<p>I'm developing a Astronomical software using the formulas from the book: &quot;<a href="https://www.cambridge.org/gb/academic/subjects/physics/amateur-and-popular-astronomy/practical-astronomy-your-calculator-or-spreadsheet-4th-edition?format=PB&amp;isbn=9781108436076" rel="nofollow noreferrer">Practical astronomy with your Calculator and Spreadsheet</a>&quot;, but I'm having some problems to get the right ascension from the hour angle.</p>
<p>I'm using these input data:</p>
<pre><code>Hour Angle: 20:29:20.19999999999999
Decimal Hour angle: 20.488944000000000
Longitude   -3.9290699958801270
Time: 18:30:00, July 17th, 2024 UTC+2
</code></pre>
<p>To get the right ascension, I use this algorithm:</p>
<ol>
<li>Find the UT and Greenwich calendar date corresponding to the local time and date</li>
<li>Find the corresponding Greenwich sidereal time</li>
<li>. . . hence find the local sidereal time</li>
<li>Subtract the decimal hour angle from the LST. If the answer is negative, add 24. This is the right ascension.</li>
</ol>
<p>To find the Local Sidereal Time I use the user's longitude and GST to get it:</p>
<ol>
<li>Convert GST to decimal hours.</li>
<li>Convert the geographical longitude in degrees to its equivalent in hours by dividing by 15.</li>
<li>Add this to the GST. Bring the result into the range 0 to 24 by adding or subtracting 24 if necessary.This is the local sidereal time (LST).</li>
</ol>
<p>With the above data, I get these results:</p>
<pre><code>UT Time: 16:30:00, July 17th, 2024 UTC+2
Greenwich sidereal time: 12:13:57.229999999999997
Local sidereal time:    11:58:14.250000000000000
Decimal Local sidereal time: 11.970625000000000
Right Ascension: -8.518319000000000
                15.481681000000000
</code></pre>
<p><strong>Unfortunately, they are wrong</strong>.</p>
<p>But, if I change the sign of the longitude, I get the right one.</p>
<p>Using the same data, but with longitude positive, <strong>Longitude: 3.9290699958801270</strong>, I get these results.</p>
<p><strong>Input</strong></p>
<pre><code>Hour Angle: 20:29:20.19999999999999
Decimal Hour angle: 20.488944000000000
Longitude   3.9290699958801270
Time: 18:30:00, July 17th, 2024 UTC+2
</code></pre>
<p><strong>Output</strong></p>
<pre><code>UT Time: 16:30:00, July 17th, 2024 UTC+2
Greenwich sidereal time: 12:13:57.229999999999997
Local sidereal time:    12:29:40.210000000000001
Decimal Local Sidereal Time: 12.494503000000000
Right Ascension: -7.994441000000000
                16.005558999999998
</code></pre>
<p>Why do I get the correct result when I change the sign of the longitude? Is the algorithm wrong?</p>
<p>Or maybe, the right right ascension is 15.481681000000000.</p>
<p>I have also tried to find the formula to compute all of these data, but I haven't found it. Maybe because I'm not English and I haven't used the right key words in Google.</p>
<p>Do you know if there is a C++ library with all of these formulas implemented? Nasa's SPICE Toolkit?</p>

CC BY-SA 4.0
2024-07-20T21:00:06.007Z
Positive or negative longitude changes between Eastern and Western hemisphere. Obviously, an object’s hour angle won’t be the same from two different locations at the same UT. That’s why you get good results when using a positive longitude; because you’re then using the right Eastern/Western hemisphere.
Pierre Paquette
CC BY-SA 4.0
2024-07-21T00:29:25.390Z
Some of those older books (or new editions of old books) consider East longitudes as negative.  Not sure if that is one, but Astronomical Algorithms is one.
Greg Miller
<right-ascension>
Hour angle to Right Ascension correct when the longitude is positive
VansFannel
# Hour angle to Right Ascension correct when the longitude is positive

(Asked by: username_0 on 2024-07-20)

I'm developing a Astronomical software using the formulas from the book: "Practical astronomy with your Calculator and Spreadsheet", but I'm having some problems to get the right ascension from the hour angle.
I'm using these input data:
Hour Angle: 20:29:20.19999999999999
Decimal Hour angle: 20.488944000000000
Longitude   -3.9290699958801270
Time: 18:30:00, July 17th, 2024 UTC+2

To get the right ascension, I use this algorithm:

Find the UT and Greenwich calendar date corresponding to the local time and date
Find the corresponding Greenwich sidereal time
. . . hence find the local sidereal time
Subtract the decimal hour angle from the LST. If the answer is negative, add 24. This is the right ascension.

To find the Local Sidereal Time I use the user's longitude and GST to get it:

Convert GST to decimal hours.
Convert the geographical longitude in degrees to its equivalent in hours by dividing by 15.
Add this to the GST. Bring the result into the range 0 to 24 by adding or subtracting 24 if necessary.This is the local sidereal time (LST).

With the above data, I get these results:
UT Time: 16:30:00, July 17th, 2024 UTC+2
Greenwich sidereal time: 12:13:57.229999999999997
Local sidereal time:    11:58:14.250000000000000
Decimal Local sidereal time: 11.970625000000000
Right Ascension: -8.518319000000000
                15.481681000000000

Unfortunately, they are wrong.
But, if I change the sign of the longitude, I get the right one.
Using the same data, but with longitude positive, Longitude: 3.9290699958801270, I get these results.
Input
Hour Angle: 20:29:20.19999999999999
Decimal Hour angle: 20.488944000000000
Longitude   3.9290699958801270
Time: 18:30:00, July 17th, 2024 UTC+2

Output
UT Time: 16:30:00, July 17th, 2024 UTC+2
Greenwich sidereal time: 12:13:57.229999999999997
Local sidereal time:    12:29:40.210000000000001
Decimal Local Sidereal Time: 12.494503000000000
Right Ascension: -7.994441000000000
                16.005558999999998

Why do I get the correct result when I change the sign of the longitude? Is the algorithm wrong?
Or maybe, the right right ascension is 15.481681000000000.
I have also tried to find the formula to compute all of these data, but I haven't found it. Maybe because I'm not English and I haven't used the right key words in Google.
Do you know if there is a C++ library with all of these formulas implemented? Nasa's SPICE Toolkit?

**Tags:** right-ascension

> **Comments:**
> **username_1**: Positive or negative longitude changes between Eastern and Western hemisphere. Obviously, an object’s hour angle won’t be the same from two different locations at the same UT. That’s why you get good results when using a positive longitude; because you’re then using the right Eastern/Western hemisphere.  
> **username_2**: Some of those older books (or new editions of old books) consider East longitudes as negative.  Not sure if that is one, but Astronomical Algorithms is one.  

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## 0 answers

