Editing Terrestrial Time (section)

==Current definition==

TT differs from Geocentric Coordinate Time (TCG) by a constant rate.  Formally it is defined by the equation

<math display="block">\mathrm{TT} = \bigl(1-L_\mathrm{G}\bigr) \times \mathrm{TCG} + E,</math>

where TT and TCG are linear counts of [[SI]] [[second]]s in Terrestrial Time and Geocentric Coordinate Time respectively, <math>L_\mathrm{G}</math> is the constant difference in the rates of the two time scales, and <math>E</math> is a constant to resolve the [[epoch (reference date)|epoch]]s (see below). <math>L_\mathrm{G}</math> is defined as exactly {{val|6.969290134|e=−10}}. Due to the term <math>1-L_\mathrm{G}</math> the rate of TT is very slightly slower than that of TCG.

The equation linking TT and TCG more commonly has the form given by the IAU,

<math display="block">\mathrm{TT} = \mathrm{TCG} - L_\mathrm{G} \times \bigl(\mathrm{JD_{TCG}} - 2443144.5003725\bigr) \times 86400,</math>

where <math>\mathrm{JD_{TCG}}</math> is the TCG time expressed as a [[Julian day|Julian date (JD)]]. The Julian Date is a linear transformation of the raw count of seconds represented by the variable TCG, so this form of the equation is not [[Computer algebra#Simplification|simplified]]. The use of a Julian Date specifies the [[Epoch (astronomy)|epoch]] fully. The above equation is often given with the Julian Date {{gaps|2443|144.5}} for the epoch, but that is inexact (though inappreciably so, because of the small size of the multiplier <math>L_\mathrm{G}</math>). The value {{gaps|2443|144.500|3725}} is exactly in accord with the definition.

Time coordinates on the TT and TCG scales are specified conventionally using traditional means of specifying days, inherited from non-uniform time standards based on the rotation of Earth. Specifically, both Julian Dates and the [[Gregorian calendar]] are used. For continuity with their predecessor [[Ephemeris Time]] (ET), TT and TCG were set to match ET at around Julian Date {{gaps|2443|144.5}} {{nowrap|(1977-01-01T00Z).}} More precisely, it was defined that TT instant {{nowrap|1977-01-01T00:00:32.184}} and TCG instant {{nowrap|1977-01-01T00:00:32.184}} exactly correspond to the [[International Atomic Time]] (TAI) instant {{nowrap|1977-01-01T00:00:00.000.}} This is also the instant at which TAI introduced corrections for [[gravitational time dilation]].

TT and TCG expressed as Julian Dates can be related precisely and most simply by the equation

<math display="block">\mathrm{JD_{TT}} = E_\mathrm{JD} + \bigl(\mathrm{JD_{TCG}} - E_\mathrm{JD}\bigr) \times \bigl(1 - L_\mathrm{G}\bigr),</math>

where <math>E_\mathrm{JD}</math> is {{gaps|2443|144.500|3725}} exactly.