Coordinate time
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In the theory of relativity, it is convenient to express results in terms of a spacetime coordinate system relative to an implied observer. An event is specified by one time coordinate and three spatial coordinates. The time measured by the time coordinate is referred to as coordinate time to distinguish it from proper time.
In special relativity, the coordinate time (relative to an inertial observer) at an event is the proper time measured by a clock that is at the same location as the event, that is stationary relative to the observer and that has been synchronised to the observer's clock using the Einstein synchronisation convention.
In general relativity, coordinate systems can be chosen more freely. For a clock whose spatial coordinates are constant, the relationship between coordinate time t and proper time τ is given by
,
where g00 is a component of the metric tensor, which incorporates gravitational time dilation.
[edit] Coordinate time scales
A coordinate time scale (or coordinate time standard) is a time standard designed for use as the time coordinate in calculations that need to take account of relativistic effects. The choice of a time coordinate implies the choice of an entire frame of reference.
It is most convenient to use as a time coordinate the proper time of a clock that is notionally infinitely far away from the objects of interest. This notional clock, because it is outside all gravity wells, is not influenced by gravitational time dilation. The proper time of objects within a gravity well will pass more slowly than the coordinate time, even when they are at rest with respect to the coordinate reference frame. Gravitational time dilation must therefore be considered for each object of interest, but the effect is a simple function of the gravitational potential.
There are two purpose-designed coordinate time scales in use in astronomy. Barycentric Coordinate Time is based on a reference frame comoving with the barycentre of the Solar system, and is used for calculating motion of bodies within the Solar system. Geocentric Coordinate Time is based on a reference frame comoving with the geocentre (the centre of Terra), and is used for calculations concerning planetary rotation and satellites.
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