<p>This figure from
<a href="https://en.wikipedia.org/wiki/Spherical_law_of_cosines" rel="nofollow noreferrer">Wikipedia:Spherical law of cosines</a>
applies if the ground station is at the center of the sphere, 
<strong>u</strong> is the ground station's zenith, and <strong>v</strong> and <strong>w</strong> are the apparent positions of the satellites as seen from the ground station.</p>

<p><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/38/Law-of-haversines.svg/240px-Law-of-haversines.svg.png" alt="spherical triangle diagram"></p>

<p>Then <strong><em>a</em></strong> and <strong><em>b</em></strong> are the satellites' zenith angles, i.e. 90&deg; minus their elevation angles.
<strong><em>C</em></strong> is the difference between the satellites' azimuths, and <strong><em>c</em></strong> is the angle you want.</p>

<p>Using the cosine rule for sides
<span class="math-container">$$\cos c = \cos a \cos b  + \sin a  \sin b  \cos C$$</span>
and the rules for sines and cosines of complementary angles,
the expression in the question looks correct if the absolute value operations are omitted.</p>

CC BY-SA 4.0
2019-11-05T02:02:56.120Z
2019-11-05T02:02:56.120Z
Mike G
<p>If you only need angles, you need interior angle triangle forumula, all angles in interior sum is equal to  180° . only you need  Angle Sat 1 + Angle Sat 2 + Angle Sat 1-2 = 180°, if you need  distances A, B , C you need use polar coordenates. lat, long and elevation.</p>

CC BY-SA 4.0
2019-11-04T16:54:52.737Z
I don't know the angle between the two satellites, only the AZ and EL to each from the GS.  Think of the GS as the center of a sphere, and the two satellites are points on that sphere and I have two angles from the center of the sphere that give the position of where each Satellite is on the surface of the sphere.  I need the angle that is formed by that GS looking at each Satellite.
Shaps
CC BY-SA 4.0
2019-11-04T17:43:55.003Z
AZ is Azimuth , and EL is Elevation ? because Azimuth is a angular meassure
Adrian R
CC BY-SA 4.0
2019-11-04T21:44:40.210Z
I should clarify.  I know the AZ (angle) and Elevation Angle to each.  So imagine my Ground Station is sitting at the center.  My AZ to one satellite is the angle I rotate myself to look at it and then my elevation is how high I need to look at it.  I have both of those for each Satellite.  I need to figure out the angle that is formed between the first satellite, the Ground Station, and then the second satellite.  I hope that this makes sense.
Shaps
CC BY-SA 4.0
2019-11-05T01:08:29.340Z
This answer is for Euclidian planar geometry but the question is about spherical trigonometry; triangles drawn on the surface of a unit sphere.
uhoh
CC BY-SA 4.0
2019-11-04T16:36:05.223Z
2019-11-04T16:36:05.223Z
Adrian R
<p>I am trying to check my work on calculating the angle between two sats and a ground station observing those two sats. I have the az and elevation angles to each sat from the ground station. What would be the equation to get the angle Sat1-GS-Sat2?</p>

<p>I know that it uses the law of Cosines, but not sure if I was using the correct equation.  Here is what I am using:  </p>

<p>Angle = acos((abs(sin("V_Sat_1_EL")*sin("V_Sat_2_EL")))+(cos("V_Sat_1_EL")*cos("V_Sat_2_EL")*cos(abs("V_Sat_2_AZ"-"V_Sat_1_AZ"))))</p>

<p>Thanks</p>

<satellite>
Angle formed between a satellite, a ground station, and then another Satellite
Shaps
# Angle formed between a satellite, a ground station, and then another Satellite

(Asked by: username_0 on 2019-11-04)

I am trying to check my work on calculating the angle between two sats and a ground station observing those two sats. I have the az and elevation angles to each sat from the ground station. What would be the equation to get the angle Sat1-GS-Sat2?

I know that it uses the law of Cosines, but not sure if I was using the correct equation. Here is what I am using:

Angle = acos((abs(sin("V\_Sat\_1\_EL")\*sin("V\_Sat\_2\_EL")))+(cos("V\_Sat\_1\_EL")\*cos("V\_Sat\_2\_EL")\*cos(abs("V\_Sat\_2\_AZ"-"V\_Sat\_1\_AZ"))))

Thanks

**Tags:** satellite

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## 2 answers

### Answer by username_1 on 2019-11-05. Score: 3

This figure from
[Wikipedia:Spherical law of cosines](https://en.wikipedia.org/wiki/Spherical_law_of_cosines)
applies if the ground station is at the center of the sphere,
**u** is the ground station's zenith, and **v** and **w** are the apparent positions of the satellites as seen from the ground station.

![spherical triangle diagram](https://upload.wikimedia.org/wikipedia/commons/thumb/3/38/Law-of-haversines.svg/240px-Law-of-haversines.svg.png)

Then ***a*** and ***b*** are the satellites' zenith angles, i.e. 90° minus their elevation angles.
***C*** is the difference between the satellites' azimuths, and ***c*** is the angle you want.

Using the cosine rule for sides
$$\cos c = \cos a \cos b + \sin a \sin b \cos C$$
and the rules for sines and cosines of complementary angles,
the expression in the question looks correct if the absolute value operations are omitted.


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### Answer by username_2 on 2019-11-04. Score: 0

If you only need angles, you need interior angle triangle forumula, all angles in interior sum is equal to 180° . only you need Angle Sat 1 + Angle Sat 2 + Angle Sat 1-2 = 180°, if you need distances A, B , C you need use polar coordenates. lat, long and elevation.

> **Comments:**
> **username_0**: I don't know the angle between the two satellites, only the AZ and EL to each from the GS.  Think of the GS as the center of a sphere, and the two satellites are points on that sphere and I have two angles from the center of the sphere that give the position of where each Satellite is on the surface of the sphere.  I need the angle that is formed by that GS looking at each Satellite.  
> **username_2**: AZ is Azimuth , and EL is Elevation ? because Azimuth is a angular meassure  
> **username_0**: I should clarify.  I know the AZ (angle) and Elevation Angle to each.  So imagine my Ground Station is sitting at the center.  My AZ to one satellite is the angle I rotate myself to look at it and then my elevation is how high I need to look at it.  I have both of those for each Satellite.  I need to figure out the angle that is formed between the first satellite, the Ground Station, and then the second satellite.  I hope that this makes sense.  
> **username_3**: This answer is for Euclidian planar geometry but the question is about spherical trigonometry; triangles drawn on the surface of a unit sphere.  

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