The date of a double star observation should be expressed as the year in fractional form, usually to three or four decimal places. This is known as the epoch of the observation. There are two forms of epoch: the Besselian epoch and the Julian epoch.

The Besselian epoch is based on the length of the Besselian year of approximately 365.2422 days and is given by

Besselian epoch = B1900 + (JD - 2415020.31352) / 365.242198781

where the prefix B indicates that it is a Besselian epoch, JD is the Julian date and the constant 2415020.31352 is the Julian date of the standard epoch B1900, i.e. 1900 January 0 (= 1899 December 31).

The Julian epoch was introduced with the new astronomical constants in 1984. It is based on the length of the Julian year of exactly 365.25 days and is given by

where the prefix J indicates that the epoch is a Julian epoch and the constant 2451,545 is the Julian date of the standard epoch J2000, i.e. 2000 January 1 at 12 hours Universal Time (UT).

The prefixes B and J are used only where context or accuracy make them necessary.

The Besselian epoch is the one normally used for dating double stars observations and is quoted to three decimal places for visual observations. This means effectively dating each observation to an accuracy of nearly nine hours, so a single epoch value could serve for a whole observing session.

The Julian date (JD) can be found from the following algorithm, where year, month, day and hour refer of course to the time the observation was made.

IF month > 2 THEN ym = year + 1 ELSE ym = year L = INT(7 * ym / 4) + INT(3 * INT((ym + 99) / 100) / 4) J0 = day + INT(275 * month / 9) + 367 * year -

INT means the "integer part of ", or more precisely, the highest integer less than the number, e.g. INT(5.6) = 5, but INT(-5.6) = 6.

The hour is expressed in decimal form, i.e.

so if the time were 21:22:30 then the hour would be 21.375.

J0 is the Julian date at 0 hours UT. Dividing the hour by 24 and adding it to J0 gives JD.

As an example the Julian date and the two epochs for 9 pm UT on Christmas Day 2003 would be:

Julian date = 2452999.375 Besselian epoch = 2003.9832 Julian epoch = 2003.9819.

The Julian date for which both the Besselian and Julian epochs have the same value is 2429698.882870183, i.e. 1940 March 10 at 9:11:20 UT.

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