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44-664: The Pawnee Indian Museum State Historic Site , designated by the Smithsonian trinomial 14RP1, is an archaeological site and museum located near the city of Republic in the state of Kansas in the Midwestern United States . It is listed in the National Register of Historic Places under the name Pawnee Indian Village Site . At the site are the remains of a village once occupied by the Kitkehahki, or Republican, band of

88-529: A 1 MOA rifle should be capable, under ideal conditions, of repeatably shooting 1-inch groups at 100 yards. Most higher-end rifles are warrantied by their manufacturer to shoot under a given MOA threshold (typically 1 MOA or better) with specific ammunition and no error on the shooter's part. For example, Remington's M24 Sniper Weapon System is required to shoot 0.8 MOA or better, or be rejected from sale by quality control . Rifle manufacturers and gun magazines often refer to this capability as sub-MOA , meaning

132-495: A visual angle of one minute of arc, from a distance of twenty feet . A 20/20 letter subtends 5 minutes of arc total. The deviation from parallelism between two surfaces, for instance in optical engineering , is usually measured in arcminutes or arcseconds. In addition, arcseconds are sometimes used in rocking curve (ω-scan) x ray diffraction measurements of high-quality epitaxial thin films. Some measurement devices make use of arcminutes and arcseconds to measure angles when

176-4402: A block code (A-K) within each county, with sequential numbers for each block. Hawaii uses a four-part identifier, "50" for the state, a two-digit code for the island, then a two-digit code to designate the USGS topographical quad, plus a four digit sequential site number for sites on each island. NN: One or two digit number, 1 though 16, identifying rectangles (15 ' USGS maps) in a quadrangle map. AA: Alamance (AM)  · Alexander (AX)  · Alleghany (AL)  · Anson (AN)  · Ashe (AH)  · Avery (Av)  · Beaufort (BF)  · Bertie (BR)  · Bladen (BL)  · Brunswick (BW)  · Buncombe (BN)  · Burke (BK)  · Cabarrus (CA)  · Caldwell (CW)  · Camden (CM)  · Carteret (CR)  · Caswell (CS)  · Catawba (CT)  · Chatham (CH)  · Cherokee (CE)  · Chowan (CO)  · Clay (CY)  · Cleveland (CL)  · Columbus (CB)  · Craven (CV)  · Cumberland (CD)  · Currituck (CK)  · Dare (DR)  · Davidson (DV)  · Davie (DE)  · Duplin (DP)  · Durham (DH)  · Edgecombe (ED)  · Forsyth (FY)  · Franklin (FK)  · Gaston (GS)  · Gates (GA)  · Graham (GH)  · Granville (GV)  · Greene (GR)  · Guilford (GF)  · Halifax (HX)  · Harnett (HT)  · Haywood (HW)  · Henderson (HN)  · Hertford (HF)  · Hoke (HK)  · Hyde (HY)  · Iredell (ID)  · Jackson (JK)  · Johnston (JT)  · Jones (JN)  · Lee (LE)  · Lenoir (LR)  · Lincoln (LN)  · Macon (MA)  · Madison (MD)  · Martin (MT)  · McDowell (MC)  · Mecklenburg (MK)  · Mitchell (ML)  · Montgomery (MG)  · Moore (MR)  · Nash (NS)  · New Hanover (NH)  · Northampton (NP)  · Onslow (ON)  · Orange (OR)  · Pamlico (PM)  · Pasquotank (PK)  · Pender (PD)  · Perquimans (PQ)  · Person (PR)  · Pitt (PT)  · Polk (PL)  · Randolph (RD)  · Richmond (RH)  · Robeson (RB)  · Rockingham (RK)  · Rowan (RW)  · Rutherford (RF)  · Sampson (SP)  · Scotland (SC)  · Stanly (ST)  · Stokes (SK)  · Surry (SR)  · Swain (SW)  · Transylvania (TV)  · Tyrrell (TY)  · Union (UN)  · Vance (VN)  · Wake (WA)  · Warren (WR)  · Washington (WH)  · Watauga (WT)  · Wayne (WY)  · Wilkes (WK)  · Wilson (WL)  · Yadkin (YD)  · Yancey (YC) AA: Abbeville (AB) · Aiken (AK) · Allendale (AL) · Anderson (AN) · Bamberg (BA) · Barnwell (BR) · Beaufort (BU) · Berkeley (BK) · Calhoun (CL) · Charleston (CH) · Cherokee (CK) · Chester (CS) · Chesterfield (CT) · Clarendon (CR) · Colleton (CN) · Darlington (DA) · Dillon (DN) · Dorchester (DR) · Edgefield (ED) · Fairfield (FA) · Florence (FL) · Georgetown (GE) · Greenville (GV) · Greenwood (GN) · Hampton (HA) · Horry (HR) · Jasper (JA) · Kershaw (KE) · Lancaster (LA) · Laurens (LU) · Lee (LE) · Lexington (LX) · Marion (MA) · Marlboro (ML) · McCormick (MC) · Newberry (NB) · Oconee (OC) · Orangeburg (OR) · Pickens (PK) · Richland (RD) · Saluda (SA) · Spartanburg (SP) · Sumter (SU) · Union (UN) · Williamsburg (WG) · York (YK) Minute and second of arc#Cartography A minute of arc , arcminute ( arcmin ), arc minute , or minute arc , denoted by

220-687: A circle with a diameter of 1.047 inches (which is often rounded to just 1 inch) at 100 yards (2.66 cm at 91 m or 2.908 cm at 100 m), a traditional distance on American target ranges . The subtension is linear with the distance, for example, at 500 yards, 1 MOA subtends 5.235 inches, and at 1000 yards 1 MOA subtends 10.47 inches. Since many modern telescopic sights are adjustable in half ( ⁠ 1 / 2 ⁠ ), quarter ( ⁠ 1 / 4 ⁠ ) or eighth ( ⁠ 1 / 8 ⁠ ) MOA increments, also known as clicks , zeroing and adjustments are made by counting 2, 4 and 8 clicks per MOA respectively. For example, if

264-459: A degree) and specify locations within about 120 metres (390 feet). For navigational purposes positions are given in degrees and decimal minutes, for instance The Needles lighthouse is at 50º 39.734’N 001º 35.500’W. Related to cartography, property boundary surveying using the metes and bounds system and cadastral surveying relies on fractions of a degree to describe property lines' angles in reference to cardinal directions . A boundary "mete"

308-553: A degree/day in the Earth's annual rotation around the Sun, which is off by roughly 1%. The same ratios hold for seconds, due to the consistent factor of 60 on both sides. The arcsecond is also often used to describe small astronomical angles such as the angular diameters of planets (e.g. the angular diameter of Venus which varies between 10″ and 60″); the proper motion of stars; the separation of components of binary star systems ; and parallax ,

352-510: A double quote " (U+0022) is commonly used where only ASCII characters are permitted. One arcsecond is thus written as 1″. It is also abbreviated as arcsec or asec . In celestial navigation , seconds of arc are rarely used in calculations, the preference usually being for degrees, minutes, and decimals of a minute, for example, written as 42° 25.32′ or 42° 25.322′. This notation has been carried over into marine GPS and aviation GPS receivers, which normally display latitude and longitude in

396-422: A fraction of a mrad) are collectively called a mrad reticle. If the markings are round they are called mil-dots . In the table below conversions from mrad to metric values are exact (e.g. 0.1 mrad equals exactly 10 mm at 100 metres), while conversions of minutes of arc to both metric and imperial values are approximate. In humans, 20/20 vision is the ability to resolve a spatial pattern separated by

440-481: A group measuring 0.7 inches followed by a group that is 1.3 inches, this is not statistically abnormal. The metric system counterpart of the MOA is the milliradian (mrad or 'mil'), being equal to 1 ⁄ 1000 of the target range, laid out on a circle that has the observer as centre and the target range as radius. The number of milliradians on a full such circle therefore always is equal to 2 × π × 1000, regardless

484-400: A gun consistently shooting groups under 1 MOA. This means that a single group of 3 to 5 shots at 100 yards, or the average of several groups, will measure less than 1 MOA between the two furthest shots in the group, i.e. all shots fall within 1 MOA. If larger samples are taken (i.e., more shots per group) then group size typically increases, however this will ultimately average out. If a rifle

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528-455: A line running from the starting point 85.69 feet in a direction 65° 39′ 18″ (or 65.655°) away from north toward the west. The arcminute is commonly found in the firearms industry and literature, particularly concerning the precision of rifles , though the industry refers to it as minute of angle (MOA). It is especially popular as a unit of measurement with shooters familiar with the imperial measurement system because 1 MOA subtends

572-431: A modern second. Since antiquity, the arcminute and arcsecond have been used in astronomy : in the ecliptic coordinate system as latitude (β) and longitude (λ); in the horizon system as altitude (Alt) and azimuth (Az); and in the equatorial coordinate system as declination (δ). All are measured in degrees, arcminutes, and arcseconds. The principal exception is right ascension (RA) in equatorial coordinates, which

616-468: A precision-oriented firearm's performance will be measured in MOA. This simply means that under ideal conditions (i.e. no wind, high-grade ammo, clean barrel, and a stable mounting platform such as a vise or a benchrest used to eliminate shooter error), the gun is capable of producing a group of shots whose center points (center-to-center) fit into a circle, the average diameter of circles in several groups can be subtended by that amount of arc. For example,

660-407: A quadrangle, a sequential number within the rectangle, and a code identifying the agency issuing the sequential number. California uses a three-letter abbreviation for counties. Connecticut and Rhode Island do not use any sub-state codes, with site identifiers consisting of the state abbreviation and a sequential number series for the whole state. Delaware uses a single letter code for counties and adds

704-515: A radian. These units originated in Babylonian astronomy as sexagesimal (base 60) subdivisions of the degree; they are used in fields that involve very small angles, such as astronomy , optometry , ophthalmology , optics , navigation , land surveying , and marksmanship . To express even smaller angles, standard SI prefixes can be employed; the milliarcsecond (mas) and microarcsecond (μas), for instance, are commonly used in astronomy. For

748-537: A space or dash between parts of the identifier, i.e., "nn AA nnnn" or "nn-AA-nnnn". Some states use variations of the trinomial system. Arizona, California, Connecticut, Maine, Rhode Island, and Vermont use two-letter abbreviations of the state name instead of the Smithsonian number. Alaska uses three-letter abbreviations for USGS map quadrangles in place of the county code. Arizona uses a five-part identifier based on USGS maps, specifying quadrangles, then rectangles within

792-413: A three-dimensional area such as on a sphere, square arcminutes or seconds may be used. The prime symbol ′ ( U+ 2032 ) designates the arcminute, though a single quote ' (U+0027) is commonly used where only ASCII characters are permitted. One arcminute is thus written as 1′. It is also abbreviated as arcmin or amin . Similarly, double prime ″ (U+2033) designates the arcsecond, though

836-753: Is also the angle subtended by One milliarcsecond is about the size of a half dollar, seen from a distance equal to that between the Washington Monument and the Eiffel Tower . One microarcsecond is about the size of a period at the end of a sentence in the Apollo mission manuals left on the Moon as seen from Earth. One nanoarcsecond is about the size of a penny on Neptune 's moon Triton as observed from Earth. Also notable examples of size in arcseconds are: The concepts of degrees, minutes, and seconds—as they relate to

880-486: Is described with a beginning reference point, the cardinal direction North or South followed by an angle less than 90 degrees and a second cardinal direction, and a linear distance. The boundary runs the specified linear distance from the beginning point, the direction of the distance being determined by rotating the first cardinal direction the specified angle toward the second cardinal direction. For example, North 65° 39′ 18″ West 85.69 feet would describe

924-423: Is measured in time units of hours, minutes, and seconds. Contrary to what one might assume, minutes and seconds of arc do not directly relate to minutes and seconds of time, in either the rotational frame of the Earth around its own axis (day), or the Earth's rotational frame around the Sun (year). The Earth's rotational rate around its own axis is 15 minutes of arc per minute of time (360 degrees / 24 hours in day);

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968-527: Is operated by the Kansas Historical Society . In 1971, the site was added to the National Register of Historic Places. The 1901 monument at the site was damaged by a tornado in 2004. As a historically significant structure, it has been restored, but not to its original height and appearance. Smithsonian trinomial Most states use trinomials of the form "nnAAnnnn", but some specify

1012-496: Is roughly 30 metres (98 feet). The exact distance varies along meridian arcs or any other great circle arcs because the figure of the Earth is slightly oblate (bulges a third of a percent at the equator). Positions are traditionally given using degrees, minutes, and seconds of arcs for latitude , the arc north or south of the equator, and for longitude , the arc east or west of the Prime Meridian . Any position on or above

1056-621: Is that some MOA scopes, including some higher-end models, are calibrated such that an adjustment of 1 MOA on the scope knobs corresponds to exactly 1 inch of impact adjustment on a target at 100 yards, rather than the mathematically correct 1.047 inches. This is commonly known as the Shooter's MOA (SMOA) or Inches Per Hundred Yards (IPHY). While the difference between one true MOA and one SMOA is less than half of an inch even at 1000 yards, this error compounds significantly on longer range shots that may require adjustment upwards of 20–30 MOA to compensate for

1100-432: Is very near 21 600  nmi . A minute of arc is ⁠ π / 10 800 ⁠ of a radian . A second of arc , arcsecond (arcsec), or arc second , denoted by the symbol ″ , is ⁠ 1 / 60 ⁠ of an arcminute, ⁠ 1 / 3600 ⁠ of a degree, ⁠ 1 / 1 296 000 ⁠ of a turn, and ⁠ π / 648 000 ⁠ (about ⁠ 1 / 206 264 .8 ⁠ ) of

1144-701: The Pawnee tribe of Native Americans . It is one of four known Kitkehahki sites in the Republican River valley. The dates of occupation of this particular village are not known; the Kitkehahki intermittently occupied the Republican valley from the 1770s to the 1820s. After the 1803 Louisiana Purchase , Spain and the United States disputed possession of the Louisiana Territory . Both nations sought allies among

1188-451: The Earth's reference ellipsoid can be precisely given with this method. However, when it is inconvenient to use base -60 for minutes and seconds, positions are frequently expressed as decimal fractional degrees to an equal amount of precision. Degrees given to three decimal places ( ⁠ 1 / 1000 ⁠ of a degree) have about ⁠ 1 / 4 ⁠ the precision of degrees-minutes-seconds ( ⁠ 1 / 3600 ⁠ of

1232-596: The Earth's atmosphere but are diffraction limited . For example, the Hubble Space Telescope can reach an angular size of stars down to about 0.1″. Minutes (′) and seconds (″) of arc are also used in cartography and navigation . At sea level one minute of arc along the equator equals exactly one geographical mile (not to be confused with international mile or statute mile) along the Earth's equator or approximately one nautical mile (1,852 metres ; 1.151 miles ). A second of arc, one sixtieth of this amount,

1276-471: The Earth's rotational rate around the Sun (not entirely constant) is roughly 24 minutes of time per minute of arc (from 24 hours in day), which tracks the annual progression of the Zodiac. Both of these factor in what astronomical objects you can see from surface telescopes (time of year) and when you can best see them (time of day), but neither are in unit correspondence. For simplicity, the explanations given assume

1320-843: The Native American peoples of the territory, including the Pawnees. In 1806, Lieutenant Zebulon Pike led an expedition into the southwestern portions of the Territory. He visited a Pawnee village soon after the departure of a much larger Spanish expedition; there, he persuaded the inhabitants to haul down a Spanish flag and to replace it with that of the United States. In the 1870s, Elizabeth A. Johnson of Republic County became interested in Pike's flag episode. She discovered this site in 1875 and, after studying Pike's journals and investigating another reported Pawnee site in southern Nebraska , concluded that this

1364-451: The angle, measured in arcseconds, of the object's apparent movement caused by parallax. The European Space Agency 's astrometric satellite Gaia , launched in 2013, can approximate star positions to 7 microarcseconds (μas). Apart from the Sun, the star with the largest angular diameter from Earth is R Doradus , a red giant with a diameter of 0.05″. Because of the effects of atmospheric blurring , ground-based telescopes will smear

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1408-628: The bullet drop. If a shot requires an adjustment of 20 MOA or more, the difference between true MOA and SMOA will add up to 1 inch or more. In competitive target shooting, this might mean the difference between a hit and a miss. The physical group size equivalent to m minutes of arc can be calculated as follows: group size = tan( ⁠ m / 60 ⁠ ) × distance. In the example previously given, for 1 minute of arc, and substituting 3,600 inches for 100 yards, 3,600 tan( ⁠ 1 / 60 ⁠ ) ≈ 1.047 inches. In metric units 1 MOA at 100 metres ≈ 2.908 centimetres. Sometimes,

1452-405: The image of a star to an angular diameter of about 0.5″; in poor conditions this increases to 1.5″ or even more. The dwarf planet Pluto has proven difficult to resolve because its angular diameter is about 0.1″. Techniques exist for improving seeing on the ground. Adaptive optics , for example, can produce images around 0.05″ on a 10 m class telescope. Space telescopes are not affected by

1496-409: The latter format by default. The average apparent diameter of the full Moon is about 31 arcminutes, or 0.52°. One arcminute is the approximate distance two contours can be separated by, and still be distinguished by, a person with 20/20 vision . One arcsecond is the approximate angle subtended by a U.S. dime coin (18 mm) at a distance of 4 kilometres (about 2.5 mi). An arcsecond

1540-585: The measure of both angles and time—derive from Babylonian astronomy and time-keeping. Influenced by the Sumerians , the ancient Babylonians divided the Sun's perceived motion across the sky over the course of one full day into 360 degrees. Each degree was subdivided into 60 minutes and each minute into 60 seconds. Thus, one Babylonian degree was equal to four minutes in modern terminology, one Babylonian minute to four modern seconds, and one Babylonian second to ⁠ 1 / 15 ⁠ (approximately 0.067) of

1584-403: The point of impact is 3 inches high and 1.5 inches left of the point of aim at 100 yards (which for instance could be measured by using a spotting scope with a calibrated reticle, or a target delineated for such purposes), the scope needs to be adjusted 3 MOA down, and 1.5 MOA right. Such adjustments are trivial when the scope's adjustment dials have a MOA scale printed on them, and even figuring

1628-463: The preservation of this site, whereas the Nebraska site had been degraded by years of cultivation. Some archaeological investigation at the site was conducted in 1933, 1949, and 1957. Intensive investigation took place from 1965 to 1968. In 1967, a museum was constructed around one of the earth lodges prior to its excavation; the excavated lodge has been left open, with many artifacts in situ . The museum

1672-669: The recent American victory in the Spanish–American War . In 1906, a four-day celebration was held to mark the centennial of the Pike episode. Subsequent research showed that Pike's expedition had not visited this village, but the Kitkehahki village now known as the Pike-Pawnee Village Site , located on the Republican River in Webster County in south-central Nebraska. The error was a fortunate one, however: it led to

1716-470: The right number of clicks is relatively easy on scopes that click in fractions of MOA. This makes zeroing and adjustments much easier: Another common system of measurement in firearm scopes is the milliradian (mrad). Zeroing an mrad based scope is easy for users familiar with base ten systems. The most common adjustment value in mrad based scopes is ⁠ 1 / 10 ⁠  mrad (which approximates 1 ⁄ 3 MOA). One thing to be aware of

1760-411: The small change of position of a star or Solar System body as the Earth revolves about the Sun. These small angles may also be written in milliarcseconds (mas), or thousandths of an arcsecond. The unit of distance called the parsec , abbreviated from the par allax angle of one arc sec ond, was developed for such parallax measurements. The distance from the Sun to a celestial object is the reciprocal of

1804-409: The symbol ′ , is a unit of angular measurement equal to ⁠ 1 / 60 ⁠ of one degree . Since one degree is ⁠ 1 / 360 ⁠ of a turn, or complete rotation , one arcminute is ⁠ 1 / 21 600 ⁠ of a turn. The nautical mile (nmi) was originally defined as the arc length of a minute of latitude on a spherical Earth, so the actual Earth's circumference

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1848-419: The target range. Therefore, 1 MOA ≈ 0.2909 mrad. This means that an object which spans 1 mrad on the reticle is at a range that is in metres equal to the object's linear size in millimetres (e.g. an object of 100 mm subtending 1 mrad is 100 metres away). So there is no conversion factor required, contrary to the MOA system. A reticle with markings (hashes or dots) spaced with a one mrad apart (or

1892-513: Was the village that Pike had visited. To protect the site from being plowed, she and her husband bought the land. In 1901, the Johnsons donated the site to the state of Kansas for historic preservation. The state appropriated $ 3,000 to fence the land and build a 26-foot (7.9 m) granite monument commemorating the 1806 flag incident. At the 1901 dedication ceremony, several of the speakers drew parallels between Pike's symbolic triumph over Spain and

1936-446: Was truly a 1 MOA rifle, it would be just as likely that two consecutive shots land exactly on top of each other as that they land 1 MOA apart. For 5-shot groups, based on 95% confidence , a rifle that normally shoots 1 MOA can be expected to shoot groups between 0.58 MOA and 1.47 MOA, although the majority of these groups will be under 1 MOA. What this means in practice is if a rifle that shoots 1-inch groups on average at 100 yards shoots

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