Читать книгу Foundations of Space Dynamics - Ashish Tewari - Страница 21

Instead of the calendar year of 365 mean solar days, the tropical year of 365.242 mean solar days, and the sidereal year of 365.25636 mean solar days, it is much more convenient to use a Julian year of 365.25 mean solar days, which avoids the addition of leap years in carrying out astronomical calculations. A Julian day number () is defined to be the continuous count of the number of mean solar days elapsed since 12:00 noon universal time (UT) on January 1, 4713 BC. Universal time refers to the time taken as 12:00 noon when the sun is directly over the Greenwich meridian (which is defined to be zero longitude). The Julian day number 0 is assigned to the day starting at that time on the Julian proleptic calendar. The Julian date of a general time instant is expressed as the JDN plus the fraction of the 24‐hour day elapsed since the preceding noon UT. Julian dates are thus expressed as a Julian day number plus a decimal fraction. For example, the Julian date for 10:00 a.m. UT on April 21, 2020, is given by J2458960.91667, and the JDN is 2458960. Epochs are listed in ephemeris charts and nautical almanacs according to their Julian dates. Hence a Julian date serves as a common time measure for astronautical calculations involving two events separated in time.

Computation of the Julian date (JD) from a Gregorian calendar date is complicated due to the three calendar cycles used to produce the Julian calendar, namely the solar, the lunar, and the indiction cycles of 28, 19, and 15 year periods, respectively (Seidelmann, 1992). A product of these gives the Julian period of 7980 years. The Julian period begins from 4713 BC, which is chosen to be the first year of solar, lunar, and indiction cycles beginning together. The next epoch when the three cycles begin together will happen at noon UT on January 1, 3268. The following conversion formula for the JDN, truncated to the last integer, uses the numbering of the months from January to December as ; the Gregorian calendar years are numbered such that the year 1 BC is the year zero, , (i.e., 2 BC is , 4713 BC is , etc.); and the day number, , is the last completed day of the month up to noon UT:

(1.4)

This formula calculates the JDN for 09:25 a.m. UT on June 25, 1975, by taking , , , and yields the last truncated integer value as . Then the time elapsed from noon UT on June 24 to 09:25 a.m. UT on June 25 is added as a fraction to give the following Julian date:

An epoch in the Julian date is designated with the prefix , and the suffix being the closest Gregorian calendar date. For example, refers to 12:00 noon UT on January 1, 2000, and has the Julian date of 2451545. Similarly, the epoch , which occurs exactly 100 Julian years before 12:00 noon UT on January 1, 2000, must refer to 12 noon UT on January 0, 1900; hence its date in the Gregorian calendar is December 31, 1899, and its Julian date is 2415020. The difference in the epochs and is therefore mean solar days (which is exactly 100 Julian years).

Since Julian day numbers with the epoch can become very large, it is often convenient to use a later epoch for computing . Epochs can be chosen with simpler figures, such as 12:00 hr. UT on November 16, 1858, which has . Then Julian dates can be converted to this epoch by replacing with . For example, the Julian date for 09:25 a.m. UT, June 25, 1975, converted to the epoch of Nov. 16, 1858, is . For the consistency of data, all modern astronomical calculations are reduced to the epoch, , by international agreement. This means that all the Julian dates must be converted to this epoch by replacing with .