File:Sundial solstice declination lines for different latitudes - slow.gif
Page contents not supported in other languages.
Appearance
Sundial_solstice_declination_lines_for_different_latitudes_-_slow.gif (400 × 400 pixels, file size: 553 KB, MIME type: image/gif, looped, 50 frames, 50 s)
This is a file from the Wikimedia Commons. Information from its description page there is shown below. Commons is a freely licensed media file repository. You can help. |
Summary
DescriptionSundial solstice declination lines for different latitudes - slow.gif |
English: Gnomon height is 1, its base point is denoted by g. The tip of the gnomon during a day casts a shadow along a declination line. Here the declination line at winter solstice is in blue, and the declination at summer solstice is in red, while the declination line at equinox is in magenta. North is up. Eccentricity of the declination line is denoted by e. Latitude of the point on the Earth where the gnomon is located is denoted by lat. The origin of corresponding horizontal sundial is denoted by h.Two small black dots are foci of declination lines.
To obtain the equation for declination lines I used the approach attributed to Apollonius of Perga: the double cone formed by lines from the tip of the gnomon to positions of the Sun at each day of the year, is cut by the plane of the ground. For hyperbolas I verified the equation using a formula from this book. Using this approach, for eccentricity we get a very simple formula: e=cos(latitude)/sin(Sun's declination).So, on the equator eccentricity of solstice lines is the highest, approx. 2.52. Русский: Высота гномона — 1, его основание обозначено g. Верхушка гномона в течение дня отбрасывает тень вдоль особой кривой, являющейся коническим сечением. Эта кривая для дня зимнего солнцестояния — синяя, для летнего — красная. Эксцентриситет их обозначен e. В день равноденствия это — линия, показанная фиолетовым. Широта точки на земной поверхности, где установлен гномон — lat. Начальная точка соответствующих горизонтальных солнечных часов — h. Две маленькие черные точки — фокусы конического сечения.
При выводе уравнения кривой использован подход, приписываемый Аполлонию Пергскому. В частности, в результате получается очень простая формула для эксцентриситета:e=cos(широта)/sin(склонение Солнца). Поэтому максимальный эксцентриситет кривых для солнцестояний — на экваторе, примерно равен 2,52. |
Date | |
Source | Own work |
Author | Cmapm |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
Captions
Add a one-line explanation of what this file represents
gnomon<\/a>"}},"text\/plain":{"en":{"P180":"gnomon"}}}}" class="wbmi-entityview-statementsGroup wbmi-entityview-statementsGroup-P180 oo-ui-layout oo-ui-panelLayout oo-ui-panelLayout-framed">
URL<\/a>"}},"text\/plain":{"en":{"":"URL"}}},"{\"value\":\"https:\\\/\\\/commons.wikimedia.org\\\/wiki\\\/user:Cmapm\",\"type\":\"string\"}":{"text\/html":{"en":{"P2699":"https:\/\/commons.wikimedia.org\/wiki\/user:Cmapm<\/a>"}},"text\/plain":{"en":{"P2699":"https:\/\/commons.wikimedia.org\/wiki\/user:Cmapm"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":4174,\"id\":\"P4174\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":"Wikimedia username<\/a>"}},"text\/plain":{"en":{"":"Wikimedia username"}}},"{\"value\":\"Cmapm\",\"type\":\"string\"}":{"text\/html":{"en":{"P4174":"Cmapm<\/a>","P2093":"Cmapm"}},"text\/plain":{"en":{"P4174":"Cmapm","P2093":"Cmapm"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":2093,\"id\":\"P2093\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":"author name string<\/a>"}},"text\/plain":{"en":{"":"author name string"}}}}" class="wbmi-entityview-statementsGroup wbmi-entityview-statementsGroup-P170 oo-ui-layout oo-ui-panelLayout oo-ui-panelLayout-framed">
copyrighted<\/a>"}},"text\/plain":{"en":{"P6216":"copyrighted"}}}}" class="wbmi-entityview-statementsGroup wbmi-entityview-statementsGroup-P6216 oo-ui-layout oo-ui-panelLayout oo-ui-panelLayout-framed">
Creative Commons Attribution-ShareAlike 3.0 Unported<\/a>"}},"text\/plain":{"en":{"P275":"Creative Commons Attribution-ShareAlike 3.0 Unported"}}}}" class="wbmi-entityview-statementsGroup wbmi-entityview-statementsGroup-P275 oo-ui-layout oo-ui-panelLayout oo-ui-panelLayout-framed">
3 October 2012
original creation by uploader<\/a>"}},"text\/plain":{"en":{"P7482":"original creation by uploader"}}}}" class="wbmi-entityview-statementsGroup wbmi-entityview-statementsGroup-P7482 oo-ui-layout oo-ui-panelLayout oo-ui-panelLayout-framed">
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 16:17, 3 October 2012 | 400 × 400 (553 KB) | Cmapm | User created page with UploadWizard |
File usage
The following pages on the English Wikipedia use this file (pages on other projects are not listed):
Global file usage
The following other wikis use this file:
- Usage on no.wikipedia.org