Delta T
A Note by Jean Meeus

The quantity Delta T is very important in the calculation of solar eclipses and occultations by the Moon. I cannot go into great details here, so let me limit to the following.

Delta T is the difference (at a given instant) between the uniform time-scale known as Dynamical Time, and the Universal Time. The quantity Delta T increases with time, and this occurs more and more rapidly, because the rate of rotation of the Earth is decreasing. Delta T is needed not only for the calculation of exact times of an eclipse or occultation, but also for determining the position of the central line or the zone of visibility (graze line in the case of an occultation, for instance). Indeed, this position depends on Delta T because during the time interval Delta T the Earth is rotating. Knowing that 1 degree corresponds to 4 minutes of time, an error of 240 seconds in Delta T would shift the central line (and all other limits) over 1 degree in the East (or West) direction, the geographical latitudes remaining unchanged.

The bad thing is that Delta T is not increasing uniformly. There are irregular (and hence unpredictable) fluctuations. For instance, from 1968 to 1980 Delta T increased by about 1 second per year, but from December 1997 to December 1998 the increase is only half a second. Not only are these fluctuations not predictable, but even the mean variation of Delta T is not known accurately. This mean variation is proportional to the square of the time T elapsed (since a given starting epoch). During the future centuries, and if we express Delta T in seconds of time, will this variation be equal to 25 times the square of T, or to 26 times the square of T? The difference seems not important. It amounts to just 1 second after 1 century, but it is equal to 100 seconds after 10 centuries, and to 900 seconds after 30 centuries. And don't forget that an error of 900 seconds in Delta T results in a shift of almost 4 degrees (to the East or to the West) in the position of the track of a total solar eclipse.

On 2001-01-24 CE Felix Verbelen wrote to Miguel Barcenas:

Originally I wrote the page on delta T in 1999, and at that time of course the dT value for 2000 was an extrapolation.

The rounded value is indeed 64 seconds (increasing from 63.83 sec on 1 Jan 2000 to 64.09 sec on 31 Dec 2000).

At present the value of delta T is increasing very slowly.

Other delta T links:

Jean Meeus's Astronomical Algorithms

Lunar Calendars and Eclipse Finder Index
Hermetic Systems Home Page