock (as pendulum clocks cannot function accurately on a tilting ship, or indeed a moving vehicle of any kind). Two useful methods evolved during the 18th century and are still practiced today: [[Lunar distance (navigation)|lunar distance]], which does not involve the use of a chronometer, and the use of an accurate timepiece or chronometer.

Presently, layperson calculations of longitude can be made by noting the exact local time (leaving out any reference for [[daylight saving time]]) when the Sun is at its highest point in Earth's sky. The calculation of noon can be made more easily and accurately with a small, exactly vertical rod driven into level ground—take the time reading when the shadow is pointing due north (in the northern hemisphere). Then take your local time reading and subtract it from GMT ([[Greenwich Mean Time|Greenwich Mean]] Time), or the time in London, England. For example, a noon reading (12:00) near central Canada or the US would occur at approximately 6 p.m. (18:00) in London. The 6-hour difference is one quarter of a 24-hour day, or 90 degrees of a 360-degree circle (the Earth). The calculation can also be made by taking the number of hours (use decimals for fractions of an hour) multiplied by 15, the number of degrees in one hour. Either way, it can be demonstrated that much of central North America is at or near 90 degrees west longitude. Eastern longitudes can be determined by adding the local time to GMT, with similar calculations.

====Lunar distance====
{{unreferenced section|date=February 2022}}
{{Main|lunar distance (navigation)|l1=Lunar distance}}

An older but still useful and practical method of determining accurate time at sea before the advent of precise timekeeping and satellite-based time systems is called "'''lunar distances,"''' or "lunars," which was used extensively for a short period and refined for daily use on board ships in the 18th century. Use declined through the middle of the 19th century as better and better timepieces (chronometers) became available to the average vessel at sea. Although most recently only used by sextant hobbyists and historians, it is now becoming more common in celestial navigation courses to reduce total dependence on [[GNSS]] systems as potentially the only accurate time source aboard a vessel. Designed for use when an accurate timepiece is not available or timepiece accuracy is suspect during a long sea voyage, the navigator precisely measures the angle between the Moon and the Sun or between the Moon and one of several stars near the [[ecliptic]]. The observed angle must be corrected for the effects of refraction and parallax, like any celestial sight. To make this correction, the navigator measures the altitudes of the Moon and Sun (or another star) at about the same time as the lunar distance angle. Only rough values for the altitudes are required. A calculation with suitable published tables (or longhand with logarithms and graphical tables) requires about 10 to 15&nbsp;minutes' work to convert the observed angle(s) to a geocentric lunar distance. The navigator then compares the corrected angle against those listed in the appropriate almanac pages for every three hours of Greenwich time, using interpolation tables to derive intermediate values. The result is a difference in time between the time source (of unknown time) used for the observations and the actual prime meridian time (that of the "Zero Meridian" at Greenwich, also known as UTC or GMT). Knowing UTC/GMT, a further set of sights can be taken and reduced by the navigator to calculate their exact position on the Earth as a local latitude and longitude.

====Use of time====
{{Main|Longitude by chronometer|Marine 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&nbsp;century (see [[John Harrison]]). Today, time is measured with a chronometer, a [[Quartz clock|quartz watch]], a [[Time signal#Radio time signals|shortwave radio time signal]] broadcast from an [[atomic clock]], or the time displayed on a [[Atomic clock#Global navigation satellite systems|satellite time signal]] receiver.<ref>{{cite web |last=Mehaffey |first=Joe |title=How accurate is the TIME DISPLAY on my GPS? |url=http://gpsinformation.net/main/gpstime.htm |url-status=live |archive-url=https://web.archive.org/web/20170804120341/http://gpsinformation.net/main/gpstime.htm |archive-date=4 August 2017 |access-date=9 May 2018 |website=gpsinformation.net}}</ref> A [[Watch#Electronic|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. When time at the [[prime meridian]] (or another starting point) is accurately known, celestial navigation can determine longitude, and the more accurately latitude and time are known, the more accurate the longitude determination. [[Earth's rotation#Angular speed|The angular speed of the Earth]] is latitude-dependent. At the poles, or latitude 90°, the rotation velocity of the Earth reaches zero. At 45° latitude, one second of time is equivalent in longitude to {{convert|1077.8|ft|2|lk=on|abbr=on}}, or one-tenth of a second means {{convert|107.8|ft|2|abbr=on}}<ref>[http://adsabs.harvard.edu/pdf/1914JRASC...8...85M Errors in Longitude, Latitude and Azimuth Determinations — I] by F. A. McDiarmid, The Royal Astronomical Society of Canada, 1914.</ref> At the slightly bulged-out equator, or latitude 0°, the rotation velocity of Earth or its equivalent in longitude reaches its maximum at {{convert|465.10|m/s|1|lk=on|abbr=on}}.<ref name="Cox2000">{{cite book |editor=Arthur N. Cox |title=Allen's Astrophysical Quantities |url=https://books.google.com/books?id=w8PK2XFLLH8C&pg=PA244 |edition=4th |date=2000 |publisher=AIP Press |location=New York |isbn=978-0-387-98746-0 |page=244 |access-date=17 August 2010}}</ref>

Traditionally, a navigator checked their chronometer(s) with their sextant at a geographic marker surveyed by a professional astronomer. This is now a rare skill, and most [[harbormaster]]s cannot locate their harbor's marker. Ships often carried more than one chronometer. Chronometers were kept on [[gimbals]] in a dry room near the center of the ship. They were used to set a [[hack watch]] for the actual sight, so that no chronometers were ever exposed to the wind and salt water on deck. Winding and comparing the chronometers was a crucial duty of the navigator. Even today, it is still logged daily in the ship's deck log and reported to the captain before [[Ship's bell|eight bells]] on the forenoon watch (shipboard noon). Navigators also set the ship's clocks and calendar. Two chronometers provided [[dual modular redundancy]], allowing a backup if one ceases to work but not allowing any [[error correction]] if the two displayed a different time, since in case of contradiction between the two chronometers, it would be impossible to know which one was wrong (the [[error detection]] obtained would be the same as having only one chronometer and checking it periodically: every day at noon against [[dead reckoning]]). Three chronometers provided [[triple modular redundancy]], allowing [[error correction]] if one of the three was wrong, so the pilot would take the average of the two with closer readings (average precision vote). There is an old adage to this effect, stating: "Never go to sea with two chronometers; take one or three."<ref>{{Cite book |title=[[The Mythical Man-Month]] |last=Brooks |first=Frederick J. |publisher=Addison-Wesley |year=1995 |isbn=0-201-83595-9 |page=[https://archive.org/details/mythicalmonth00broo/page/64 64] |author-link=Fred Brooks |orig-year=1975}}</ref> Vessels engaged in survey work generally carried many more than three chronometers{{snd}} for example, [[HMS Beagle|HMS ''Beagle'']] carried [[List of chronometers on HMS Beagle|22 chronometers]].<ref>{{cite web |url=http://darwin-online.org.uk/content/frameset?viewtype=side&itemID=F10.2&pageseq=41 |title=Volume II: Proceedings of the Second Expedition |page=18 |author=R. Fitzroy}}</ref>