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41-608: In January 2009, μFUN merged with the Probing Lensing Anomalies NETwork (PLANET). Organizations like μFUN provide a forum and a listserv for instant notification to amateur and professional astronomers all over the globe, so that microlensing events can be mined for all the information that can be gathered. Thus, amateur astronomers have a useful role in significant discoveries, as well as a clear and democratic path to authorship on any peer-reviewed scientific publications that result. Gravitational lensing

82-413: A prime meridian , is mathematically related to time differences up to 12 hours by a factor of 15. Thus, a time differential (in hours) between two points is multiplied by 15 to obtain a longitudinal difference (in degrees). Historically, times used for calculating longitude have included apparent solar time , local mean time , and ephemeris time , with mean time being the one most used for navigation of

123-477: A difference of 15° longitude corresponds to a one-hour difference in local time, due to the differing position in relation to the Sun. Comparing local time to an absolute measure of time allows longitude to be determined. Depending on the era, the absolute time might be obtained from a celestial event visible from both locations, such as a lunar eclipse, or from a time signal transmitted by telegraph or radio. The principle

164-637: A few of the more prevalent ones. Longitude is given as an angular measurement with 0° at the Prime Meridian , ranging from −180° westward to +180° eastward. The Greek letter λ (lambda) is used to denote the location of a place on Earth east or west of the Prime Meridian. Each degree of longitude is sub-divided into 60 minutes , each of which is divided into 60 seconds . A longitude is thus specified in sexagesimal notation as, for example, 23° 27′ 30″ E. For higher precision,

205-474: A method of determining longitude by comparing the local time of a lunar eclipse at two different places, thus demonstrating an understanding of the relationship between longitude and time. Claudius Ptolemy (2nd century CE) developed a mapping system using curved parallels that reduced distortion. He also collected data for many locations, from Britain to the Middle East. He used a prime meridian through

246-433: A network of telescopes to rapidly sample photometric measurements of the magnification of stars in the galactic bulge undergoing gravitational microlensing by intervening foreground stars (or other compact massive objects). This network consists of five 1m-class optical telescopes distributed in longitude around the southern hemisphere in order to perform quasi-continuous round-the-clock precision monitoring. On

287-464: A target-of-opportunity basis, less frequent spectroscopic measurements complement the rapid photometry for selected prime targets. Since 2005, PLANET performs a common microlensing campaign with RoboNet -1.0, a network of UK-operated 2.0m robotic telescopes. In January 2009, PLANET has merged with the MicroFUN collaboration. For the 2006 observing season, the telescopes involved were (apart from

328-483: A vast impact on astronomy, specifically in the search for extrasolar planets. If a planet orbiting a star passes within our line of sight to that star, it very slightly changes the brightness of the star. These changes can last a few hours or a few days. Astronomers can estimate the ratio of the planet's mass to the star's mass, as well as the radius of the planet's orbit around the star, by comparing actual brightness measurements to theoretical models. Expensive equipment

369-553: Is cos φ decreases from 1 at the equator to 0 at the poles, which measures how circles of latitude shrink from the equator to a point at the pole, so the length of a degree of longitude decreases likewise. This contrasts with the small (1%) increase in the length of a degree of latitude (north–south distance), equator to pole. The table shows both for the WGS84 ellipsoid with a = 6 378 137 .0 m and b = 6 356 752 .3142 m . The distance between two points 1 degree apart on

410-529: Is a geographic coordinate that specifies the east – west position of a point on the surface of the Earth , or another celestial body. It is an angular measurement , usually expressed in degrees and denoted by the Greek letter lambda (λ). Meridians are imaginary semicircular lines running from pole to pole that connect points with the same longitude. The prime meridian defines 0° longitude; by convention

451-436: Is an effect of Albert Einstein 's general relativity , which says that all matter bends light that passes by it. Strong gravitational lensing drastically alters the shape of an object on the sky; weak gravitational lensing slightly alters the shape of the object; and gravitational microlensing alters only the brightness of the object, instead of its shape. Gravitational lensing in general, and especially microlensing, has had

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492-615: Is required to detect a microlensing event, but because of the magnification, less sophisticated telescopic equipment can monitor the magnified area for changes in brightness caused by planets. Equipment that is now available has become more efficient at detecting microlensing events, but this equipment is in high demand for all sorts of astronomical observations and cannot be dedicated to monitoring these events for disruptions caused by planets. Amateur astronomers have no access restriction to their equipment and can "follow up" on microlensing events that have been detected, therefore contributing to

533-402: Is straightforward, but in practice finding a reliable method of determining longitude took centuries and required the effort of some of the greatest scientific minds. A location's north–south position along a meridian is given by its latitude , which is approximately the angle between the equatorial plane and the normal from the ground at that location. Longitude is generally given using

574-663: The International Reference Meridian for the Earth passes near the Royal Observatory in Greenwich , south-east London on the island of Great Britain . Positive longitudes are east of the prime meridian, and negative ones are west. Because of the Earth's rotation , there is a close connection between longitude and time measurement . Scientifically precise local time varies with longitude:

615-587: The RoboNet telescopes): As of late 2006, PLANET had 31 members from 11 countries: France, United Kingdom, Germany, Denmark, Austria, Chile, Australia, New Zealand, South Africa and the United States. This article about a specific observatory, telescope or astronomical instrument is a stub . You can help Misplaced Pages by expanding it . Longitude Longitude ( / ˈ l ɒ n dʒ ɪ tj uː d / , AU and UK also / ˈ l ɒ ŋ ɡ ɪ -/ )

656-522: The geodetic normal or the gravity direction . The astronomical longitude can differ slightly from the ordinary longitude because of vertical deflection , small variations in Earth's gravitational field (see astronomical latitude ). The concept of longitude was first developed by ancient Greek astronomers. Hipparchus (2nd century BCE) used a coordinate system that assumed a spherical Earth, and divided it into 360° as we still do today. His prime meridian passed through Alexandria . He also proposed

697-542: The 12th century, astronomical tables were prepared for a number of European cities, based on the work of al-Zarqālī in Toledo . The lunar eclipse of September 12, 1178 was used to establish the longitude differences between Toledo, Marseilles , and Hereford . Christopher Columbus made two attempts to use lunar eclipses to discover his longitude, the first in Saona Island , on 14 September 1494 (second voyage), and

738-655: The British parliament in 1714. It offered two levels of rewards, for solutions within 1° and 0.5°. Rewards were given for two solutions: lunar distances, made practicable by the tables of Tobias Mayer developed into an nautical almanac by the Astronomer Royal Nevil Maskelyne ; and for the chronometers developed by the Yorkshire carpenter and clock-maker John Harrison . Harrison built five chronometers over more than three decades. This work

779-775: The Canary Islands, so that all longitude values would be positive. While Ptolemy's system was sound, the data he used were often poor, leading to a gross over-estimate (by about 70%) of the length of the Mediterranean. After the fall of the Roman Empire, interest in geography greatly declined in Europe. Hindu and Muslim astronomers continued to develop these ideas, adding many new locations and often improving on Ptolemy's data. For example al-Battānī used simultaneous observations of two lunar eclipses to determine

820-493: The Poles. Also the discontinuity at the ± 180° meridian must be handled with care in calculations. An example is a calculation of east displacement by subtracting two longitudes, which gives the wrong answer if the two positions are on either side of this meridian. To avoid these complexities, some applications use another horizontal position representation . The length of a degree of longitude (east–west distance) depends only on

861-471: The West Indies, and as far as Japan and China in the years 1874–90. This contributed greatly to the accurate mapping of these areas. While mariners benefited from the accurate charts, they could not receive telegraph signals while under way, and so could not use the method for navigation. This changed when wireless telegraphy (radio) became available in the early 20th century. Wireless time signals for

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902-556: The advantages that both the observations and the calculations were simpler, and as they became cheaper in the early 19th century they started to replace lunars, which were seldom used after 1850. The first working telegraphs were established in Britain by Wheatstone and Cooke in 1839, and in the US by Morse in 1844. It was quickly realised that the telegraph could be used to transmit a time signal for longitude determination. The method

943-489: The article "Detecting Exoplanets by Gravitational Microlensing using a Small Telescope" by Grant Christie of the Auckland Observatory. Microlensing events with medium aperture telescopes are discovered primarily through observatories and typically require a heftier computer system and observation team. The basic set up and data requirements are also described in detail on the μFUN website. Getting involved at

984-757: The convention of negative for east is also sometimes seen, most commonly in the United States ; the Earth System Research Laboratories used it on an older version of one of their pages, in order "to make coordinate entry less awkward" for applications confined to the Western Hemisphere . They have since shifted to the standard approach. The longitude is singular at the Poles and calculations that are sufficiently accurate for other positions may be inaccurate at or near

1025-421: The development of telescopes and pendulum clocks until the mid-18th century saw a steady increase in the number of places whose longitude had been determined with reasonable accuracy, often with errors of less than a degree, and nearly always within 2° to 3°. By the 1720s errors were consistently less than 1°. At sea during the same period, the situation was very different. Two problems proved intractable. The first

1066-509: The difference in longitude between Antakya and Raqqa with an error of less than 1°. This is considered to be the best that can be achieved with the methods then available: observation of the eclipse with the naked eye, and determination of local time using an astrolabe to measure the altitude of a suitable "clock star". In the later Middle Ages, interest in geography revived in the west, as travel increased, and Arab scholarship began to be known through contact with Spain and North Africa. In

1107-465: The discovery of several extrasolar planets. The short duration and unpredictable nature of disruptions during microlensing events require this kind of coverage, making amateur efforts very important to searching for extrasolar planets using microlensing. μFUN facilitates the collaboration between amateur and professional astronomers that is necessary for the continued discovery of extrasolar planets. μFUN played an important role in discovery and analysis of

1148-409: The early 17th century. Initially an observation device, developments over the next half century transformed it into an accurate measurement tool. The pendulum clock was patented by Christiaan Huygens in 1657 and gave an increase in accuracy of about 30 fold over previous mechanical clocks. These two inventions would revolutionise observational astronomy and cartography. On land, the period from

1189-408: The established method for commercial shipping until replaced by GPS in the early 1990s. The main conventional methods for determining longitude are listed below. With one exception (magnetic declination), they all depend on a common principle, which is to determine the time for an event or measurement and to compare it with the time at a different location. Longitude, being up to 180° east or west of

1230-523: The following extrasolar planets: There are various ways to get involved with μFUN. Since μFUN is a follow-up network, initial data and observations come from outside sources, primarily OGLE-III and MOA. However, many planetary successes come from amateur observers with small and medium-aperture telescopes. Because microlensing requires diligence and precision, μFUN has formulated data requirements that observers must meet. Data requirements and techniques for using small telescopes for microlensing can be found in

1271-446: The medium-aperture telescope level most likely would mean joining an observation group in a professional research lab. There are many observation sites around the globe, and they are primarily in the southern hemisphere. A full list of observation groups and their corresponding equipment can be found at μFUN's website . Probing Lensing Anomalies NETwork The Probing Lensing Anomalies NETwork ( PLANET ) collaboration coordinates

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1312-454: The radius of a circle of latitude. For a sphere of radius a that radius at latitude φ is a cos φ , and the length of a one-degree (or ⁠ π / 180 ⁠ radian ) arc along a circle of latitude is When the Earth is modelled by an ellipsoid this arc length becomes where e , the eccentricity of the ellipsoid, is related to the major and minor axes (the equatorial and polar radii respectively) by An alternative formula

1353-414: The same circle of latitude, measured along that circle of latitude, is slightly more than the shortest ( geodesic ) distance between those points (unless on the equator, where these are equal); the difference is less than 0.6 m (2 ft). A geographical mile is defined to be the length of one minute of arc along the equator (one equatorial minute of longitude) therefore a degree of longitude along

1394-428: The sea. See also the equation of time for details on the differences. With the exception of magnetic declination, all proved practicable methods. Developments on land and sea, however, were very different. Several newer methods for navigation, location finding, and the determination of longitude exist. Radio navigation , satellite navigation , and Inertial navigation systems , along with celestial navigation , are

1435-568: The second in Jamaica on 29 February 1504 (fourth voyage). It is assumed that he used astronomical tables for reference. His determinations of longitude showed large errors of 13° and 38° W respectively. Randles (1985) documents longitude measurement by the Portuguese and Spanish between 1514 and 1627 both in the Americas and Asia. Errors ranged from 2° to 25°. The telescope was invented in

1476-473: The seconds are specified with a decimal fraction . An alternative representation uses degrees and minutes, and parts of a minute are expressed in decimal notation, thus: 23° 27.5′ E. Degrees may also be expressed as a decimal fraction: 23.45833° E. For calculations, the angular measure may be converted to radians , so longitude may also be expressed in this manner as a signed fraction of π ( pi ), or an unsigned fraction of 2 π . For calculations,

1517-658: The use of ships were transmitted from Halifax, Nova Scotia , starting in 1907 and from the Eiffel Tower in Paris from 1910. These signals allowed navigators to check and adjust their chronometers frequently. Radio navigation systems came into general use after World War II . The systems all depended on transmissions from fixed navigational beacons. A ship-board receiver calculated the vessel's position from these transmissions. They allowed accurate navigation when poor visibility prevented astronomical observations, and became

1558-472: The west/east suffix is replaced by a negative sign in the western hemisphere . The international standard convention ( ISO 6709 )—that east is positive—is consistent with a right-handed Cartesian coordinate system , with the North Pole up. A specific longitude may then be combined with a specific latitude (positive in the northern hemisphere ) to give a precise position on the Earth's surface. Confusingly,

1599-622: Was soon in practical use for longitude determination, especially in North America, and over longer and longer distances as the telegraph network expanded, including western Europe with the completion of transatlantic cables. The United States Coast Survey, renamed the United States Coast and Geodetic Survey in 1878, was particularly active in this development, and not just in the United States. The Survey established chains of mapped locations through Central and South America, and

1640-569: Was supported and rewarded with thousands of pounds from the Board of Longitude, but he fought to receive money up to the top reward of £20,000, finally receiving an additional payment in 1773 after the intervention of parliament. It was some while before either method became widely used in navigation. In the early years, chronometers were very expensive, and the calculations required for lunar distances were still complex and time-consuming. Lunar distances came into general use after 1790. Chronometers had

1681-483: Was the need of a navigator for immediate results. The second was the marine environment. Making accurate observations in an ocean swell is much harder than on land, and pendulum clocks do not work well in these conditions. In response to the problems of navigation, a number of European maritime powers offered prizes for a method to determine longitude at sea. The best-known of these is the Longitude Act passed by

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