Following Meeus's Astronomical Algorithms for the Calculation of JD

Question

For the Calculation of Julian Day (JD), I followed Chapter 7 of Meeus's Astronomical Algorithms. I could get the numbers mentioned in Example 7.a and 7.b.

On the basis of these methodology, proceeded to calculate JD for the Date 1992 October 13 at 0^h TD (Date mentioned in Example 25.a, Meeus). My Code provides JD for this Date as JD = 2448921.50.

However, for this Date (1992 October 13 00:00:00 UT), each of the URL:

• https://quasar.as.utexas.edu/BillInfo/JulianDateCalc.html
• https://neoprogrammics.com/perpetual_calendar_algorithms/jd_number/index.php

provide 2448921.50 as JDN (Julian Day Number).

However, each of the URL:

• https://www.onlineconversion.com/julian_date.htm
• https://ssd.jpl.nasa.gov/tools/jdc/#/cd
• https://planetcalc.com/503/
• https://milwaukeeastro.org/variable/JD.asp

provide JD = 2448908.5 (Julian Day).

Now, the number 2448908.5 is described as JDE in Example 25.a of Meeus.

Kindly help with the:

1. Calculation of the correct JD corresponding to the Date 1992 October 13 at 0^h TD (Ex.25.a, Meeus).
2. How to obtain JDE from JD.

Thank you.

Answer 1

Please bear in mind first the difference between the Julian calendar and the Julian Date or Julian Day Number. The Julian date or day number is a chronological measure from a continuous count of days. In contrast, the old Julian calendar was a civil calendar in widespread use before the Gregorian calendar reform of the year 1582 (which took quite some time to become accepted in some countries, e.g. in Britain and North America not accepted until 1752). The Julian and Gregorian calendar dates for one and the same natural day are now (20th and 21st centuries) 13 nominal days apart, the difference was 10 days from 1582 to 1700, increasing by one in each recent centurial year except 2000.

JD 2448908.5 is the Julian day reckoning that matches the Gregorian calendar (modern calendar) date of 1992 Oct 13 0h.

JD 2448921.5 is the Julian day reckoning that matches the old unreformed Julian calendar date of 1992 Oct 13 0h, i.e. 13 natural days later than the previous.

Julian day numbers were introduced long ago, when dates and times were always referred to solar time, and when the new scientific time scales had not yet been developed.

The abbreviation 'JDE' was introduced for use on occasions when the date+time was referred to the scientific/astronomical Ephemeris Time scale, which was replaced in turn by Terrestrial Dynamical Time (short-lived in official use) and then Terrestrial Time scales. So far, and for 20th-21st-century dates, the dates+times measured on these various scientific time scales are within a couple of minutes of each other and the mean solar time scale (see the links above). So they make little difference for calendrical purposes. The difference between the Julian date+time expressed in terms of Universal Time UT1 (close to mean solar time) and the same instant in terms of Terrestrial Time is just the quantity ΔT.

Although there is nothing wrong with the Meeus algorithms when carefully and correctly applied, a number of people have found it more convenient and less error-prone to do the calendrical part of the calculations in integer arithmetic. See the following answer
(Calculation of Julian day is off for negative dates) where full details are given.