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 celestial mechanics or its subfield orbital mechanics (for predicting orbital paths and positions for bodies in motion under the gravitational effects of other bodies) can be used to generate an ephemeris, a table of values giving the positions and velocities of astronomical objects in the sky at a given time or times.
Alternatively, the time-varying astronomical quantity can be expressed as a constant, equal to the measure that it had at the epoch, leaving its variation over time to be specified in some other way—for example, by a table, as was common during the 17th and 18th centuries.
[2] 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).
These are defined relative to the (moving) vernal equinox position, which itself is determined by the orientations of the Earth's rotation axis and orbit around the Sun.
An example is as follows: For minor planet (5145) Pholus, orbital elements have been given including the following data:[3] where the epoch is expressed in terms of Terrestrial Time, with an equivalent Julian date.
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 perturbations specified appropriately.
In that case, their period of validity may stretch over several centuries or even millennia on either side of the stated epoch.
So, some stellar positions read from a star atlas or catalog for a sufficiently old epoch require proper motion corrections as well, for reasonable accuracy.
Due to precession and proper motion, star data become less useful as the age of the observations and their epoch, and the equinox and equator to which they are referred, get older.
The following standard ways of specifying epochs and equinoxes seem the most popular: All three of these are expressed in TT = Terrestrial Time.
In addition, an epoch optionally prefixed by "J" and designated as a year with decimals (2000 + x), where x is either positive or negative and is quoted to 1 or 2 decimal places, has come to mean a date that is an interval of x Julian years of 365.25 days away from the epoch J2000 = JD 2451545.0 (TT), still corresponding (in spite of the use of the prefix "J" or word "Julian") to the Gregorian calendar date of January 1, 2000, at 12h TT (about 64 seconds before noon UTC on the same calendar day).
On the other hand, there has also been an astronomical tradition of retaining observations in just the form in which they were made, so that others can later correct the reductions to standard if that proves desirable, as has sometimes occurred.
But in older astronomical usage, it was usual, until January 1, 1925, to reckon by a noon epoch, 12 hours after the start of the civil day of the same denomination, so that the day began when the mean sun crossed the meridian at noon.
This may be related to the fact that the Egyptians regulated their year by the heliacal rising of the star Sirius, a phenomenon which occurs in the morning just before dawn.
[12] In some cultures following a lunar or lunisolar calendar, in which the beginning of the month is determined by the appearance of the New Moon in the evening, the beginning of the day was reckoned from sunset to sunset, following an evening epoch, e.g. the Jewish and Islamic calendars[13] and in Medieval Western Europe in reckoning the dates of religious festivals,[14] while in others a morning epoch was followed, e.g. the Hindu and Buddhist calendars.