[guide-user] Delta-T oddities

Paul Schlyter Apr 6, 2001

From: "Bill J. Gray" <pluto@...>

> Hi Chris,
>
> Errrmmm... we _do_ have something odd going on here.
>
> Instead of getting SkyMap's value of Delta-T=+9117.5 seconds, I
> got Delta-T=+9921.5 seconds! (This information is given in "Help...
> Quick Info".) This is a difference of 804 seconds. Not enough to
> push this event into visibility, by any means, but it did surprise me.
>
> I ran that test thinking that we probably were both using the Delta-T
> formula from Meeus' _Astronomical Algorithms_ for "dates before A.D. 948":
>
> Delta-T = 2715.6 + 573.36 * T + 46.5 * T^2
>
> ...where T=centuries from J2000 = (JD-2451545.0) / 36525.
>
> Therefore, I assumed that we'd have virtually identical values of
> Delta-T, which would have allowed me to repeat comments about not taking
> agreement between any two programs too seriously; they may just be
> copying each other's mistakes.
>
> Checking by hand (T=-20.0566) again got me Delta-T=+9921.5. Perhaps
> you've dug up a more recent expression? The one given in Meeus dates
> back to 1986, and it wouldn't surprise me at all if something better
> has been determined since then.
>
> The code I use for Delta-T is available as part of the "basic
> astronomical source code" at
>
> http://www.projectpluto.com/source.htm#astrocalc

There are indeed a number of different Delta-T formulae around.
Some examples:


Def. of T Validity Formula Delta-T at year 0

Meeus "Astronomical Algorithms", 1st ed

(y-2000)/100 -390 to +948 1360 + 320 T + 44.3 T^2 12680 s
(y-948)/100 before +948 1830 - 405 T + 46.5 T^2 9848 s
(y-2000)/100 before +948 2715.6 + 573.36 T + 46.5 T^2 9848 s

Meeus "Astronomical Algorithms", 2nd ed

(y-2000)/100 before +948 2177 + 497 T + 44.1 T^2 9877 s


Meeus "Astronomical Formulae for Calculators", 1st, 2nd, 4th ed's

(y-2000)/100 before 1710 25 + 72.3 T + 30.0 T^2 10579 s


Seidelmann "Explanatory Supplement to the Astronomical Almanac", p 83

(y-1800)/100 before 1650 5.156 + 13.3066*(T-0.19)^2 4407 s


The older "Explanatory Supplement to the Ephemeris", p 87

(y-1900)/100 "to ancient times" 24.3 + 72.3 T + 29.95 T^2 9463 s



Note that the difference between the largest and the smallest Delta-T
at year 0 is as large as 8200 seconds, or 2.3 hours !



And none of the values agree very closely with Chris Marriot's
Delta-T near year 0. So Chris: what formula do you use to compute
Delta-T? And from where did you obtain it?

----------------------------------------------------------------
Paul Schlyter, Swedish Amateur Astronomer's Society (SAAF)
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