The main use of astronomical quantities specified in this way is to calculate other relevant parameters of motion, in order to predict future positions and velocities. The applied tools of the disciplines of
Astronomical quantities can be specified in any of several ways, for example, as a
The word epoch was often used in a different way in older astronomical literature, e.g. during the 18th century, in connection with astronomical tables. At that time, it was customary to denote as "epochs", not the standard date and time of origin for time-varying astronomical quantities, but rather the values at that date and time of those time-varying quantities themselves. In accordance with that alternative historical usage, an expression such as 'correcting the epochs' would refer to the adjustment, usually by a small amount, of the values of the tabulated astronomical quantities applicable to a fixed standard date and time of reference (and not, as might be expected from current usage, to a change from one date and time of reference to a different date and time).
Astronomical data are often specified not only in their relation to an epoch or date of reference but also in their relations to other conditions of reference, such as coordinate systems specified by "
When the data are dependent for their values on a particular coordinate system, the date of that coordinate system needs to be specified directly or indirectly.
The epoch of the coordinate system need not be the same, and often in practice is not the same, as the epoch for the data themselves.
The difference between reference to an epoch alone, and a reference to a certain
The equinox with equator/ecliptic of a given date defines which coordinate system is used.
Most standard coordinates in use today refer to 2000 TT (i.e. to 12h on the
There is a special meaning of the expression "equinox (and ecliptic/equator) of date". When coordinates are expressed as
It can be seen that the date of the coordinate system need not be the same as the epoch of the astronomical quantities themselves. But in that case (apart from the "equinox of date" case described above), two dates will be associated with the data: one date is the epoch for the time-dependent expressions giving the values, and the other date is that of the coordinate system in which the values are expressed.
Epoch 2010 Jan. 4.0 TT . . . =
M 72.00071 . . . . . . . .(2000.0)
n. 0.01076162 .. . . . Peri . 354.75938
a 20.3181594 . . . . . Node . 119.42656
e. 0.5715321 . . . . . Incl .. 24.66109
where the epoch is expressed in terms of Terrestrial Time, with an equivalent Julian date. Four of the elements are independent of any particular coordinate system: M is mean anomaly (deg), n: mean daily motion (deg/d), a: size of semi-major axis (AU), e: eccentricity (dimensionless). But the argument of perihelion,
In the particular set of coordinates exampled above, much of the time-dependence of the elements has been omitted as unknown or undetermined; for example, the element n allows an approximate time-dependence of the element M to be calculated, but the other elements and n itself are treated as constant, which represents a temporary approximation (see
Thus a particular coordinate system (equinox and equator/ecliptic of a particular date, such as J2000.0) could be used forever, but a set of osculating elements for a particular epoch may only be (approximately) valid for a rather limited time, because osculating elements such as those exampled above do not show the effect of future
Nevertheless, the period of validity is a different matter in principle and not the result of the use of an epoch to express the data. In other cases, e.g. the case of a complete analytical theory of the motion of some astronomical body, all of the elements will usually be given in the form of polynomials in interval of time from the epoch, and they will also be accompanied by trigonometrical terms of periodical
Some data and some epochs have a long period of use for other reasons. For example, the boundaries of the