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=== Ecliptic coordinates === |
=== Ecliptic coordinates === |
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These equations, from the ''[[Astronomical Almanac]]'',<ref> |
These equations, from the ''[[Astronomical Almanac]]'',<ref> |
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{{cite book |
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{{cite book |author=U.S. Naval Observatory |url=https://archive.org/details/astronomicalalma0000unse_n8r6 |title=The Astronomical Almanac for the Year 2010 |author2=U.K. Hydrographic Office, H.M. Nautical Almanac Office |date=2008 |publisher=U.S. Govt. Printing Office |isbn=978-0-7077-4082-9 |page=C5}}</ref><ref> |
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| author = U.S. Naval Observatory |
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| author2 = U.K. Hydrographic Office, H.M. Nautical Almanac Office |
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| title = The Astronomical Almanac for the Year 2010 |
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| publisher = U.S. Govt. Printing Office |
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| date = 2008 |
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| isbn = 978-0-7077-4082-9 |
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|page=C5}}</ref><ref> |
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Much the same set of equations, covering the years 1800 to 2200, can be found at [http://aa.usno.navy.mil/faq/docs/SunApprox.php Approximate Solar Coordinates], at the [http://www.usno.navy.mil/USNO U.S. Naval Observatory website] {{webarchive|url=https://web.archive.org/web/20160131231447/http://www.usno.navy.mil/USNO |date=2016-01-31 }}. Graphs of the error of these equations, compared to an accurate [[ephemeris]], can also be viewed.</ref> |
Much the same set of equations, covering the years 1800 to 2200, can be found at [http://aa.usno.navy.mil/faq/docs/SunApprox.php Approximate Solar Coordinates], at the [http://www.usno.navy.mil/USNO U.S. Naval Observatory website] {{webarchive|url=https://web.archive.org/web/20160131231447/http://www.usno.navy.mil/USNO |date=2016-01-31 }}. Graphs of the error of these equations, compared to an accurate [[ephemeris]], can also be viewed.</ref> |
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can be used to calculate the apparent coordinates of the [[Sun]], [[Epoch (astronomy)|mean equinox and ecliptic of date]], to a precision of about 0°.01 (36″), for dates between 1950 and 2050. Similar equations are coded into a [[Fortran]] 90 routine in Ref.<ref name="Zhangetal">Zhang, T., Stackhouse, P.W., Macpherson, B., and Mikovitz, J.C., 2021. A solar azimuth formula that renders circumstantial treatment unnecessary without compromising mathematical rigor: Mathematical setup, application and extension of a formula based on the subsolar point and atan2 function. ''Renewable Energy'', 172, 1333-1340. DOI: https://doi.org/10.1016/j.renene.2021.03.047</ref> and are used to calculate the [[solar zenith angle]] and [[solar azimuth angle]] as observed from the surface of the Earth. |
can be used to calculate the apparent coordinates of the [[Sun]], [[Epoch (astronomy)|mean equinox and ecliptic of date]], to a precision of about 0°.01 (36″), for dates between 1950 and 2050. Similar equations are coded into a [[Fortran]] 90 routine in Ref.<ref name="Zhangetal">Zhang, T., Stackhouse, P.W., Macpherson, B., and Mikovitz, J.C., 2021. A solar azimuth formula that renders circumstantial treatment unnecessary without compromising mathematical rigor: Mathematical setup, application and extension of a formula based on the subsolar point and atan2 function. ''Renewable Energy'', 172, 1333-1340. DOI: https://doi.org/10.1016/j.renene.2021.03.047</ref> and are used to calculate the [[solar zenith angle]] and [[solar azimuth angle]] as observed from the surface of the Earth. |
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:<math> Z = R \sin \epsilon \sin \lambda </math> |
:<math> Z = R \sin \epsilon \sin \lambda </math> |
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:Where <math>X</math> axis is in the direction of the [[Equinox#Celestial coordinate systems|March equinox]], the <math>Y</math> axis towards [[June solstice|June Solstice]], and the <math>Z</math> axis towards the [[Celestial pole|North celestial pole]].<ref> |
:Where <math>X</math> axis is in the direction of the [[Equinox#Celestial coordinate systems|March equinox]], the <math>Y</math> axis towards [[June solstice|June Solstice]], and the <math>Z</math> axis towards the [[Celestial pole|North celestial pole]].<ref> |
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{{cite book |
{{cite book|author=U.S. Naval Observatory Nautical Almanac Office|title=Explanatory Supplement to the Astronomical Almanac|date=1992|publisher=University Science Books, Mill Valley, CA|isbn=0-935702-68-7|editor=P. Kenneth Seidelmann|page=12}}</ref> |
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=== Horizontal coordinates === |
=== Horizontal coordinates === |
Copy and paste: – — ° ′ ″ ≈ ≠ ≤ ≥ ± − × ÷ ← → · § Cite your sources: <ref></ref>
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Latin: A a Á á À à  â Ä ä Ǎ ǎ Ă ă Ā ā à ã Å å Ą ą Æ æ Ǣ ǣ B b C c Ć ć Ċ ċ Ĉ ĉ Č č Ç ç D d Ď ď Đ đ Ḍ ḍ Ð ð E e É é È è Ė ė Ê ê Ë ë Ě ě Ĕ ĕ Ē ē Ẽ ẽ Ę ę Ẹ ẹ Ɛ ɛ Ǝ ǝ Ə ə F f G g Ġ ġ Ĝ ĝ Ğ ğ Ģ ģ H h Ĥ ĥ Ħ ħ Ḥ ḥ I i İ ı Í í Ì ì Î î Ï ï Ǐ ǐ Ĭ ĭ Ī ī Ĩ ĩ Į į Ị ị J j Ĵ ĵ K k Ķ ķ L l Ĺ ĺ Ŀ ŀ Ľ ľ Ļ ļ Ł ł Ḷ ḷ Ḹ ḹ M m Ṃ ṃ N n Ń ń Ň ň Ñ ñ Ņ ņ Ṇ ṇ Ŋ ŋ O o Ó ó Ò ò Ô ô Ö ö Ǒ ǒ Ŏ ŏ Ō ō Õ õ Ǫ ǫ Ọ ọ Ő ő Ø ø Œ œ Ɔ ɔ P p Q q R r Ŕ ŕ Ř ř Ŗ ŗ Ṛ ṛ Ṝ ṝ S s Ś ś Ŝ ŝ Š š Ş ş Ș ș Ṣ ṣ ß T t Ť ť Ţ ţ Ț ț Ṭ ṭ Þ þ U u Ú ú Ù ù Û û Ü ü Ǔ ǔ Ŭ ŭ Ū ū Ũ ũ Ů ů Ų ų Ụ ụ Ű ű Ǘ ǘ Ǜ ǜ Ǚ ǚ Ǖ ǖ V v W w Ŵ ŵ X x Y y Ý ý Ŷ ŷ Ÿ ÿ Ỹ ỹ Ȳ ȳ Z z Ź ź Ż ż Ž ž ß Ð ð Þ þ Ŋ ŋ Ə ə
Greek: Ά ά Έ έ Ή ή Ί ί Ό ό Ύ ύ Ώ ώ Α α Β β Γ γ Δ δ Ε ε Ζ ζ Η η Θ θ Ι ι Κ κ Λ λ Μ μ Ν ν Ξ ξ Ο ο Π π Ρ ρ Σ σ ς Τ τ Υ υ Φ φ Χ χ Ψ ψ Ω ω {{Polytonic|}}
Cyrillic: А а Б б В в Г г Ґ ґ Ѓ ѓ Д д Ђ ђ Е е Ё ё Є є Ж ж З з Ѕ ѕ И и І і Ї ї Й й Ј ј К к Ќ ќ Л л Љ љ М м Н н Њ њ О о П п Р р С с Т т Ћ ћ У у Ў ў Ф ф Х х Ц ц Ч ч Џ џ Ш ш Щ щ Ъ ъ Ы ы Ь ь Э э Ю ю Я я ́
IPA: t̪ d̪ ʈ ɖ ɟ ɡ ɢ ʡ ʔ ɸ β θ ð ʃ ʒ ɕ ʑ ʂ ʐ ç ʝ ɣ χ ʁ ħ ʕ ʜ ʢ ɦ ɱ ɳ ɲ ŋ ɴ ʋ ɹ ɻ ɰ ʙ ⱱ ʀ ɾ ɽ ɫ ɬ ɮ ɺ ɭ ʎ ʟ ɥ ʍ ɧ ʼ ɓ ɗ ʄ ɠ ʛ ʘ ǀ ǃ ǂ ǁ ɨ ʉ ɯ ɪ ʏ ʊ ø ɘ ɵ ɤ ə ɚ ɛ œ ɜ ɝ ɞ ʌ ɔ æ ɐ ɶ ɑ ɒ ʰ ʱ ʷ ʲ ˠ ˤ ⁿ ˡ ˈ ˌ ː ˑ ̪ {{IPA|}}
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