<p>From the book "Fundamental Astronomy" by H. Karttunen et al. we have the following expression (to calculate the hour angle when the altitude is <span class="math-container">$0$</span>):</p>

<blockquote>
  <p><span class="math-container">$\cos(h) = -\tan(\delta)\tan(\phi)$</span> (<span class="math-container">$\phi$</span> is the latitude, <span class="math-container">$\delta$</span> the
  declination)</p>
</blockquote>

<p><br>Since <span class="math-container">$\Theta = \alpha + h$</span> (<span class="math-container">$\Theta$</span> is the Mean Sidereal Time, <span class="math-container">$\alpha$</span> the right ascension), we can use this formula to calculate rising and setting times. <br></p>

<p><span class="math-container">$\Theta$</span> matches GMT at the time of the Autumnal Equinox (roughly, and we're talking about Mean Sidereal Time), and every sidereal day is roughly 23h 56min so if you know the time of the observation, you can approximate the rising/setting time.<br></p>

<p>This of course does not take refraction, precession and other effects into account, which I assumed you do not need since you gave rather vague culmination times (stars rarely culminate around such "exact" times).</p>

CC BY-SA 4.0
2018-11-29T12:05:19.350Z
2018-11-30T07:03:18.403Z
2018-11-30T07:03:18.403Z
Tosic
<p>For a star, the time from rising to culmination is the same length as the time from culmination to setting. From knowing the time of culmination and setting, you can calculate that difference and subtract it from the time of culmination to obtain the time of rising.</p>

<p>This method is generally accurate for the planets and Sun, but it is not always accurate for the Moon. Culmination refers to when an object is highest in the sky. For a star, this is when the object is on the meridian. For the Moon, there can be a significant difference between the time the Moon crosses the meridian (transits) and when it culminates. See <a href="http://www.geoastro.de/TransitCulm/index.html" rel="noreferrer">Transit and Culmination</a> (although the images on that site were not working today).</p>

<p>P.S. I have never seen tables that give the time of culmination for the Sun and Moon. Times are generally given for transits (when the object is on the meridian).</p>

CC BY-SA 4.0
2018-11-29T17:11:26.457Z
2018-11-29T17:11:26.457Z
JohnHoltz
<p>I want to know how to calculate the rising time of a star, if 
culmination and setting times are available with me?</p>

<p>Say Culmination time is 03:00 on 28-Nov-2018
and Setting time is 05:30 on 28-Nov-2018.</p>

CC BY-SA 4.0
2018-11-29T11:45:20.437Z
How accurately do you want the answer?  If it's within a minute or so, then use the fact that culmination is midway between rising and setting.
Dr Chuck
<time>
calculating rising time from culmination time
John
# calculating rising time from culmination time

(Asked by: username_0 on 2018-11-29)

I want to know how to calculate the rising time of a star, if
culmination and setting times are available with me?

Say Culmination time is 03:00 on 28-Nov-2018
and Setting time is 05:30 on 28-Nov-2018.

**Tags:** time
> **Comments:**
> **username_1**: How accurately do you want the answer?  If it's within a minute or so, then use the fact that culmination is midway between rising and setting.  

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## 2 answers

### Answer by username_3 on 2018-11-29. Score: 4 | Accepted answer

For a star, the time from rising to culmination is the same length as the time from culmination to setting. From knowing the time of culmination and setting, you can calculate that difference and subtract it from the time of culmination to obtain the time of rising.

This method is generally accurate for the planets and Sun, but it is not always accurate for the Moon. Culmination refers to when an object is highest in the sky. For a star, this is when the object is on the meridian. For the Moon, there can be a significant difference between the time the Moon crosses the meridian (transits) and when it culminates. See [Transit and Culmination](http://www.geoastro.de/TransitCulm/index.html) (although the images on that site were not working today).

P.S. I have never seen tables that give the time of culmination for the Sun and Moon. Times are generally given for transits (when the object is on the meridian).


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### Answer by username_2 on 2018-11-29. Score: 2

From the book "Fundamental Astronomy" by H. Karttunen et al. we have the following expression (to calculate the hour angle when the altitude is $0$):

> $\cos(h) = -\tan(\delta)\tan(\phi)$ ($\phi$ is the latitude, $\delta$ the
> declination)

Since $\Theta = \alpha + h$ ($\Theta$ is the Mean Sidereal Time, $\alpha$ the right ascension), we can use this formula to calculate rising and setting times.

$\Theta$ matches GMT at the time of the Autumnal Equinox (roughly, and we're talking about Mean Sidereal Time), and every sidereal day is roughly 23h 56min so if you know the time of the observation, you can approximate the rising/setting time.

This of course does not take refraction, precession and other effects into account, which I assumed you do not need since you gave rather vague culmination times (stars rarely culminate around such "exact" times).


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