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Q: Relative azimuth angle (between Sun and polar orbiting satellite) ( Answered 5 out of 5 stars,   0 Comments )
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.
Subject: Re: Relative azimuth angle (between Sun and polar orbiting satellite)
Answered By: livioflores-ga on 23 Nov 2005 08:42 PST
Rated:5 out of 5 stars

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:

If you have troubles regarding the following values: SolarHourAngle,
SolarDeclination, SolarZenithAngle, please see the following page for
additional help:
"General Solar Position Calculations":

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":

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.

"Astronomical Algorithms":
This page is associated with the above one and give you formulas for calculations .

"Astronomy Answers: Position of the Sun":
This is a more advanced page (in my understand).

To compare your results you can use this online calculator:
"Calculation of Sun Position, Sunrise and Sunset"

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.


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:

Good luck!!

Request for Answer Clarification by clavr-ga on 23 Nov 2005 11:17 PST
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

I will try to find more sources regarding the satellite azimuth angle
computation as you requested and post my finds tonight.


Clarification of Answer by livioflores-ga on 24 Nov 2005 02:18 PST

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:

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
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.

For better understand see the following graphics:

"Zenith Angle":

I hope that this helps you. Feel free to continue using the
clarification feature if you need it.


Request for Answer Clarification by clavr-ga on 24 Nov 2005 03:56 PST

Thanks a lot. 
This seems very useful and fits to the input information that I have.


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!!


Clarification of Answer by livioflores-ga on 27 Nov 2005 06:16 PST

One thing that I forgot to give you is my search strategy, here is it:
At I searched for the following keywords:
Relative azimuth angle formula
azimuth angle satellite
azimuth angle calculation

clavr-ga rated this answer:5 out of 5 stars

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