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 |