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Sidereal Time formula / 1 second divergence

 
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Petr9



Joined: 30 May 2017
Posts: 6
Location: Prague, CZ

Posted: Thu Aug 03, 2017 9:58 pm    Post subject: Sidereal Time formula / 1 second divergence Reply with quote

Hello,
I'm trying to calculate exact Sideral Time (ST0).

I found several formulas based on Julian Dates (JD and JD0) which differ very slightly:

===
T = (JD0 - 2451545.0)/36525;
ST0 = (6.697374558) + (2400.051336 * T) + (0.000025862 * T*T);
===
T = (JD0 - 2451545.0)/36525;
ST0 = (6.697374558) + (2400.05133691 * T) + (0.000025862 * T*T) - (0.0000000017 * T*T*T);
===
D0 = JD0 - 2451545.0;
T = (JD - 2451545.0)/36525;
ST0 = 6.697374558 + (0.06570982441908 * D0) + (0.000026 T*T);
===

All of these formulas give almost the same results rounded to 0.000x seconds (00:00:00.000x). But if I compare the results with astro.com or Morinus software, there is almost always +-1 second divergence (00:00:0x)

eg: May 9, 1983 (00:00UT)
ST0 15:04:59.081x (all formulas)
ST0 15:04:58 (astro.com)
ST0 15:04:57 (morinus)

eg: December 16, 2009 (00:00UT)
ST0 05:39:04.144x (all formulas)
ST0 05:39:05 (astro.com)
ST0 05:39:05 (morinus)

Do you know, if there is another formula; or something wrong, with these formulas, please?

===

EDIT: I know it's just 1'' second divergence, but this 1 second is causing bigger divergences in further calculations - especially in Primary Directions to angles MC/ASC
(1'' in ST0 <=> cca 15'' in RA arcs <=> cca 1,5 days in PD)

I would be thankful for any help.
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Petr9



Joined: 30 May 2017
Posts: 6
Location: Prague, CZ

Posted: Thu Aug 10, 2017 8:23 am    Post subject: Reply with quote

Maybe I figured it out.
Astrodienst and Morinus is (probably) using Apparent Sidereal Time, which takes into account nutation and differs 1.2s from Mean Sideral Time.

I found additional equations and corrections for nutation and now it calculates the same results.
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