<p>I know the equatorial coordinates of a “beam” pointing from an Earth-based observer toward some distant star. I have converted those coordinates to altazimuth coordinates for that observer <em>and</em> a second observer elsewhere on earth.</p>
<p>Now, I’d like to turn both pairs of coordinates into vectors so that I can subtract them to determine a vector between the two observers. Is there a formula for this? I’ve only found this:</p>
<p><span class="math-container">\begin{align} 
z &amp;= \sin(alt)\\
hyp &amp; = \cos(alt)\\
y &amp; = hyp \cos(az)\\
x &amp; = hyp \sin(az)\\
vec &amp; = (x,y,z)\\
\end{align}</span></p>
<p>But I’m not sure if this will actually work. Would they both be in the same coordinate system so that I can, in fact, subtract them to determine a vector between the two points on Earth? Is there an easier/better way to do this? In the end, I need to determine the angle between the “baseline” vector (the vector between the two observers) and the vector pointing from one observer to the star.</p>

CC BY-SA 4.0
2020-07-18T13:08:14.390Z
In order to calculate alt and az of that object for the two observers, you must already know their locations on Earth, for example latitude and longitude.  So I’d keep things in that system for calculating your baseline, e.g. find your observers’ (x, y, z) locations in an Earth-centered frame and then find the vector between those two points.
Eric Jensen
CC BY-SA 4.0
2020-07-18T13:13:44.083Z
Strictly speaking you need elevations of each observer, too, but you could assume them to be zero if needed.  [Here’s a tool](https://geodesy.noaa.gov/NCAT/) that will calculate for you, or search for “geodetic coordinates” to find more info.
Eric Jensen
<observational-astronomy><coordinate><mathematics>
Using altitude, azimuth to determine a baseline vector?
PerplexedDimension
# Using altitude, azimuth to determine a baseline vector?

(Asked by: username_0 on 2020-07-18)

I know the equatorial coordinates of a “beam” pointing from an Earth-based observer toward some distant star. I have converted those coordinates to altazimuth coordinates for that observer *and* a second observer elsewhere on earth.

Now, I’d like to turn both pairs of coordinates into vectors so that I can subtract them to determine a vector between the two observers. Is there a formula for this? I’ve only found this:

\begin{align}
z &= \sin(alt)\\
hyp & = \cos(alt)\\
y & = hyp \cos(az)\\
x & = hyp \sin(az)\\
vec & = (x,y,z)\\
\end{align}

But I’m not sure if this will actually work. Would they both be in the same coordinate system so that I can, in fact, subtract them to determine a vector between the two points on Earth? Is there an easier/better way to do this? In the end, I need to determine the angle between the “baseline” vector (the vector between the two observers) and the vector pointing from one observer to the star.

**Tags:** observational-astronomy, coordinate, mathematics

> **Comments:**
> **username_1**: In order to calculate alt and az of that object for the two observers, you must already know their locations on Earth, for example latitude and longitude.  So I’d keep things in that system for calculating your baseline, e.g. find your observers’ (x, y, z) locations in an Earth-centered frame and then find the vector between those two points.  
> **username_1**: Strictly speaking you need elevations of each observer, too, but you could assume them to be zero if needed.  [Here’s a tool](https://geodesy.noaa.gov/NCAT/) that will calculate for you, or search for “geodetic coordinates” to find more info.  

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## 0 answers

