## Epochs for coordinate systems

The equatorial coordinate system used for celestial measurements depends on the orientation of the earth, and this is a continuously changing function of time

(Section 3.2). The time chosen during some period (usually decades) for the specification of celestial coordinates in catalogs and communications between astronomers is called the standard epoch, traditionally expressed in years.

The standard epochs in use in the last century, B1900.0 and B1950.0 were based on the Besselian year which begins when the mean sun is at a = 18 h 40 m. As noted in Section 3.2, B1950.0 occurred about 2 hours before the New Year of 1950.

The standard epoch in use today is J2000.0 (TDB); it is based on the Julian century/day/second system just described. The epoch J2000.000 was set to occur exactly at 2000 Jan. 1,12 h (TDB), i.e., at JD 2 451 545.0 (TDB). All other epochs E are defined relative to this,

where E is the epoch in years, e.g., E = 1991.25 is the approximate mean epoch of the observations made by the Hipparcos satellite. From (17) one finds

J1900.0 = JD 2415 020.0 (TDB) = 1899 Dec. 31, 12 h TDB J1991.25 = JD 2448 349.0625 (TDB) = 1991 Apr. 2, 13 h 30 m TDB J2000.0 = JD 2451 545.0 (TDB) = 2000 Jan. 1, 12 h TDB (4.18) J2100.0 = JD 2488 070.0 (TDB) = 2100 Jan. 1, 12 h TDB J2200.0 = JD 2 524595.0 (TDB) = 2200 Jan. 2, 12 h TDB

Each of the century epochs in (17) will occur somewhat before UTC noon according to the TT - UTC offsets; see Table 1. Recall that TDB differs from TT by at most 1.7 ms. Although the definition of epoch is based on TDB time, one would do well to eliminate the possibility of confusion by writing J2000.0 (TDB). Sometimes one sees J2000.0 (TT) which is effectively the same thing, within 1.7 ms. One often sees simply J2000.

The two epochs J1900 and J2000 are separated by a Julian century, exactly 36 525 d; see (17). This leads to a one-day date shift in the Gregorian calendar date because it has no leap day added in 1900 February whereas the older Julian calendar does. (See Section 3 above, "Calendar".) Thus this Gregorian century was one day shorter than the Julian century, namely 36 524 d (to better match the tropical year). The next century yielded identical dates because 2000 was a leap year in both calendars, and the following century again differs because 2100 will not be a (Gregorian) leap year.

This system of Julian centuries thus gradually gets out of step with the Gregorian calendar just as Caesar's calendar got out of step with the seasons, by 3 d every 400 yr or 15 d in 2000 yr. Does this mean that astronomers have adopted again

Caesar's calendar for the epoch definition? Not really, because they do not give month names to it, nor do they live by it. Although they do use the length of the Julian century, they chose not to set the J2000.0 epoch to the extrapolation of the New Year from Caesar's Julian calendar, but rather defined J2000.0 to be on 2000 Jan. 1 of the Gregorian calendar, and set it at noon rather than at midnight, following Scaliger's convention for the Julian date.

In another 2000 yr, J4000.0 will occur on Jan. 16 12 h (TDB). On this date, at a rate of insertion of leap seconds into UTC of somewhat less than one per year, TT time will be advanced over UTC by, say, 1500 s more than today's ~1 min offset. Thus J4000.0 should occur roughly 26 minutes before UTC noon on 4000 Jan. 16.

A modified Julian date (MJD) defined as MJD = JD - 2 400 000.5 is sometimes used. It starts at midnight in Greenwich rather than at noon. MJD is a smaller number than JD and thus is less cumbersome to use in plots and text. Again, if precision is required, one should specify MJD(UTC), MJD(TT) or MJD(TDB).

### Signals from pulsars

The timing of signals from outer space has long been a fundamental part of astronomy. The discovery of radio pulsars extended this aspect of astronomy to very short time scales, to seconds and milliseconds. These rotating neutron stars emit a pulse of radio noise once each rotation. The pulse is probably due to acceleration of electrons along the magnetic field lines emerging from the pole of the star. The rotation rate of these stars can be very stable if they have minimal energy loss from magnetic dipole radiation. The pulsar PSR 1937 + 21 is particularly stable; it has a pulse period of 1.6 ms, and its stability rivals that of atomic time. The time standard does not now make use of the signals from such pulsars, but it may come to pass that certain pulsars will become an important time keeping standard.

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