On December 31st (UTC 00:00:00), d = 364. Distances within our solar system are usually measured in Astronomical Units (AU). The graph below represents the variation in the solar declination angle with time. are also often used in the literature. Cafe Astrology is brimming with free articles, features, interpretations, and tools that will appeal to people with a casual interest in learning Astrology, as well as beginning through advanced students of Astrology. and get an answer to your love questions with this fun oracle based on cartomancy. Select a location from the City pulldown menu, OR select "Enter Lat/Long ->" from the pulldown menu, and manually enter the latitude, longitude and time zone information in the appropriate text boxes. For a listing of Declinations (non-graphical) see the Declinations Ephemeris page. 0000019707 00000 n
The result is the solar declination in degrees for that day of the year. For example, the number of days between January 1st and February 14th is 44. The day is 24 hours long south of the Antarctic Circle. It is believed that the early in its formation, the Earth was struck by another planet or large body, the remains of which may have became our moon. (Hint: Label your answer "degrees N" or "degrees S" - the symbol for degrees can be difficult to type) Expert Answer On October 26th the sun present in the southern hemisphere, so the declination of the sun should be in negative. %PDF-1.4
%
This principle is used to explain why we have different seasons, why there are four in some countries and there are only two in some. For a given UTC time, it is the same throughout the globe. 2. The equation also assumes that the suns orbit is a perfect circle and the factor of 360/365 converts the day number to a position in the orbit. As seen from locations in the Earth's Northern Hemisphere, celestial objects with declinations greater than 90 (where = observer's latitude) appear to circle daily around the celestial pole without dipping below the horizon, and are therefore called circumpolar stars. It reverts to zero declination when fall equinox comes and drops to the negative 23.5 declination during the winter solstice. When planets are transiting through the upper portions of the Hidek**, within a degree of transiting Out of Bounds, they will appear in red. The Astrology of 2023: This Year in Astrology. The various trajectories of the sun's in the sky are bounded by those of the 21st day (solstice) of each month from December 21 until June 21. What Is Declination? By using this site, you agree to the Terms of Use. 2003-2023 Chegg Inc. All rights reserved. The solar declination angle is a concept of astronomy, but its understanding is also helpful in solar energy and photovoltaic (PV) systems. Declination in astronomy is comparable to geographic latitude, projected onto the celestial sphere, and right ascension is likewise comparable to longitude. These "ups and downs" are measured as the distance between a planet's current position and the earth's equator (as projected into the sky). The Arctic and Antarctic circles today are 1.2 m (4 ft) closer to the poles, and the Tropic of Cancer and Tropic of Capricorn are equally closer to the equator . They are referred to the equinoxes instead so use sin instead of cos. Find the cosine of the result from Step 4. As we might think, the earths axis of rotation is not perpendicular to the direction of the orbit. Midwinter in AntarcticaThe June solstice is easily the biggest celebration in Antarctica, marking the day when the sun may begin to appear on the horizon after months of polar night. The few scientists who overwinter at the bases in Antarctica celebrate with feasts, shared presents and an icy polar plunge! Constellation: One of 88 recognized regions of the celestial sphere in which the object appears. All times are local time ( CDT) for 3226'59.7"N, 9353'03.4"W. Partial Eclipse begins The Moon touches the Sun's edge. You might also be interested in Out of Bounds planets (when planets exceed 23 degrees and 27 minutes of declination, either North or South). The positions of asteroids are calculated from orbital elements published by Ted Bowell of the Lowell Observatory. 50 - 23.5 = Noon Sun Angle Equation Noon Sun Angle = 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract! A positive value means the Sun is north of the Earths equator, and a negative value means the Sun is South of the equator. Below is a table of approximate solar declination values for every day of the year, calculated using the more accurate of the two solar declination calculation equations presented above. On these days, the earths axis of rotation becomes perpendicular to the rays of the sun. The Earth's axis rotates slowly westward about the poles of the ecliptic, completing one circuit in about 26,000 years. Magnetic declination changes over time and with location. The rotation of the Earth around the sun and the change in the declination angle is shown in the animation below. 0000019451 00000 n
Extraterrestrial SolsticesEvery planet in our solar system experiences solstices. Since ancient times, many cultures have marked the solstices with holidays and festivals. for noon on the 1st January, N = 0, for noon on 2nd January, N = 1etc. ), which is equivalent to 90 (declination). St. John's DayOne of the most prevalent solstice celebrations is St. Johns Day, marked in the Christian calendar on the June solstice. This effect, known as precession, causes the coordinates of stationary celestial objects to change continuously, if rather slowly. The polar night surrounds the winter solstice, when the sun remains below the horizon during the weeks leading up to and following the event. (An ellipsoid is an approximation to sea level that is mathematically manageable). In other words, the sun moves over our heads in summer. Write this number down. Exercise Questions 18 degrees N Q8 What is the solar declination on May 15? The points included in this transit list are: For a listing of Declinations (non-graphical) see the, Ceres, Juno, Vesta, & Pallas Signs: Tables. The Sun's declination varies with the seasons. Pagans and neopagans, followers of early European religious traditions, still celebrate the winter solstice as a holiday called Yule. Experts are tested by Chegg as specialists in their subject area. The derivation of the declination angle assumes a circular orbit and gives the following result: $$sin\ \delta=\sin{\left({-23.45}^0\right)}\cos{\left[\frac{360}{365}\left(d+10\right)\right]}$$. II. The value of the declination angle is 23.44, the lowest, on December 21st (or 22nd). Magnetic declination, sometimes called magnetic variation, is the angle between magnetic north and true north. !`V}nO(qQKR"PLD(D(#"Pl`!%X e":5E2`&DHD d[DyhiPhZ$4Je Although the tilt of the Earth's axis changes slowly over thousands of years, on smaller timescales it seems perfectly consistent, and the solar declination can be calculated based on what day of the year it is. 2023 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. The solar declination angle ( ) is the angle made by the sun rays with the equator of the earth. For instance, if the declination at a certain point were 10 W, then a compass at that location pointing north (magnetic) would actually align 10 W of true North. The chart above is based on the DE430 planetary ephemeris computed by the Jet Propulsion Laboratory (JPL). Declination's angle is measured north or south of the celestial equator, along the hour circle passing through the point in question. . The declination of the Sun is the measurement of the angle between the Sun's rays and the Earth's equatorial plane. Not all planets transit into the extreme declinations. This means that from time to time, affiliate commissions are earned after a reader purchases a product that we recommend. Declination: The angle of difference between true North and magnetic North. The rst type of method is to directly calculate the solar declination and equation of time with an empirical formula [5-10] and then calculate the sun position of the observation . The Sun reaches its highest altitude above the horizon each day every noon in the northern hemisphere. [1], The root of the word declination (Latin, declinatio) means "a bending away" or "a bending down". %%EOF
Planets travel in a 360-degree circle around the Sun, but they do not constantly stay at the same latitude. in a tintinnid. During an equinox, solar declination is 0the Equatorand both the Northern and Southern Hemisphere receive equal sunlight.) 2005 - 2023 Mike Brackenridge, sunposition.info - SP v1.7. So, whether you are in Los Angeles, Phoenix, Denver, or Boston, the solar declination will be the same for the same UTC time. Generally, if a star whose declination is is circumpolar for some observer (where is either positive or negative), then a star whose declination is never rises above the horizon, as seen by the same observer. National Geographic News: Summer Solstice Facts, National Geographic: Summer Solstice Radiaiton, NASA: Visible EarthSeeing Equinoxes and Solstices from Space. what is the solar declination on october 26th. The full calendar of months for 2023 Declination Graphs: From the excellent Day Watch software by Matrix. Saturnalia was celebrated the weeks leading up to the actual solstice. The angle of the collision and the size of the body (or bodies) which hit the Earth may have had a significant effect on its tilt and rotation speed (day length). She or he will best know the preferred format. The declination, in degrees, for any given day may be calculated in first approximation with the equation: Choose the best possible answer. RESEARCH METHODS . In some 18th and 19th century astronomical texts, declination is given as North Pole Distance (N.P.D. fremont high school yearbook 2020; dave willis pastor quotes; rochester gymnastics academy. hobby caravan spares or repair; cincinnati cyclones roster; daniella karagach and pasha pashkov wedding. Determine how many days have passed since January 1st. # = 23 2602100.448 000.46816 T +900.20cos(W)+000.57cos(2L0) (16) The latter two items are for nutation correction, which can also be ignored in further on the equatorial plane of the earth is called the declination angle. The points included in this transit list are: 2023 Astro Events On this page: Astrological events for 2023, including transits, eclipses, sign ingresses, and lunations (New Moon, Full 2023 Astrological Aspects Astrological transits for 2023, including transits of the Sun through Pluto (excluding the Moon) as well as 2022 Midpoint Transits Astrological transits for 2022 with hard aspects to midpoints. Average relative humidity is 75% in . As winter approaches, the declination angle goes negative, and the solar elevation decreases. 0000000918 00000 n
It is this inclination that causes the sun's seasonal change of height in the skyhigh in the summer and low in the winter for the northern hemisphere. The Earths axis is tilted by 23.5 degrees away from the solar plane. The declination of the Sun is the measurement of the angle between the Suns rays and the Earths equatorial plane. The Declination Graph is another way of looking at aspects. Solarsena.com is enrolled in the Amazon Affiliate program. As a result of Mars larger orbital eccentricity and axial tilt, the Red Planet experiences extreme seasonal variations and its solstices are about 11 months apart. Another transition period is when planets transit over the equator which is referred to as zero degrees "0." If the earth were not tilted, the declination angle would be zero. and its declination varies between +2326' and -2326'. There are 12 hours of daylight and 12 hours of darkness at all latitudes. The declination angle can be calculated by the equation 1: = - 23. The author shares his thoughts on solar technology on solarsena.com. Saturnalia was a wild carnival, as well as a time to mark the passing of the seasons. In the play, fairies enchant two couples in a magical forestand haphazardly get enchanted themselves. Take note of dates that this is occurring as there will tend to be an extra emotional intensity during those periods, as well. 0000000995 00000 n
It is usually denoted by . Solar declination angle is very useful in calculating the sun elevation and the azimuth angle. Sirius, the brightest star in the night sky, appeared soon after the summer solstice. Solar declination angle can be calculated using the following equation =23.45*Sin (360/365 (n-81)) Where n is the number of days from the beginning of the year. 16E/ouFw! The equation above gives much more accurate values for solar declination throughout the year as it takes into account the eccentricity of the Earths orbit around the Sun and the true length of a year (365.24 days). In the northern hemisphere, this day is called the summer solstice, while in the southern hemisphere is called the winter solstice. Multiply it by -23.44, the tilt of the Earth's axis in degrees. On Earth, solstices are twice-yearly phenomena in which solar declination reaches the Tropic of Cancer in the north and the Tropic of Capricorn in the south. When you reach out to him or her, you will need the page title, URL, and the date you accessed the resource. The declination of Mars. The sun's declination is defined by the fact that the earth's axis of rotation is not perpendicular to its orbit. It is what makes days and nights. 0000009444 00000 n
0000016509 00000 n
This is when they are neither above nor below the celestial equator (the middle line in the graph). 26.7 C in March, 29.8 C in April, 30 . We can calculate the solar declination angle using the following formula: In the above formula, d is the number of days since January 1st (UTC 00:00:00). A declination circle represents the continuous position during a 24-hour period. The following graph depicts the planetary declinations of the Sun through Pluto for the given month, with more months below. Credits. The summer solstice is the longest day of the year, meaning it experiences the maximum intensity of the suns rays and has the most hours of sunlight. These ups and downs are measured as the distance between a planets current position and the earths equator (as projected into the sky). Therefore the Sun appears approximately 47 degrees lower in the sky at noon on the winter solstice than it does at noon on the summer solstice. It will be different every single day. With the help of SolarSena, the author intends to promote solar power and wants to spread the use of clean technology. The minus sign "-" represents the Southern declinations. google_ad_client = "pub-6551255594736534"; Comet positions are computed from orbital elements published by the Minor Planet Center (MPC). (The only times of the year when the intensity of the suns rays is not unequal are the appropriately named equinoxes. Many festivities emphasize light, recognizing the winter solstice as the shortest, darkest day of the year. Finally, there are many algorithms for more accurate determinations of declination angle to account for the elliptic and yearly movement of the earth's orbit. From the poles, declination is uniform around the entire horizon, approximately 0. Mercury, Venus and Mars typically transit Out of Bounds once or twice a year. is declination angle. At the poles, a solstice is the peak of a radical exposure to daylight, while at the Equator, the solstices are barely marked at all. The declination is zero at the equinoxes (March 22 and September 22), positive during the northern hemisphere summer and negative during the northern hemisphere winter. 0000000016 00000 n
The solar elevation increases with the declination angle, and it is highest in months of summer. This calculation is relatively simple and is accurate to within tenths of a degree. @X(VeFgaBbA14t*hx. Other terms used for it are the sun declination angle or the declination angle of the sun. a c c r e t i o n [sed] ( a )The gradual or imperceptible increase or exten- a c c e s s o r y e l e m e n t trace element. Animation showing how the tilt angle changes from the summer solstice in the northern hemisphere (or winter in the southern hemisphere) to the northern hemisphere winter solstice (summer in the south). The following equation gives a more accurate value of the declination angle. also known as the winter solstice. Love Cards Ask a question Asia Pacific; EMEA; Latin America; UK Solicitors; UK Bar; United States Also, it revolves around our sun and has its own orbit. HM6Ds As we might think, the earth's axis of rotation is not perpendicular to the direction of the orbit. 3K Shares Oct 26 National Pumpkin Day Pumpkins are so much more than just a fun holiday accessory. The declination, in degrees, for any given day may be calculated in first approximation with the equation: The results given are accurate to within 0.2 degrees (and even greater accuracy can be obtained with a few modifications which are beyond this introductory article). L vs fork mount trade offs - posted in ATM, Optics and DIY Forum: Pluss and minuss? Note: Read your Analemma to the nearest 0.5 degree., Using the Analemma, determine the sun's declination on May 14. The declination angle is negative from September 22nd (Autumnal equinox) to March 20th (spring equinox). The sun angle and direction to the local horizon define the Sun's position in the local sky, which is the sky viewed from a given location on Earth. For instance an object marked as declination 5 would have an N.P.D. Monuments to midwinter holidays can be seen at Stonehenge, in Great Britain, and the so-called Intihuatana Stone (the so-called hitching post of the sun) at the Incan ruin of Machu Picchu in Peru. 0000009987 00000 n
0000012404 00000 n
As the compass points with local magnetic fields, declination value is needed to obtain true north.. more trailer
Declination - analogous to latitude - is one component of an object's position. During the spring and summer months, and part of autumn it corresponds to 1 PM Central Daylight Time. Las Vegas, Nevada (36N) on December 21 (23.5S solar declination) Zenith angle = 36 - (-23.5) Zenith angle = 36 + 23.5 Zenith angle = 59.5 SAA = 90 - 59.5 SAA = 30.5 Q13. Declinations with magnitudes greater than 90 do not occur, because the poles are the northernmost and southernmost points of the celestial sphere. Add ten to the number of days passed. Surgical operations are generally recommended during the Waning Moon, because human body is healing better after surgery. (_0 The solar declination angle reaches a maximum on June 20th (or 21st). A star's direction remains nearly fixed due to its vast distance, but its right ascension and declination do change gradually due to precession of the equinoxes and proper motion, and cyclically due to annual parallax. Declination angle can . Non-circumpolar stars are visible only during certain days or seasons of the year. Love Dice Oracle Ask a question or inquire about a wish. We only require the number of days (d) to know the angle. With respect to the celestial equator, it reaches the highest altitude of 73.5 degrees and this occurs on the first day of the summer while its altitude reaches the minimum 26.5 during the first day of the winter. The minimum value, 23 27', is reached on 20 December. These are only needed for concentrators that require more accurate tracking of the sun. It comes from the same root as the words incline ("bend foward") and recline ("bend backward").[2]. From the example, 54 times .9863 equals 53.2603. The declination angle becomes zero twice a year. The Earth rotates around the Sun like a spinning top. These organs are more sensitive when the Moon is . But the change is practically insignificant in a short period of time. [4], The currently used standard epoch is J2000.0, which is January 1, 2000 at 12:00 TT. Mid-latitudesEarths solstices are largely marked by the transition of the subsolar point across the tropics. To make things simple, we will assume you live in the US or a country from the northern hemisphere. The seasonal variation of the declination angle is shown in the animation below. Again with respect to the celestial equator, the northern hemisphere experiences the longest daylight during the summer solstice. And it is negative for the rest of the portion of the year. Menu Home; Rankings. If you have questions about how to cite anything on our website in your project or classroom presentation, please contact your teacher. These two days are called equinoxes. By definition, the solar hour angle is zero degrees at solar noon. The Sun will never appear beyond the maximum declination of 23 degrees 27 minutes. 0000012369 00000 n
It occurs at d= 172.5, which is around June 21st (summer solstice). 0000010848 00000 n
of 180. Deaths. Any units of angular measure can be used for declination, but it is customarily measured in the degrees (), minutes (), and seconds () of sexagesimal measure, with 90 equivalent to a quarter circle. Planetary Positions Calculations/Report. what is the solar declination on october 26th. Upon flat terrain, the distance has to be within approximately 2km, although this varies based upon the observer's altitude and surrounding terrain). October 1993 (NASA-TM-106321) SOLAR RADIATION N94-14730 ON MARS: STATIONARY PHOTOVOLTAIC ARRAY (NASA) 21 p 77i Unclas G3/33 0189389 . [21][22][23] [24] [25][26], and the azimuth angle is considered 0(facing South . Historical Events on October 26. Polar RegionsThe subsolar point never reaches Arctic and Antarctic regions. This is 4.2 days before the Moon reaches perigee. At the solstices, the angle between the rays of the Sun and the plane of the Earth's equator reaches its maximum value of 23 . 18 hours Universal Time corresponds to noon in the Central time zone of the United States when standard time is in effect. Whether you are at the poles or the equator, the angle of declination will not change for the same UTC time. When you see planets that are at the same degree and in the same up or down space, they are said to be parallel. The prefix "J" indicates that it is a Julian epoch. The suns vertical rays strike the Tropic of Cancer, 23.5 north of the Equator, during the June solstice. In the northern hemisphere, the declination angle for the winter solstice is 23.44, while in the southern hemisphere, it is 23.44. The value of is maximum (23.44) when the cosine is equal to the negative one. when the Sun crosses the equator on its northward passage, and has for the moment no declination , The entry of the Sun into the first point of Cancer, about . in the solar nebula came together to form larger bodies, eventually a c c e s s o r y c o m b The line of large cilia within t h e preoral cavity of planetary size. . [9], Last edited on 8 September 2022, at 04:15, MEASURING THE SKY A Quick Guide to the Celestial Sphere, Celestial Equatorial Coordinate Explorers, https://en.wikipedia.org/w/index.php?title=Declination&oldid=1109130974, celestial equator has a declination of 0, This page was last edited on 8 September 2022, at 04:15. Every year has 365 days except leap years. West East.2. During the Shalako, dancers representing the Zuni fire god and rain god, help the communities bid farewell to the old year and seek blessings in the new. During the December solstice (marked between December 20 and December 23), solar declination is about 23.5S (the Tropic of Capricorn). On June 21, the summer solstice for the Northern Hemisphere, the northern end of the axis of rotation is pointing most directly toward the Sun, and the declination is 23.5. //-->, * Exdek = Extreme declinations of latitudes beyond 23 degrees 27 minutes (2327'). Solar declination is defined as the angle between the Suns rays and the equatorial plane. At the north point, it is 90||, and at the south point, 90 + ||. When the northern hemisphere is tilted towards the Sun, summer season occurs while it becomes winter in the southern hemisphere. English Gematria, Hebrew Gematria and Jewish Gematria - Numerology I was in charge of the deployment of the Hydril and Vetco drilling business in the . During the summer solstice, when maximum declination of 23.5 is reached, a specific region north of the Arctic Circle receives sunlight 24 hours a day while the Antarctica receives 24 hours of darkness. The change in the Suns declination results in yearly cycles which are observed as each season progresses. At lower values of in radians, sin() . This equation treats the Earths orbit as being round rather than its true elliptical shape along with some other approximations which render it inaccurate by as much as 2 degrees (4 times the width of the Sun) at some times during the year. The Culture of the Solstices Solstices now mark the beginning of winter and summer, but because some ancient cultures only recognized these two seasons (there was no autumn or spring), the solstices occurred in the middle of the season. 2016 Solar Pump Controller with LCD Display and Datalogger, 2014 Solar Pump Controller with LCD Display, 2013 Solar Pump Controller with Fitted 10A Relay, Buy REUK Programmable Low Voltage Disconnect with Display and Datalogger, REUK Programmable Low Voltage Disconnect with OLED Display, REUK Programmable Low Voltage Disconnect with Display, Mini 12V Programmable Low Voltage Disconnect LVD, Buy User Programmable 12V Dump Load Controller, Mini 24V Programmable Low Voltage Disconnect LVD, REUK Programmable Low Voltage Disconnect LVD, Mini 12 Volt Regulator with Fuse and Switch Terminals, 12 Volt Regulator with Fuse and Switch Terminals, 12 Volt Regulator with Low Voltage Disconnect, Converted Programmable Digital Timer Relay, REUK Super LDR Dawn Dusk Relay Controller, REUK Mini LDR Dusk Dawn Lighting Controller. The author is an engineer, a solar energy enthusiast, and a strong supporter of renewable energy. All rights reserved. Since the Earth is tilted on its axis and rotates every year, the angle of declination changes throughout the year. .N8kwyfiMKaeqmpSTt-_j*2*".":*" A better formuation is mentioned in the following section. For instance, if your energy demands increase during winter due to increased electrical heating, adjust the tilt of the panels +15. New! Yes, the solar declination angle does change daily. Noon Sun Angle Equation Noon Sun Angle = 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract! On Earth, solstices are twice-yearly phenomena in which solar declination reaches the Tropic of Cancer in the north and the Tropic of Capricorn in the south. Automated page speed optimizations for fast site performance, Arizona Solar Incentives: A Brief Introduction, The Pros and Cons of Solar Panels on a Metal Roof, Optimal Solar Panel Tilt Angle Calculator, Solar Elevation Angle Calculating Altitude of Sun. The monthly averaged daily solar extra-terrestrial radiation Distance: The physical distance from Earth to the astronomical object. These aspects are similar to the conjunction and the opposition aspect. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Every year the solar declination goes from -23.44 degrees to +23.44 degrees in line with the Earth's seasons. Venus at superior solar conjunction: 28 Oct 2021 - Venus at dichotomy: 29 Oct 2021 - Venus at greatest elongation east: . In Alpine and Germanic regions, summer solstice bonfires are so ingrained in the cultures they have their own name: Sonnwendfeuer. In Concord, NH in Winter you would do 43.208 + 15 = 58.208. The site is run by astrologer Annie Heese. One of the most famous expressions of this romantic sentiment is the comic play A Midsummer Nights Dream, by the English writer William Shakespeare. Likewise, near the local winter solstice, the Sun remains below the horizon all day, which is called polar night. In astronomy, declination (abbreviated dec; symbol ) is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. (This neglects the effect of atmospheric refraction.) The timing and extent of solstices are largely determined by the planets axial tilt, orbital eccentricity, and distance from the sun. The angle of tilt is +2326', which is called the obliquity of the ecliptic (symbol ). The June solstice is the summer solstice in the Northern Hemisphere and the winter solstice in the Southern Hemisphere. These have not yet . Earth rotates around its own axis. $J''H'B)R/~TXo$*_~3,[ZO. From the example, the cosine of 53.2603 is 0.5982; multiply it by -23.44 to get -14.02 degrees. If you have any questions, please feel free to contact me at info@solarsena.com. 0000019202 00000 n
You only need the date and time. For instance the SPA algorithm 2(http://www.psa.es/sdg/sunpos.htm) uses: dOmega=2.1429-0.0010394594*dElapsedJulianDays; dMeanLongitude = 4.8950630+ 0.017202791698*dElapsedJulianDays; // Radians dMeanAnomaly = 6.2400600+ 0.0172019699*dElapsedJulianDays; dEclipticLongitude = dMeanLongitude + 0.03341607*sin( dMeanAnomaly ) + 0.00034894*sin( 2*dMeanAnomaly )-0.0001134 -0.0000203*sin(dOmega); dEclipticObliquity = 0.4090928 - 6.2140e-9*dElapsedJulianDays +0.0000396*cos(dOmega); dSin_EclipticLongitude= sin( dEclipticLongitude ); dY = cos( dEclipticObliquity ) * dSin_EclipticLongitude; dRightAscension = atan2( dY,dX ); if( dRightAscension < 0.0 ) dRightAscension = dRightAscension + twopi; dDeclination = asin( sin( dEclipticObliquity )*dSin_EclipticLongitude ); dElapsedJulian days is the number of days since January 1, 2000 and dDeclination is the resulting declination.