<p>I was trying to help my son with a project and thought it shouldn't be hard but turned out I'm not as smart as I thought I was.</p>

<p>His project is about celestial navigation. The first step is, given the J2000 ra/dec of a specific star and a UTC time of observation first find the geographical lat/lon ground point (substellar point) for the star.</p>

<p>My assumption was lat = dec and lon was simply the ra - sidereal time from UTC time. So we knocked up a simple program to perform this. Then we used Stellarium (with refraction off for now) to test the output. And the star is indeed overhead but it is always off by a number of minutes. I suspected precession but that seems to be measured in arcseconds per year?</p>

<p>So now I realise my simple assumption isn't correct, only approximate. Could someone more knowledgeable please fill the gap in my knowledge.</p>

<p>Thanks in advance.</p>

CC BY-SA 4.0
2019-01-28T15:40:42.793Z
Is it always almost the *same number of minutes* for different stars that are all near the celestial equator? Or do you notice a pattern that things move in one direction on one side, and the opposite direction on the other side? Precession is 50 arcsec per year, so in 19 years you'd expect a maximum shift of almost 16 minutes around a great circle intersecting the poles, but most shifts would be less. What happens if you repeat it for January 1, 2000? (or whatever the epoch is for J2000.0?)
uhoh
CC BY-SA 4.0
2019-01-28T21:23:20.647Z
"expect a maximum shift of almost 16 minutes" Hi, thanks for the reply, it differs for different stars but all around 14 to 17 or so minutes. I will try with year 2000 dates shortly.
AstroDad
CC BY-SA 4.0
2019-01-30T17:24:11.693Z
@AstroDad Your reasoning looks correct. Perhaps the problem with your calculations can be determined if you provide an actual example (lat, long, RA, dec, UTC date). In uhoh's comment, the "maximum shift of almost 16 mintues" is 16 arcminutes, not 16 minutes of time. The sky rotates 360 degrees*60 arcminutes/degree in 24 hours*60 minutes approximately, so precession only accounts for 16*(24*60)/(360*60)=1 minute of time. That does not explain your 14 to 17 minute discrepancy (assuming that is minutes of time.)
JohnHoltz
<star>
Geographical Substellar position calculation from RA/DEC
AstroDad
# Geographical Substellar position calculation from RA/DEC

(Asked by: username_0 on 2019-01-28)

I was trying to help my son with a project and thought it shouldn't be hard but turned out I'm not as smart as I thought I was.

His project is about celestial navigation. The first step is, given the J2000 ra/dec of a specific star and a UTC time of observation first find the geographical lat/lon ground point (substellar point) for the star.

My assumption was lat = dec and lon was simply the ra - sidereal time from UTC time. So we knocked up a simple program to perform this. Then we used Stellarium (with refraction off for now) to test the output. And the star is indeed overhead but it is always off by a number of minutes. I suspected precession but that seems to be measured in arcseconds per year?

So now I realise my simple assumption isn't correct, only approximate. Could someone more knowledgeable please fill the gap in my knowledge.

Thanks in advance.

**Tags:** star

> **Comments:**
> **username_1**: Is it always almost the *same number of minutes* for different stars that are all near the celestial equator? Or do you notice a pattern that things move in one direction on one side, and the opposite direction on the other side? Precession is 50 arcsec per year, so in 19 years you'd expect a maximum shift of almost 16 minutes around a great circle intersecting the poles, but most shifts would be less. What happens if you repeat it for January 1, 2000? (or whatever the epoch is for J2000.0?)  
> **username_0**: "expect a maximum shift of almost 16 minutes" Hi, thanks for the reply, it differs for different stars but all around 14 to 17 or so minutes. I will try with year 2000 dates shortly.  
> **username_2**: @username_0 Your reasoning looks correct. Perhaps the problem with your calculations can be determined if you provide an actual example (lat, long, RA, dec, UTC date). In username_1's comment, the "maximum shift of almost 16 mintues" is 16 arcminutes, not 16 minutes of time. The sky rotates 360 degrees*60 arcminutes/degree in 24 hours*60 minutes approximately, so precession only accounts for 16*(24*60)/(360*60)=1 minute of time. That does not explain your 14 to 17 minute discrepancy (assuming that is minutes of time.)  

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