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Minute and second of arc
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===Astronomy=== [[File:Comparison angular diameter solar system.svg|thumb|upright=1.5|Comparison of angular diameter of the Sun, Moon, planets and the International Space Station. True represent­ation of the sizes is achieved when the image is viewed at a distance of 103 times the width of the "Moon: max." circle. For example, if the "Moon: max." circle is 10 cm wide on a computer display, viewing it from {{convert|10.3|m|yd|abbr=in}} away will show true representation of the sizes.]] Since antiquity, the arcminute and arcsecond have been used in [[astronomy]]: in the [[ecliptic coordinate system]] as latitude (β) and longitude (λ); in the [[horizontal coordinate system|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 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); 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 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 system]]s; and [[parallax]], 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 [[Multiplicative inverse|reciprocal]] of the angle, measured in arcseconds, of the object's apparent movement caused by parallax. The [[European Space Agency]]'s [[astrometry|astrometric]] satellite [[Gaia mission|Gaia]], launched in 2013, can approximate star positions to 7 microarcseconds (μas).<ref>{{cite news |url = https://www.bbc.com/news/science-environment-37355154 |title=Celestial mapper plots a billion stars|last=Amos|first=Jonathan|date=2016-09-14|work=BBC News|access-date=2018-03-31|language=en-GB }}</ref> 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 [[astronomical seeing|blurring]], ground-based [[telescope]]s will smear 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″.<ref>{{Cite web |title=Pluto Fact Sheet |url=https://nssdc.gsfc.nasa.gov/planetary/factsheet/plutofact.html |access-date=2022-08-29 |website=nssdc.gsfc.nasa.gov}}</ref> 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 the Earth's atmosphere but are [[Diffraction limit#Diffraction limit of telescopes|diffraction limited]]. For example, the [[Hubble Space Telescope]] can reach an angular size of stars down to about 0.1″.
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