Javascript ΔT Calculator

With the following Javascript calculator, values for ΔT predicted from the several relations published in the astronomical literature can be displayed simultaneously for comparison.

ΔT Calculator
Year   Lunar acceleration
parameter ("/cy/cy)
   Click for a new
      Update the calculator
  IAU (1952)
  Astronomical Ephemeris (1960)
  Tuckerman (1962, 1964) & Goldstine (1973)
  Muller & Stephenson (1975), Stephenson & Clark (1978)
  Stephenson (1978)
  Morrison & Stephenson (1982)
  Stephenson & Morrison (1984)
  Stephenson & Houlden (1986)
  Espenak (1987, 1989)
  Borkowski (1988)
  Chapront-Touzé & Chapront (1991)
  Chapront, Chapront-Touzé & Francou (1997)
  Reingold & Dershowitz (2001, 2002)
  JPL Horizons
  Espenak & Meeus (2006)
(ΔT is given in minutes)

The influence of the lunar acceleration parameter can also be studied by changing its nominal value of –26.0 arcsec/cy/cy t ther values. Note that the following values were adopted in the original ΔT relations:

ΔT in Astronomical Software and PC Planetarium Programs

Most PC planetarium programs implicitly use one of the above ΔT algorithms in their software but often do not display the calculated value of ΔT or bother to give any details on the algorithm adopted.

One of the few laudable exceptions is Guide (Project Pluto, 1993-1999) that displays the value used for ΔT in the Quick Info section in the Help menu. Version 7 claims to use the single-parabolic fit of Morrison & Stephenson (1982), but in fact uses the double-parabolic fit of Stephenson & Houlden (1986).

The treatment of ΔT in the online ephemeris generator on the JPL Horizons website is inconsistent. One of their relations is based on a lunar acceleration parameter of –26.0 arcsec/cy/cy while their ephemerides are based on a value of –25.7376 arcsec/cy/cy. Their relations also imply a nearly 9-minute jump in ΔT around 948 CE.