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The Tibetan calendar. Calculation of the start date of months, double months, etc.

How do I calculate monthly data for a year?

     According to Tibetan astrology, it should be taken into account that there can be 12 or 13 months in a year. Accordingly, there is a certain point that can mislead and complicate further life. This refers to the calculation of the so-called extra month, which can be any of the months of the year (for example, this year 2019 has a second first month).


     Due to the ratio of 67 to 65 (the number of lunar months in relation to solar months), there is one additional month in every 33.5 months (we will need this ratio later in the calculations). That is, if we divide the month number (ordinal from the initial base date) and select the whole part, we get a number that differs from the previous one - this means the beginning of a new cycle to determine the next double month. The calculations in the material will be indicated on the basis of several years. One year without an additional month and two years with additional months. This variation will be accepted for clarity.
     So, what is the general sequence of operations? There are several stages here.
1. The definition of the first lunar month, as it was done in the previous materials.
2. Drawing up a table for 13 months (with a margin of one month) for the remaining calculations. The table contains the ordinal number of months from the start date and the ordinal number of the month in the year
3. Determining the number of cycles of double months that have passed since the beginning (divide by 33.5 and subtract a possible correction of 0.02)
4. Finding a double month when the data obtained in paragraph 3 of data.
5. If there is a double month, we change the sequence numbers of the months in the year.
6. Determination of the modified Julian date
7. Determination of the Gregorian date
8. Determining the nearest new moon
9. Determining the beginning of civil twilight on the day of the new moon to accurately determine the beginning of the month (if after twilight, then the beginning goes to the next day)
10. Publishing a list of months for the calendar
     As you can see, the number of actions is very small. In addition, some of them can be done either on a calculator, or find data on some Internet sites on astronomy.
     Next, we will focus a little more on the calculations. Calculations will be made for the following years: 2018, 2019, 2016. The results of all operations will be tabulated for convenience.

1. So. Based on the definition of the data for gyalpo-losar, we find the number of the first month (losar) for the year.
2016: 37181
2018: 37206
2019: 37218
2. We make a table with records for 13 months (adding one month to twelve, just in case, since we may not know in advance whether there will be an additional one). The table will be a summary for all three years.
Initially, it will look like this:

  2016     2018     2019  
37181 1   37206 1   37218 1  
37182 2   37207 2   37219 2  
37183 3   37208 3   37220 3  
37184 4   37209 4   37221 4  
37185 5   37210 5   37222 5  
37186 6   37211 6   37223 6  
37187 7   37212 7   37224 7  
37188 8   37213 8   37225 8  
37189 9   37214 9   37226 9  
37190 10   37215 10   37227 10  
37191 11   37216 11   37228 11  
37192 12   37217 12   37229 12  
37193 1   37218 1   37230 1  

3-5. Make the calculation according to point three and supplement the table with the obtained values

  2016     2018     2019  
37181 1 1109 37206 1 1110 37218 1 1110
37182 2 1109 37207 2 1110 37219 2 1110
37183 3 1109 37208 3 1110 37220 3 1111
37184 4 1109 37209 4 1110 37221 4 1111
37185 5 1109 37210 5 1110 37222 5 1111
37186 6 1110 37211 6 1110 37223 6 1111
37187 7 1110 37212 7 1110 37224 7 1111
37188 8 1110 37213 8 1110 37225 8 1111
37189 9 1110 37214 9 1110 37226 9 1111
37190 10 1110 37215 10 1110 37227 10 1111
37191 11 1110 37216 11 1110 37228 11 1111
37192 12 1110 37217 12 1110 37229 12 1111
37193 1 1110 37218 1 1110 37230 1 1111

     So. As we can see, there were no changes in the values of the double-month coefficient in 2018. Therefore, there is no such situation in 2018. We can safely delete entry number thirteen about the first month of next year.
     In 2016, the record change is present in the fifth and sixth months. That is, a new loop starts with an entry that starts with the sixth line. And the line before changing the value is an additional month.
     In 2019, the record change is present in the second and third months. That is, a new loop starts with an entry that starts with the third line. And the line before changing the value is an additional month. If there is a double month, the data preceding the change in the coefficient for determining the double month must be changed by one. It is also necessary to rebuild the table taking into account the received changes. As a result, we get:

  2016     2018     2019  
37181 1 1109 37206 1 1110 37218 1 1110
37182 2 1109 37207 2 1110 37219 1 1110
37183 3 1109 37208 3 1110 37220 2 1111
37184 4 1109 37209 4 1110 37221 3 1111
37185 4 1109 37210 5 1110 37222 4 1111
37186 5 1110 37211 6 1110 37223 5 1111
37187 6 1110 37212 7 1110 37224 6 1111
37188 7 1110 37213 8 1110 37225 7 1111
37189 8 1110 37214 9 1110 37226 8 1111
37190 9 1110 37215 10 1110 37227 9 1111
37191 10 1110 37216 11 1110 37228 10 1111
37192 11 1110 37217 12 1110 37229 11 1111
37193 12 1110       37230 12 1111

6-10. At the moment, we have determined which months will be double, which will not.

     Now we need to define modified Julian dates to approximate the start time of a new month. The table will change its appearance somewhat, since we no longer need columns with coefficients. Now let's build the tables for each year separately (for clarity)
     The calculation of the modified Julian date should be carried out according to the formula:
-1040550,3932+(номер месяца)*29,530588
     Based on various network services, we determine the Gregorian date (we will not give calculations here either, although they are simple). We can find the dates of new moons for different years on the Web. Therefore, we will not carry out the calculation (it is quite long). In the table, we will enter data for Moscow (for other cities, the occurrence of this event, and, accordingly, the months, may be different). We also determine the time of civil twilight and remember that if the date of the event occurred after them, then the event, according to Tibetan astrology, is postponed to the next day.

2016

Month number Month of the year Date (MJD) Date (Grig.) New Moon morning twilight Start of the month
37181 1 57426.399228 07.02.2016 21:34 08.02.2016 17:38:52 7:32 09.02.2016
37182 2 57455.929816 08.03.2016 10:18 09.03.2016 04:54:36 6:22 09.03.2016
37183 3 57485.460404 06.04.2016 23:02 07.04.2016 14:23:53 5:05 08.04.2016
37184 4 57514.990992 06.05.2016 11:47 06.05.2016 22:29:36 3:48 07.05.2016
37185 4 57544.52158 05.06.2016 00:31 05.06.2016 05:59:39 2:50 06.06.2016
37186 5 57574.052168 04.07.2016 13:15 04.07.2016 14:01:10 2:53 05.07.2016
37187 6 57603.582756 03.08.2016 01:59 02.08.2016 23:44:45 3:50 03.08.2016
37188 7 57633.113344 01.09.2016 14:43 01.09.2016 12:03:25 4:56 02.09.2016
37189 8 57662.643932 01.10.2016 03:27 01.10.2016 03:11:49 5:56 01.10.2016
37190 9 57692.17452 30.10.2016 16:11 30.10.2016 20:38:38 6:53 31.10.2016
37191 10 57721.705108 29.11.2016 04:55 29.11.2016 15:18:40 7:47 30.11.2016
37192 11 57751.235696 28.12.2016 17.39 29.12.2016 09:53:32 8:12 30.12.2016
37193 12 57780.766284 27.01.2017 06:23 28.01.2017 03:07:12 7:51 28.01.2017

 

2018

Month number Month of the year Date (MJD) Date (Grig.) New Moon morning twilight Start of the month
37206 1 58164.663928 15.02.2018 03:56 16.02.2018 00:05:08 7:14 16.02.2018
37207 2 58194.194516 16.03.2018 16:40 17.03.2018 16:11:52 6:04 18.03.2018
37208 3 58223.725104 15.04.2018 05:24 16.04.2018 04:57:12 4:43 17.04.2018
37209 4 58253.255692 14.05.2018 18:08 15.05.2018 14:47:31 3:29 16.05.2018
37210 5 58282.78628 13.06.2018 06:52 13.06.2018 22:43:15 2:44 14.06.2018
37211 6 58312.316868 12.07.2018 19:36 13.07.2018 05:47:56 3:06 14.07.2018
37212 7 58341.847456 11.08.2018 08:20 11.08.2018 12:57:37 4:08 12.08.2018
37213 8 58371.378044 09.09.2018 21:04 09.09.2018 21:01:32 5:10 10.09.2018
37214 9 58400.908632 09.10.2018 09:48 09.10.2018 06:46:59 6:10 10.10.2018
37215 10 58430.43922 07.11.2018 22:32 07.11.2018 19:01:53 7:06 08.11.2018
37216 11 58459.969808 07.12.2018 11:16 07.12.2018 10:20:21 7:57 08.12.2018
37217 12 58489.500396 06.01.2019 00:00 06.01.2019 04:28:19 8:11 06.01.2019

 

2019

 

Month number Month of the year Date (MJD) Date (Grig.) New Moon morning twilight Start of the month
37218 1 58519.030984 04.02.2019 12:44 05.02.2019 00:03:21 7:36 05.02.2019
37219 1 58548.561572 06.03.2019 01:28 06.03.2019 19:03:50 6:32 07.03.2019
37220 2 58578.09216 04.04.2019 14:12 05.04.2019 11:50:33 5:13 06.04.2019
37221 3 58607.622748 04.05.2019 02:56 05.05.2019 01:45:16 3:53 05.05.2019
37222 4 58637.153336 02.06.2019 15:40 03.06.2019 13:01:38 2:54 03.04.2019
37223 5 58666.683924 02.07.2019 04:24 02.07.2019 22:16:09 2:50 03.07.2019
37224 6 58696.214512 31.07.2019 17:08 01.08.2019 06:11:51 3:45 02.08.2019
37225 7 58725.7451 30.08.2019 05:52 30.08.2019 13:37:00 4:49 31.08.2019
37226 8 58755.275688 08.09.2019 18:36 28.09.2019 21:26:19 5:48 29.09.2019
37227 9 58784.806276 28.10.2019 07:21 28.10.2019 06:38:27 6:47 28.10.2019
37228 10 58814.336864 26.11.2019 20:05 26.11.2019 18:05:37 7:41 27.11.2019
37229 11 58843.867452 26.12.2019 08:49 26.12.2019 08:13:12 8:12 27.12.2019
37230 12 58873.39804 24.01.2020 21:33 25.01.2020 00:41:54 7:54 25.01.2020


10. Publishing a list of months for the calendar

2016

Month Start
1 09.02.2016
2 09.03.2016
3 08.04.2016
4 07.05.2016
4 (d) 06.06.2016
5 05.07.2016
6 03.08.2016
7 02.09.2016
8 01.10.2016
9 31.10.2016
10 30.11.2016
11 30.12.2016
12 28.01.2017

2018

Month Start
1 16.02.2018
2 18.03.2018
3 17.04.2018
4 16.05.2018
5 14.06.2018
6 14.07.2018
7 12.08.2018
8 10.09.2018
9 10.10.2018
10 08.11.2018
11 08.12.2018
12 06.01.2019

2019

Month Start
1 05.02.2019
1 (d) 07.03.2019
2 06.04.2019
3 05.05.2019
4 03.04.2019
5 03.07.2019
6 02.08.2019
7 31.08.2019
8 29.09.2019
9 28.10.2019
10 27.11.2019
11 27.12.2019
12 25.01.2020

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