Tropical Year - Time Scales

Time Scales

As mentioned in History, advances in time-keeping have resulted in various time scales. One useful time scale is Universal Time (especially the UT1 variant), which is the mean solar time at 0 degrees longitude (the Greenwich meridian). One second of UT is 1/86,400 of a mean solar day. This time scale is known to be somewhat variable. Since all civil calendars count actual solar days, all civil calendars are based on UT.

The other time scale has two parts. Ephemeris time (ET) is the independent variable in the equations of motion of the solar system, in particular, the equations in use from 1960 to 1984. (McCarthy & Seidelmann, 2009, p. 378) That is, the length of the second used in the solar system calculations could be adjusted until the length that gives the best agreement with observations is found. With the introduction of atomic clocks in the 1950s, it was found that ET could be better realized as atomic time. This also means that ET is a uniform time scale, as is atomic time. ET was given a new name, Terrestrial Time (TT), and for most purposes ET = TT = International Atomic Time + 32.184 SI seconds. As of January 2010, TT is ahead of UT1 by about 66 seconds. (International Earth Rotation Service, 2010; McCarthy & Seidelman, 2009, pp. 86–7).

As explained below, long term estimates of the length of the tropical year were used in connection with the reform of the Julian calendar, which resulted in the Gregorian calendar. Of course the participants in that reform were unaware of the non-uniform rotation of the earth, but now this can be taken into account to some degree. The amount that TT is ahead of UT1 is known as ΔT, or Delta T. The table below gives Morrison and Stephenson's (S & M) 2004 estimates and standard errors (σ) for dates significant in the process of developing the Gregorian calendar.

The low precision extrapolations are computed with an expression provided by Morrison and Stephenson

ΔT = −20 + 32t2

where t is measured in Julian centuries from 1820. The extrapolation is provided only to show ΔT is not negligible when evaluating the calendar for long periods; Borkowski (1991, p. 126) cautions that "many researchers have attempted to fit a parabola to the measured ΔT values in order to determine the magnitude of the deceleration of the Earth's rotation. The results, when taken together, are rather discouraging."