## Delta-T formulae in Guide, and how to modify them

Some people doing work on historical eclipses and occultations have asked for a way to change the way Guide handles Delta-T, the difference between the Dynamical Time and Universal Time scales. Others have simply inquired as to how Delta-T is computed. Click here if you just want to skip ahead to read about how to modify Guide's Delta-T formulae. (You can do this without needing to know the default algorithm used in Guide.)

First, I should note that Quick Info will tell you the value of Delta-T that Guide is using for a given time.

Delta-T is quite well-defined for the modern era (about 1620 through the present). Within that range, Guide interpolates within a table of observed values. (If you want details, you should download the source code for basic astronomical functions and look in the delta_t.cpp file. Don't be too intimidated by this thought if you're a non-programmer. The file in question is well-documented, and I think you could figure out most of it without needing to be a programming guru.)

For dates before 1620, there have been several formulae given to approximate Delta-T. By default, Guide uses the following, all taken from the Five Millennium Catalogue of Solar Eclipses by Espenak and Meeus:

Before -500:

```TD - UT = -20 + 32 * u^2
where u = (year - 1820) / 100
```

From -500 to +500:

```TD - UT = 10583.6 - 1014.41 u + 33.78311 u^2 - 5.952052 u^3
-.1798452 u^4 + .022174192 u^5 + .0090316521 u^6
where u = year / 100
```

From +500 to +1600:

```TD - UT = 1574.2 - 556.01 u + 71.23472 u^2 + .0319781 u^3
-.8503463 u^4 - .005050998 u^5 + .0083572073 u^6
where u = (year - 1000) / 100
```

From +1600 to +1620:

```TD - UT = 120 - 98.08 t - 153.2 t^2 + 140.272 t^3
where t = (year - 1600) / 100
```

Prior to March 2012, I used the following quadratic approximations for Delta-T for years before 1620, from F.R. Stephenson and M. A. Houlden, "Atlas of Historical Eclipse Maps", Cambridge University Press, England (1986), page x. These can also be found on page 73 of Meeus' Astronomical Algorithms, 1st edition.

Before the year 948:

TD - UT = 2715.6 + 573.36 * t + 46.5 * t2

Between 948 and 1620:

TD - UT = 50.6 + 67.5 * t + 22.5 * t2

where t = (year - 2000) / 100 = (JD - 2451545.) / 365.25 = Julian centuries from the year 2000, and TD-UT = Delta_T in seconds.

Modifying the Delta-T formulae: Suppose you wanted to maintain Guide's usual Delta-T behavior, except that between the years 1990 to 2010, you wanted

TD - UT = 65 + 120 * t

(This is a passable linear approximation to the actual behavior of Delta-T over those years.) You would edit the file GUIDE.DAT and add this line:

DELTA_T=1990,2010:65,120

Guide would continue using its "normal" formulae outside that range, but between 1990 and 2010, it would use your formula.

You can also specify a particular, fixed Delta-T by omitting the linear coefficient. For example, if you wanted to set Delta-T=87.3 seconds for all times, you'd use

`DELTA_T=-100000,100000:87.3 `

You can add extra ranges, separated by ';'. If you so wished, you could duplicate the (former) default behavior of Guide's Delta-T with the following:

```DELTA_T=-100000,948:2715.6,573.36,46.5;948,1620:50.6,67.5,22.5
```

In the above, for each time span, three coefficients are given: a constant, a linear, and a quadratic one. You can continue beyond this, making a cubic polynomial, or quartic, etc., with no limit. In fact, the (current) default behavior for times between -500 and 1600 uses two different sixth-degree polynomials, plus two quadratics for two other time spans. The four time spans are handled using the following very long Delta-T string, which is embedded in Guide. (For clarity, I've broken it into four lines, one for each of the four time spans of the Espenak/Meeus algorithm.)

```-100000,-500:o1820,-20,0,32;
-500,500:o0,10583.6,-1014.41,33.78311,-5.952053,-.1798452,.022174192,.0090316521;
500,1600:o1000,1574.2,-556.01,71.23472,.319781,-.8503463,-.005050998,.0083572073;
1600,1620:o1600,120,-98.08,-153.2,140.272
```

A further note: by default, the code assumes polynomials with the argument (year-2000)/100. However, some formulae (including those for all four polynomials given above) assume an offset other than the year 2000. This can be specified with o followed by the offset year. Thus, for example, in the above example, years before -500 are handled with

`delta_t = -20 + 32 * ((year-1820) / 100) ^2 `

WARNING: I think it's safe to play around with other Delta-T formulae. It's certainly safe to do so in the sense that, if worst comes to worst, you can delete the DELTA_T line in guide.dat and recover the original, default behavior. One area that concerns me, though, is that lunar/planetary theories based on one version of Delta-T may not work very well when you attempt to "drop in" a totally different Delta-T formula. That has a lot of possible effects, and I've not begun to figure them all out yet.