Photo:1
Photo:2
Photo:3
Photo:4
Photo:1 Photo:2 Photo:3 Photo:4 |
| Appearance and usage | |
| 2>
View of Earth's horizon as seen from Space Shuttle Endeavour, 2002
Historically, the distance to the visible horizon at sea has been extremely important as it represented the maximum range of communication and vision before the development of the radio and the telegraph. Even today, when flying an aircraft under Visual Flight Rules, a technique called attitude flying is used to control the aircraft, where the pilot uses the visual relationship between the aircraft's nose and the horizon to control the aircraft. A pilot can also retain his or her spatial orientation by referring to the horizon.
In many contexts, especially perspective drawing, the curvature of the Earth is disregarded and the horizon is considered the theoretical line to which points on any horizontal plane converge (when projected onto the picture plane) as their distance from the observer increases. For observers near sea level the difference between this geometrical horizon (which assumes a perfectly flat, infinite ground plane) and the true horizon (which assumes a spherical Earth surface) is imperceptible to the naked eye[dubious – discuss] (but for someone on a 1000-meter hill looking out to sea the true horizon will be about a degree below a horizontal line).
In astronomy the horizon is the horizontal plane through (the eyes of) the observer. It is the fundamental plane of the horizontal coordinate system, the locus of points that have an altitude of zero degrees. While similar in ways to the geometrical horizon, in this context a horizon may be considered to be a plane in space, rather than a line on a picture plane.
[edit] Tags:Earth,Communication,Radio,Telegraph,Visual Flight Rules,Perspective,Spherical Earth,Fundamental Plane, | |
| Distance to the horizon | |
| 2>
The approximate distance to the horizon from an observer close to the Earth's surface is given by[5]
where d is in kilometres and h is height above sea level in metres.
Examples:
For an observer standing on the ground with h = 1.70 metres (5 ft 7 in) (average eye-level height), the horizon is at a distance of 5.0 kilometres (3.1 mi).
For an observer standing on a hill or tower of 100 metres (330 ft) in height, the horizon is at a distance of 39 kilometres (24 mi).
For an observer standing at the top of the Burj Khalifa (828 metres (2,717 ft) in height), the horizon is at a distance of 111 kilometres (69 mi).
With d in miles[6] and h in feet,
Examples:
For an observer on the ground with eye level at h = 5 ft 7 in (5.583 ft), the horizon is at a distance of 3.1 miles (5.0 km).
For an observer standing on a hill or tower 100 feet (30 m) in height, the horizon is at a distance of 13.2 miles (21.2 km).
For an observer on the summit of Aconcagua (22,841 feet (6,962 m) in height), the sea-level horizon to the west is at a distance of 200 miles (320 km).
These formulas include the estimated effect of atmospheric refraction.
[edit] Tags:Atmospheric Refraction, | |
| Geometrical model | |
| 3>
Geometrical basis for calculating the distance to the horizon, secant tangent theorem
Geometrical distance to the horizon, Pythagorean theorem
Three types of horizon
If the Earth is assumed to be a perfect sphere with no atmosphere, then the theoretical formula for the distance of the horizon can easily be calculated using Euclidean geometry.
The secant tangent theorem states that
Make the following substitutions:
d = OC = distance to the horizon
D = AB = diameter of the Earth
h = OB = height of the observer above sea level
D+h = OA = diameter of the Earth plus height of the observer above sea level
The formula now becomes
or
where R is the radius of the Earth.
Alternatively, this equation can be derived using the Pythagorean theorem. Since the line of sight is a tangent to the Earth, it is perpendicular to the radius at the horizon. This sets up a right triangle, with the sum of the radius and the height as the hypotenuse. With
d = distance to the horizon
h = height of the observer above sea level
R = radius of the Earth
referring to the second figure at the right leads to the following:
Another relationship involves the distance s along the curved surface of the Earth to the horizon; with γ in radians,
then
Solving for s gives
The distance s can also be expressed in terms of the line-of-sight distance d; from the second figure at the right,
substituting for γ and rearranging gives
The distances d and s are nearly the same when the height of the object is negligible compared to the radius (that is, h ≪ R).
[edit] Tags: | |
| Approximate geometrical formulas | |
| 3>
If the observer is close to the surface of the earth, then it is valid to disregard h in the term (2R + h), and the formula becomes
Using metric units and taking the radius of the Earth as 6371 km, the distance to the horizon is
where d is in kilometres, and h is the height of the eye of the observer above ground or sea level in metres.
Using imperial units, the distance to the horizon is
where d is in miles and h is in feet.
These formulas may be used when h is much smaller than the radius of the Earth (6371 km), including all views from any mountaintops, aeroplanes, or high-altitude balloons. With the constants as given, both the metric and imperial formulas are precise to within 1% (see the next section for how to obtain greater precision).
[edit] Tags: | |
| Exact formula for a spherical Earth | |
| 3>
If h is significant with respect to R, as with most satellites, then the approximation made previously is no longer valid, and the exact formula is required:
where R is the radius of the Earth (R and h must be in the same units). For example, if a satellite is at a height of 2000 km, the distance to the horizon is 5,430 kilometres (3,370 mi); neglecting the second term in parentheses would give a distance of 5,048 kilometres (3,137 mi), a 7% error.
[edit] Tags: | |
| Objects above the horizon | |
| 3>
Geometrical horizon distance
To compute the height of an object visible above the horizon, compute the distance to the horizon for a hypothetical observer on top of that object, and add it to the real observer's distance to the horizon. For example, for an observer with a height of 1.70 m standing on the ground, the horizon is 4.65 km away. For a tower with a height of 100 m, the horizon distance is 35.7 km. Thus an observer on a beach can see the tower as long as it is not more than 40.35 km away. Conversely, if an observer on a boat (h = 1.7 m) can just see the tops of trees on a nearby shore (h = 10 m), the trees are probably about 16 km away.
Referring to the figure at the right, the lighthouse will be visible from the boat if
where DBL is in kilometres and hB and hL are in metres. If atmospheric refraction is considered, the visibility condition becomes
[edit] Tags: | |
| Effect of atmospheric refraction | |
| 3>
Because of atmospheric refraction of light rays, the actual distance to the horizon is slightly greater than the distance calculated with geometrical formulas. With standard atmospheric conditions, the difference is about 8%; however, refraction is strongly affected by temperature gradients, which can vary considerably from day to day, especially over water, so calculated values for refraction are only approximate.[5]
Rigorous method—Sweer
The distance d to the horizon is given by[7]
where RE is the radius of the Earth, ψ is the dip of the horizon and δ is the refraction of the horizon. The dip is determined fairly simply from
where h is the observer's height above the Earth, μ is the index of refraction of air at the observer's height, and μ0 is the index of refraction of air at Earth's surface.
The refraction must be found by integration of
where is the angle between the ray and a line through the center of the Earth. The angles ψ and are related by
Simple method—Young
A much simpler approach uses the geometrical model but uses a radius R′ = 7/6 RE. The distance to the horizon is then[5]
Taking the radius of the Earth as 6371 km, with d in km and h in m,
with d in mi and h in ft,
Results from Young's method are quite close to those from Sweer's method, and are sufficiently accurate for many purposes.
[edit] Tags: | |
| Curvature of the horizon | |
| 2>
From a point above the surface the horizon appears slightly bent (it is a circle, after all). There is a basic geometrical relationship between this visual curvature κ, the altitude and the Earth's radius. It is
The curvature is the reciprocal of the curvature angular radius in radians. A curvature of 1 appears as a circle of an angular radius of 45° corresponding to an altitude of approximately 2640 km above the Earth's surface. At an altitude of 10 km (33,000 ft, the typical cruising altitude of an airliner) the mathematical curvature of the horizon is about 0.056, the same curvature of the rim of circle with a radius of 10 m that is viewed from 56 cm. However, the apparent curvature is less than that due to refraction of light in the atmosphere and because the horizon is often masked by high cloud layers that reduce the altitude above the visual surface.
A man dives against the horizon into the Great South Bay of Long Island
[edit] Tags:Great South Bay,Long Island, | |
| Notes and References | |
| 2>
^ "offing", Webster's Third New International Dictionary, Unabridged.
^ "ὁρίζων", Henry George Liddell and Robert Scott, A Greek-English Lexicon. On Perseus Digital Library. Accessed 19 April 2011.
^ "ὁρίζω", Liddell and Scott, A Greek-English Lexicon.
^ "ὅρος", Liddell and Scott, A Greek-English Lexicon.
^ a b c Andrew T. Young, "Distance to the Horizon". Accessed 16 April 2011.
^ In this article, mile refers to a "land" mile of 5,280 feet (1,609.344 m).
^ John Sweer, "The Path of a Ray of Light Tangent to the Surface of the Earth", Journal of the Optical Society of America, 28 (September 1938):327–29. Available as paid download.
[edit] Tags:Greek,A Greek-english Lexicon,Perseus Digital Library, | |
| External links | |
| 2>
Derivation of the distance to the horizon. Steve Sque.
Dip of the Horizon. Andrew T. Young.
Retrieved from "http://en.wikipedia.org/w/index.php?title=Horizon&oldid=473837291"
Categories: Horizontal coordinate systemCelestial coordinate systemGreek loanwordsHidden categories: All accuracy disputesArticles with disputed statements from December 2011
Personal tools
Log in / create account
Namespaces
Article
Talk
Variants
Views
Read
Edit
View history
Actions
Search
Navigation
Main page
Contents
Featured content
Current events
Random article
Donate to Wikipedia
Interaction
Help
About Wikipedia
Community portal
Recent changes
Contact Wikipedia
Toolbox
What links here
Related changes
Upload file
Special pages
Permanent link
Cite this page
Print/export
Create a bookDownload as PDFPrintable version
Languages
العربية
Asturianu
Aymar aru
Беларуская
Беларуская (тарашкевіца)
Български
བོད་ཡིག
Brezhoneg
Català
Česky
Dansk
Deutsch
Eesti
Ελληνικά
Español
Esperanto
فارسی
Français
Gàidhlig
Galego
한국어
हिन्दी
Hrvatski
Ido
ইমার ঠার/বিষ্ণুপ্রিয়া মণিপুরী
Bahasa Indonesia
Íslenska
Italiano
עברית
ქართული
Қазақша
Latviešu
Lëtzebuergesch
Lietuvių
Magyar
मराठी
مصرى
Bahasa Melayu
Nederlands
日本語
Norsk (bokmål)
Polski
Português
Română
Runa Simi
Русский
Саха тыла
Scots
Shqip
Simple English
Slovenčina
Slovenščina
Српски / Srpski
Srpskohrvatski / Српскохрватски
Basa Sunda
Suomi
Svenska
ไทย
Türkçe
Українська
اردو
Winaray
中文
This page was last modified on 29 January 2012 at 11:14.
Text is available under the Creative Commons Attribution-ShareAlike License;
additional terms may apply.
See Terms of use for details.
Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.Contact us
Privacy policy
About Wikipedia
Disclaimers
Mobile view
if ( window.isMSIE55 ) fixalpha();
if ( window.mediaWiki ) {
mw.loader.load(["mediawiki.user", "mediawiki.util", "mediawiki.page.ready", "mediawiki.legacy.wikibits", "mediawiki.legacy.ajax", "mediawiki.legacy.mwsuggest", "ext.gadget.wmfFR2011Style", "ext.vector.collapsibleNav", "ext.vector.collapsibleTabs", "ext.vector.editWarning", "ext.vector.simpleSearch", "ext.UserBuckets", "ext.articleFeedback.startup", "ext.articleFeedbackv5.startup", "ext.markAsHelpful"]);
}
if ( window.mediaWiki ) {
mw.user.options.set({"ccmeonemails":0,"cols":80,"date":"default","diffonly":0,"disablemail":0,"disablesuggest":0,"editfont":"default","editondblclick":0,"editsection":1,"editsectiononrightclick":0,"enotifminoredits":0,"enotifrevealaddr":0,"enotifusertalkpages":1,"enotifwatchlistpages":0,"extendwatchlist":0,"externaldiff":0,"externaleditor":0,"fancysig":0,"forceeditsummary":0,"gender":"unknown","hideminor":0,"hidepatrolled":0,"highlightbroken":1,"imagesize":2,"justify":0,"math":1,"minordefault":0,"newpageshidepatrolled":0,"nocache":0,"noconvertlink":0,"norollbackdiff":0,"numberheadings":0,"previewonfirst":0,"previewontop":1,"quickbar":5,"rcdays":7,"rclimit":50,"rememberpassword":0,"rows":25,"searchlimit":20,"showhiddencats":false,"showjumplinks":1,"shownumberswatching":1,"showtoc":1,"showtoolbar":1,"skin":"vector","stubthreshold":0,"thumbsize":4,"underline":2,"uselivepreview":0,"usenewrc":0,"watchcreations":1,"watchdefault":0,"watchdeletion":0,"watchlistdays":3,"watchlisthideanons":0,
"watchlisthidebots":0,"watchlisthideliu":0,"watchlisthideminor":0,"watchlisthideown":0,"watchlisthidepatrolled":0,"watchmoves":0,"wllimit":250,"flaggedrevssimpleui":1,"flaggedrevsstable":0,"flaggedrevseditdiffs":true,"flaggedrevsviewdiffs":false,"vector-simplesearch":1,"useeditwarning":1,"vector-collapsiblenav":1,"usebetatoolbar":1,"usebetatoolbar-cgd":1,"wikilove-enabled":1,"variant":"en","language":"en","searchNs0":true,"searchNs1":false,"searchNs2":false,"searchNs3":false,"searchNs4":false,"searchNs5":false,"searchNs6":false,"searchNs7":false,"searchNs8":false,"searchNs9":false,"searchNs10":false,"searchNs11":false,"searchNs12":false,"searchNs13":false,"searchNs14":false,"searchNs15":false,"searchNs100":false,"searchNs101":false,"searchNs108":false,"searchNs109":false,"gadget-wmfFR2011Style":1});;mw.user.tokens.set({"editToken":"+\\","watchToken":false});;mw.loader.state({"user.options":"ready","user.tokens":"ready"});
/* cache key: enwiki:resourceloader:filter:minify-js:4:b41a86ec4e0fe8329bc3ce917e792339 */
}
Tags:Categories,Celestial Coordinate System,Greek Loanwords,All Accuracy Disputes,Articles With Disputed Statements From December 2011,Main Page,Contents,Featured Content,Current Events,Random Article,Donate To Wikipedia,Help,About Wikipedia,Community Portal,Recent Changes,Contact Wikipedia,Upload File,Special Pages,العربية,Aymar Aru,Беларуская,Беларуская (тарашкевіца),Български,བོད་ཡིག,Brezhoneg,Català,Dansk, | |
zote monety |