The time it takes for a signal to travel between two locations in space in the gravitational environment of a massive point source with gravitational constant can be derived from the PPN metric Equation (4.1) in the form :
The equations of motion Equation (4.2) and the light time solution Equation (4.4) are both written in terms of an independent time variable, which is called the ephemeris time, or ET. Ephemeris time is simply coordinate time in the chosen coordinate frame, such as a solar system barycentric frame. As such, the ephemeris time differs from the standard International Atomic Time (TAI, Temps Atomique International), measured in SI (Système International) seconds relative to a given epoch, namely the beginning of the year 1958.
When a solar system barycentric frame of reference is used to integrate the equations of motion, the relationship between ET and TAI can be expressed, to an accuracy that is sufficient for the purposes of the Pioneer project18, as[89, 90, 91, 92, 235, 240] (in particular, see Equations (2–26) through (2–28) in .)
There exist alternate expressions with up to several hundred additional periodic terms, which provide greater accuracies. The use of these extended expressions provide transformations of to accuracies of 1 ns .
For the purposes of the investigation of the Pioneer anomaly, the Station Time (ST) is especially significant. The station time is the time kept by the ultrastable oscillators of DSN stations, and it is measured in Universal Coordinated Time (UTC). All data records generated by DSN stations are timestamped using ST, that is, UTC as measured by the station’s clock.
UTC is a discontinuous time scale; it is similar to TAI, except for the regular insertion of leap seconds, which are used to account for minute variations in the Earth’s rate of rotation. Converting from UTC to international atomic time (TAI) requires the addition or subtraction of the appropriate number of leap seconds (ranging between 10 and 32 during the lifetime of the Pioneer missions.) For more details see [240, 331].
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