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So our arc day starts at 20°41'32 which is midnight (0:00) and ends 24 hours later at 21°42'42. According to my calculations it traveled 0 degrees, 59 minutes, and 30 seconds or 3570 arc seconds in 24 hours. What I am looking for is, what time it will reach 21°15'30.32. For the love of God I have a brain freeze on how to get this.

This is what I came up with:

3570 arcseconds / 24 hours = 148.75 arcseconds/hour
1758.32 arcseconds / 148.75 arcseconds/hour ≈ 11.82 hours

but I do not think its accurate as the time I am looking for is 13:19:43.

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    $\begingroup$ The difference betwee 21°15'30.32 and 20°41'32 is 21*3600+15*60+30.32- (20*3600+41*60+32) = 2038.32 arcseconds. Not 1758.32 arcseconds. $\endgroup$
    – James K
    Commented Jan 14 at 23:24
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    $\begingroup$ Try converting those angles to decimal degrees first. $\endgroup$
    – Mike G
    Commented Jan 15 at 0:20
  • $\begingroup$ 21.7117−20.6922=1.0195 which makes my arcseconds also wrong as it comes to 3682.2 arcseconds $\endgroup$
    – dimitri33
    Commented Jan 15 at 0:23
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    $\begingroup$ I’m voting to close this question because there doesn't appear to be an astronomical problem, only difficulty using an online calculator to calculate sexagesimal. $\endgroup$
    – James K
    Commented Jan 15 at 18:12
  • 1
    $\begingroup$ A good clock is often effective ! $\endgroup$
    – James K
    Commented Jan 18 at 21:55

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