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Q: Relative azimuth angle (between Sun and polar orbiting satellite) ( Answered ,   0 Comments )
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 Subject: Relative azimuth angle (between Sun and polar orbiting satellite) Category: Science > Earth Sciences Asked by: clavr-ga List Price: \$10.00 Posted: 22 Nov 2005 08:46 PST Expires: 22 Dec 2005 08:46 PST Question ID: 596250
 ```I need exact procedure/formulae to compute relative azimuth angle between sun and polar orbiting satellite (which is at height about 800 KM above the earth). The input values should be : For ground pixel : year, day, time, latitude and longitude of ground pixel For satellite : satellite scan angle, satellite altitude Output should be : relative azimuth angle (and also the solar and satellite zenith and azimuth angles). Please note that I only have specified input information.```
 ```Hi!! I found a description of the equations and calculations used to compute Relative Azimuth Angle: Please check if the following pages are useful to your purposes: "ANGLE GENERATION": http://www.pcigeomatics.com/cgi-bin/pcihlp/AVHRRAD|DETAILS|ANGLE+GENERATION If you have troubles regarding the following values: SolarHourAngle, SolarDeclination, SolarZenithAngle, please see the following page for additional help: "General Solar Position Calculations": http://www.srrb.noaa.gov/highlights/sunrise/solareqns.PDF This previous answer given by me could be helpful to you at this point: "Google Answers: I need an equation or C or C++ function to know the position of the sun": http://answers.google.com/answers/threadview?id=500251 Some links at this answer are now broken, but the following working ones could be helpful: "Basics of Positional Astronomy and Ephemerides": to get the basic knowledge regarding to the positional concepts. http://www.jgiesen.de/SME/details/basics/ "Astronomical Algorithms": This page is associated with the above one and give you formulas for calculations . http://www.jgiesen.de/SME/details/basics/meeus.htm "Astronomy Answers: Position of the Sun": This is a more advanced page (in my understand). http://www.astro.uu.nl/~strous/AA/en/reken/zonpositie.html To compare your results you can use this online calculator: "Calculation of Sun Position, Sunrise and Sunset" http://www.volker-quaschning.de/datserv/sunpos/index_e.html I hope that this helps you. Feel free to request for a clarification if you find this answer unclear or incomplete, I will gladly improve the answer to make it according to your needs. Regards, livioflores-ga``` Clarification of Answer by livioflores-ga on 23 Nov 2005 08:46 PST ```In the case that the first link (the one regarding Angle Generation) does not work, try the following one: http://tinyurl.com/btwgd Good luck!!``` Request for Answer Clarification by clavr-ga on 23 Nov 2005 11:17 PST ```Hello, Thanks a lot for your response. For computation of relative azimuth angle, one needs solar and satellite azimuth angles. Most of your response covers the part of solar azimuth and zenith angles. But what about satellite azimuth angle ? I have already referred in the past to the first link given by you and I m not getting correct azimuth angles by using that procedure. I will really appreciate if you can provide more information/references on satellite azimuth angle computation. Thanks a lot.``` Clarification of Answer by livioflores-ga on 23 Nov 2005 14:32 PST ```Hi!! I will try to find more sources regarding the satellite azimuth angle computation as you requested and post my finds tonight. Regards, livioflores-ga``` Clarification of Answer by livioflores-ga on 24 Nov 2005 02:18 PST ```Hi!! I think that I found how to compute the satellite azimuth angle with the input data that you have. I found it at the following document: "The Mathematics of the Longitude" by Wong Lee Nah from Department of Mathematics - National University of Singapore: http://www.math.nus.edu.sg/aslaksen/projects/wln.pdf According to the above document this is what you must do: First recall some definitions: "The altitude, H, is the vertical angle between the horizontal plane to the line of sight to the body. The point directly overhead the observer is called the zenith... The azimuth, Az, is the horizontal direction of the body with respect to the geographic (true) north point on the horizon, measured clockwise through 360°. " From the page 18 (see also the figure 2.10 at the same page). To compute the satellite azimuth angle (AZ) use the following formula: [sin(SatDec) - sin(SatAlt) * sin(Ground Pixel Lat)] Az = -------------------------------------------------------------- [cos(SatAlt) * cos(Ground Pixel Lat)] Note that SatAlt is the satellite angle above the horizon (that is its altitude not its orbit's height, so do not confuse it with SatAltitude variable), this angle is equal to: SatAlt = (90 - SatelliteZenithAngle) And SatDec is the satellite declination, that is the latitude of the satellite's Nadir. The following correction is needed in some cases: Calculate LHA, it is the difference between the pixel's longitude and the longitude of satlellite's Nadir(the latter is usually called the "Greenwich hour angle" or GHA): LHA = Ground Pixel Long - SatLon; now if sin(LHA) < 0 , no correction is needed. if sin(LHA) > 0 , then use as the proper result (360 - Az). See for reference the page 68 of "The Mathematics of the Longitude". Also take a look to this page: "Azimuth Angle" at Math Forum: I cannot confirm if this formulas are right. http://mathforum.org/library/drmath/view/56477.html For better understand see the following graphics: "Azimuth": http://asd-www.larc.nasa.gov/SCOOL/azimuth.gif "Zenith Angle": http://asd-www.larc.nasa.gov/SCOOL/vz.sz.gif I hope that this helps you. Feel free to continue using the clarification feature if you need it. Regards, livioflores-ga``` Request for Answer Clarification by clavr-ga on 24 Nov 2005 03:56 PST ```Hello, Thanks a lot. This seems very useful and fits to the input information that I have. regards, clavr.``` Clarification of Answer by livioflores-ga on 24 Nov 2005 06:56 PST ```Thank you so much for the good rating, I am very glad to know that you can go ahead with your project!! Bestregards, livioflores-ga``` Clarification of Answer by livioflores-ga on 27 Nov 2005 06:16 PST ```Hi!! One thing that I forgot to give you is my search strategy, here is it: At Google.com I searched for the following keywords: Relative azimuth angle formula azimuth angle satellite azimuth angle calculation Regards, livioflores-ga```