Lakshmi,

do you really expect that anybody will be willing to do this extended work for you? My advice would be: Go into your library, get hold of the book 'Astronomy on the Personal Computer' by Montenbruck & Pfleger, Springer (e.g. fourth edition 2000) and learn from it how naive your question is.

Thanks Björn and Ulrich for your advice.

if you install R software (free), installing solaR library (http://cran.r-project.org/web/packages/solaR/index.html) described in http://www.jstatsoft.org/v50/i09/ paper you will be able to obtain the information you ask. Regarding the equations in any book of solar energy you will get detailed information.

There are many calculation methods, with varying accuracy--which may depend on the time frame (past, present, or years in the future). Ephemeris or Almanacs use the most possible accurate calculations. Next in line is NREL's PSA, as commented above. An interactive and GUI online version is at http://www.esrl.noaa.gov/gmd/grad/solcalc/

Then, there have been many papers published on this topic of solar position in Solar Energy, with slightly lower accuracy than SPA. The latest one is http://www.sciencedirect.com/science/article/pii/S0038092X12002800

Another way is to use SLALIB tools. It's a collection of positional astronomy libraries (written in Fortran, but you can include them in your C/C++ code of course) which inlcude many functions to calculate the position of planets, Moon and Sun at a given time (expressed in JDAY, but there are other libs to convert from/to UTC too) with respect to a given position on Earth (latitude, longitude and also height above sea-level for some fo them) or other frames of reference. You should alsto take a look at Jean Meuss - Astronomical Algorithms (Willmann-Bell). For example the one I used gives errors for Sun position of about 5 arcsec (and on its diameter of 0.01%).

Thank you Fernando, Chris and Dario for you suggestions and references.

The algorithm with the highest accuracy should be the Solar Position Algorithm (SPA) by the National Renewable Energy Laboratory (NREL) of the US.

A paper describing the algorithm is available from

http://rredc.nrel.gov/solar/codesandalgorithms/spa/

The code (written in C) is available from the same website after a registration.

(The paper is also available on researchgate:

https://www.researchgate.net/publication/222533716_Solar_position_algorithm_for_solar_radiation_applications?)

There are free versions in other programming languages avalibale too:

Python: http://pysolar.org/

Matlab: http://pvpmc.org/pv-lib/

An online calculator is avaible here:

https://www.nrel.gov/midc/solpos/spa.html

(comment: My previous answer occured twice, so I deleted one of them but after that both were deleted. so I rewrote the answer -> Conclusion: don't trust the QA software on RG)

Article Solar position algorithm for solar radiation application

Another recomendation on Python: PyEphem (Do you remember Xephem?)

http://rhodesmill.org/pyephem/

It's very useful if you need do astronomical calculus.

Hi Lakshmi, The reference to which astronomers would turn is the Astronomical Almanac published jointly by the US Naval Office and Her Majesty's Nautical Almanac Office. Sections C includes the equations used to determine the astronomical circumstances of the Sun. If you need even more details there is an Explanatory Supplement. It is step-by-step and requires knowledge of spherical trigonometry. To use these references it could help to have some understanding of solar system dynamics as as well. An on-line version is available at http://asa.usno.navy.mil/ but the details of solar calculations appear only in the printed versions.

Hi Lakhshmi, alot of good books are available to give detialed answer to your query. Also you can find valuable information on;

http://rredc.nrel.gov/solar/codesandalgorithms/spa/

http://www.esrl.noaa.gov/gmd/grad/solcalc/

https://www.nrel.gov/midc/solpos/spa.html

I believe NOAA can give you exact Sun rise, and Sun Set times for each day

of the Year if you know your exact position ( city ).

The Solpos algorithm on the nrel website at http://rredc.nrel.gov/solar/codesandalgorithms/solpos/ has good documentation. You can find a more detailed explanation in "Solar and Infrared Radiation Measurements".

This topic is covered is also covered in a variety of astronomical text books.

the web site http://www.solar-noon.com/ gives some discussion of solar dynamics and a calculator to provide solar noon times at any specified lat/long for any day of the year; the Equation of Time is discussed in a companion web site, again in fairly simple terms. The web sites and reference materials cited by others above probably provide the most accurate info, but these sites are easy to use.

A0=229.18

a1=0.000075

a2=0.001868

a3=-0.032077

a4=-0.014615

a5=-0.040849

a6=0.006918

a7=-0.399912

a8=0.070257

a9=-0.006758

a10=0.000907

a11=-0.002697

a12=0.00148

b0=90.833

pi=3.1415926

;do the calculation: ltime=local time

ga=2*pi*(jday-1+(ltime-12.)/24.)/365.

Eqtime=a0*(a1+a2*cos(ga)+a3*sin(ga)+a4*cos(2*ga)+a5*sin(2*ga))

decl=a6+a7*cos(ga)+a8*sin(ga)+a9*cos(2*ga)+a10*sin(2*ga)+a11*cos(3*ga)+a12*sin(3*ga)

time_offset=eqtime-4*lon+60.*timezone

tst=ltime*60.+time_offset

ha=(tst/4.)-180. ;degree

csza=sin(lat*pi/180.)*sin(decl)+ $

cos(lat*pi/180.)*cos(decl)*cos(ha*pi/180.)

zenith=acos(csza)*180./pi

ha1=acos(cos(b0*pi/180.)/(cos(lat*pi/180.)*cos(decl))-tan(lat*pi/180.)*tan(decl))*180./pi ;radian

sunrise=(720+4*(lon-ha1)-eqtime)/60.-timezone ;localtime

sunset =(720+4*(lon+ha1)-eqtime)/60.-timezone ;localtime

snoon =(720+4*lon-eqtime)/60.-timezone ;local noon

;if you want to eliminate low solar zenith, do the following

;if zenith gt 82 and zenith le 87.5 then zenith=-1

;if ltime ge sunrise and ltime le sunset and zenith le 82 then zenith=zenith else zenith=0

Dear Mr. Xiquan Dong, are the values of Ao, a1-a12, and bo constant for every location thoughout the world? and can you please suggest some literature using these type of calculations as an example so that I can better understand the solar energy calculations.

I will be thankful for you cooperation.

Best regards,

Dear Prof. Dong,

Thanks for the elaborate steps. May I have the reference to these formulae and constants?

With regards,

Madhavan

The formula of Dr. Dong cannot be precise because it ignores the effect of leap years and thus the exact (fractional) number of days in a year. It's only an approximation compared to the more complex methods discussed earlier.

Dear Lakshmi

you already have many responses, but if you require open source algorithms for sun tracking with matlab simulink or PLC or microprocessors then you can also check Chapter 3 of our free eBook for links to the code: 

 https://www.researchgate.net/publication/263085113_Solar_Tracking_High_precision_solar_position_algorithms_programs_software_and_source-code_for_computing_the_solar_vector_solar_coordinates__sun_angles_in_Microprocessor_PLC_Arduino_PIC_and_PC-based_sun_tracking_devices_or_dynamic_sun_following_hardware

regards

Gerro

Book Solar Tracking: High precision solar position algorithms, pr...

If you still need an answer, please check

"insol" package in r 

and

pvlib-python in python 

http://pvlib-python.readthedocs.io/en/latest/

https://cran.r-project.org/web/packages/insol/insol.pdf

Based on the nature of the application where the calculations are used, authors take some liberty in the calculations. For example, one of the application areas of calculating this Sun Heliodon is in Architectural rendering, where internal lighting calculations are done based on the sun position. 

This paper covers the basic algorithm for 3D model lighting evaluation with opensource: https://www.mssanz.org.au/modsim2011/H5/mcminn.pdf 

Other architectural work, such as Cenacle Research's ZNE building energy calculations  are done with calculations similar to that of MIT Research note 47 to arrive at the Heliodon 

Ref: http://cenacleresearch.com/demos/smart-building-energy-analysis ,

Ref: http://web.mit.edu/parmstr/Public/NRCan/brn47.pdf

http://cenacleresearch.com/demos/smart-building-energy-analysis

The algorithm that calculates the position of the sun with more precision is called Solar Position Algorithm (SPA), which is explained in the article "Solar position algorithm for solar radiation applications".

You can also read Roberto Grena's article "Five new algorithms for the computation of sun position from 2010 to 2110".

The book "Astronomical Algorithms" by Jean Meeus explains some of the coefficients and correction factors.

To compute the Sun's position (azimut and elevation I suppose) over a location on the Earth (longitude, latitude, altitude) at a certain moment in time (you need here JD=Julian Date) you must in fact compute the position of the Earth on its orbit around the Sun (Earth revolution) AND the position of the observer on the Earth relative to the Sun (Earth rotation).

The subject is retreivable as "astronomical coordinates" from astronomy or astronomy related books or documentation under the keywords "ephemeris (Sun)" or "almanac (nautical).

The complexity of the calculation depends on the precision required (the Sun itself covers a half of degree in the sky) and range from very simple to very elaborate (what is your objective/requirement?).

I may suggest:

- Jean Meeus "Astronomical Algorithms" (duplicate from above)

- Bretagnon and Simon: "Planetary Programs and tables..." (Has a chapter for simple solar calculations)

- USNO "Multiyear Interactive Computer Almanac" or MICA (may be available for Android?)

- Some documented softwares (EP2000) accompany good telescopes for hobbysts (Meade, Celestron, ...)

BTW: if your objective is solar tracking there is no need of computation as it can be done automaticaly If you state your objective I may be of furture help

Good luck

A book titled "Practical Astronomy with your Calculator or Spreadsheet" must be what you want.

Thanks for the information. I will see.

There are many programs that calculate solar position. For example see https://midcdmz.nrel.gov/spa/ mentioned by Karen Barbosa de Melo.

I actually want to go backwards. I have an image of a sunset with the date and time. I want to compute the most likely locations (lat/long) where that image might have been taken.

I am not sure that this can be done with any precision with one given date and time. Even if one assumes the time zone is given, the sunset time varies across the time zone on a given day. Not having the location, the latitude can vary in the time zone where the sunset occurs. If you had both sunrise and sunset, then your chance of getting an answer improves.

@Benjamin: I concur with Frank. You have too many degrees of freedom...

For your purposes you can freely use the following software Sun-calculator v. 4.0(freeware) at the site: https://arg.ifa.md/downloadsun4.html

By Peter Duffett-Smith

"Practical Astronomy with your Calculator"; 2nd Ed., 1981.

Attention!!! new web address of the site with Sun-calculator v. 4.0(freeware) software: https://arg.ifa.md/downloadsun4.html By Peter Duffett-Smith

"Practical Astronomy with your Calculator"; 2nd Ed., 1981.

Look at " Analemma " of the Sun and Moon. The position, and the figure 8 of the Analemme are dependent upon the distance North, or, South of the Equator, and the tilt angle of the Earth at specific days of the year as the Earth orbits the Sun.

The shape and location also changes depending on the time of the day that you photograph the analemme. It would be best to do this from a dry climate location, that wide flat terrain, and no trees. The shape will also change position slightly dependent upon whether you are near the eastern edge, center, or western edge of the time zone where you photograph the Sun.

If you do this once a week, you can have 52 pictures of the Sun on one photo.

Have fun with this project.