June 20 (or 21 or 22) a.k.a the
Summer Solstice was the longest day of the year in some countries.
For various reasons (please specify in the solution) the date varies from year to year, but (good news!) it is fully predictable.
Please describe how to find the dates of
Solstices and Equinoxes in this century and for that matter for any year, but list them for this century, to allow comparison to published lists, specifying the name and location
of your choice, Northern or Southern Hemisphere and the Time Zone.
Default: Paris, France.
The average time from one year until the next, astronomically, is 365.2422 days -- the tropical year. As you can see from the coefficients of Y in the below formulae, it's not the same for the different equinoxes or solstices. That's the result of the aphelion and perihelion of the earth's orbit around the sun moving realative to the seasons and the earth moves in its orbit fastest at perihelion, currently in January and slowest at aphelion, currently in July. The seasons themselves occur: equinox--when the plane of the earth's equator intersects the sun, and solstice, when that plane is at its maximum distance from the sun.
clearvars , clc
for Y=2000:2100
y=Y/1000;
JD1=1721139.2855+365.2421376*Y+.067919*y^2-.0027879*y^3; % March Equinox
JD2=1721233.2486+365.2417284*Y-.053018*y^2+.0093320*y^3; % June Solstice
JD3=1721325.6978+365.2425055*Y-.126689*y^2+.0019401*y^3; % September Equinox
JD4=1721414.3920+365.2428898*Y-.010965*y^2-.0084885*y^3; % December Solstice
dt1=datetime(JD1,'ConvertFrom','juliandate');
dt1.Format=('yyyy-MM-dd HH:mm');
dt2=datetime(JD2,'ConvertFrom','juliandate');
dt3=datetime(JD3,'ConvertFrom','juliandate');
dt4=datetime(JD4,'ConvertFrom','juliandate');
disp([dt1 dt2 dt3 dt4])
end
% Formulae from Astronomical Formulae for Calculators
% by Jean Meeus, Willmann-Bell, Richmond, VA, USA 1988
% which says the times will generally be no more than 15 minutes off.
Even more accurate formulae may be obtained in the same author's Astronomical Algorithms
The major change from year to year in the short term is the cycle of ordinary vs leap years. Note the average number of days between the same equinox or solstice from one year to the next is about 365.2422 days: the tropical year. That extra, almost a quarter of a day results in the event coming later in the same day in the case there is no intervening leap day or may carry over to the next day. Then, when a leap day comes along, its set back a day, but slightly more than enough to counter the forward buildup of the preceding three years. Notice how the March equinox built up from 7:26 on the 20th in 2000, all the way through to almost an hour into March 21 by 2003. Then an intervening leap year day in 2004 brought it back to March 20 but about 3/4 hour earlier than four years previous. That's why 2100, like 1800 before it, won't be a leap year, making up for the inaccuracy of the 365.25 average when having leap year every four years. In the 20th century June 22 (GMT) was quite common for the Solstice, but the fact that 1900 was retained as a leap year allowed the dates to regress so that the 21st century has no June 22 dates, only June 20 and 21 (GMT).
Notice that not all the events of the year occur the same number of fractions of a day until the next one. This is the result of the position of the perihelion and aphelion of the earth's orbit around the sun. The earth is travelling fastest around the sun in January and slowest in July. If that were constant they still would all have the same interval, but these closest (fastest) and farthest (slowest) points in the orbit are moving ever so slowly, but enough to affect how long one season lasts vs another, another way of saying the equinoxes and solstices are not only not evenly spaced in the year (which would be the case even if the apo-/perihelion were fixed points), but the relative sizes are changing so the equinox and solstice intervals from one year to the next differ for the different events depending on where in the year/orbit they occur. The square and cube terms reflect changes in the rate of change, which you can see is slow as lower case y is measured in millenia rather than years.
Knowing that the JD values calculated in the program are sequential counts of days, and doing the math, we find at the beginning of the century, winter, spring, summer and fall are respectively 88.993, 92.757, 93.650, and 89.843 days long. Winter is shortest as earth is closest to the sun and going fastest in its orbit in January. By the end of the century the respective numbers are 88.958, 92.683, 93.687, and 89.914 days, as the actual position (average date and time) within January of perihelion is changing (getting later), thus changinge the numbers so Spring is getting shorter while Fall is getting longer by a few minutes during the present century as perihelion gets closer to spring and aphelion gets closer to fall.
The program produces this list, with GMT (aka UT) shown; adjust for time zone and DST:
(remember that accuracy is to within 1/4 hour)
Also remember, you're on your own deducing Paris time from GMT, regarding time zone changes as well as observance of Daylight Saving Time, aka Summer Time. Paris is ordinarily 1 hour beyond GMT, but in summer, 2 hours. Take 2010's December solstice, at 23:41 GMT on the 21st; being 1 hour ahead of GMT, it's already 1:41 on the 22nd.
2000-03-20 07:26 2000-06-21 01:37 2000-09-22 17:13 2000-12-21 13:26
2001-03-20 13:15 2001-06-21 07:25 2001-09-22 23:01 2001-12-21 19:15
2002-03-20 19:04 2002-06-21 13:13 2002-09-23 04:50 2002-12-22 01:05
2003-03-21 00:53 2003-06-21 19:01 2003-09-23 10:38 2003-12-22 06:54
2004-03-20 06:42 2004-06-21 00:49 2004-09-22 16:27 2004-12-21 12:44
2005-03-20 12:31 2005-06-21 06:37 2005-09-22 22:15 2005-12-21 18:33
2006-03-20 18:20 2006-06-21 12:25 2006-09-23 04:04 2006-12-22 00:23
2007-03-21 00:09 2007-06-21 18:13 2007-09-23 09:52 2007-12-22 06:13
2008-03-20 05:58 2008-06-21 00:01 2008-09-22 15:41 2008-12-21 12:02
2009-03-20 11:47 2009-06-21 05:49 2009-09-22 21:29 2009-12-21 17:52
2010-03-20 17:36 2010-06-21 11:37 2010-09-23 03:18 2010-12-21 23:41
2011-03-20 23:25 2011-06-21 17:25 2011-09-23 09:06 2011-12-22 05:31
2012-03-20 05:14 2012-06-20 23:13 2012-09-22 14:55 2012-12-21 11:20
2013-03-20 11:03 2013-06-21 05:01 2013-09-22 20:43 2013-12-21 17:10
2014-03-20 16:52 2014-06-21 10:49 2014-09-23 02:32 2014-12-21 22:59
2015-03-20 22:41 2015-06-21 16:37 2015-09-23 08:20 2015-12-22 04:49
2016-03-20 04:30 2016-06-20 22:25 2016-09-22 14:09 2016-12-21 10:38
2017-03-20 10:19 2017-06-21 04:12 2017-09-22 19:57 2017-12-21 16:28
2018-03-20 16:08 2018-06-21 10:00 2018-09-23 01:46 2018-12-21 22:18
2019-03-20 21:57 2019-06-21 15:48 2019-09-23 07:34 2019-12-22 04:07
2020-03-20 03:46 2020-06-20 21:36 2020-09-22 13:23 2020-12-21 09:57
2021-03-20 09:35 2021-06-21 03:24 2021-09-22 19:11 2021-12-21 15:46
2022-03-20 15:25 2022-06-21 09:12 2022-09-23 01:00 2022-12-21 21:36
2023-03-20 21:14 2023-06-21 15:00 2023-09-23 06:48 2023-12-22 03:25
2024-03-20 03:03 2024-06-20 20:48 2024-09-22 12:37 2024-12-21 09:15
2025-03-20 08:52 2025-06-21 02:36 2025-09-22 18:25 2025-12-21 15:04
2026-03-20 14:41 2026-06-21 08:24 2026-09-23 00:14 2026-12-21 20:54
2027-03-20 20:30 2027-06-21 14:12 2027-09-23 06:02 2027-12-22 02:43
2028-03-20 02:19 2028-06-20 20:00 2028-09-22 11:51 2028-12-21 08:33
2029-03-20 08:08 2029-06-21 01:48 2029-09-22 17:39 2029-12-21 14:23
2030-03-20 13:57 2030-06-21 07:36 2030-09-22 23:28 2030-12-21 20:12
2031-03-20 19:46 2031-06-21 13:24 2031-09-23 05:16 2031-12-22 02:02
2032-03-20 01:35 2032-06-20 19:12 2032-09-22 11:05 2032-12-21 07:51
2033-03-20 07:24 2033-06-21 01:00 2033-09-22 16:53 2033-12-21 13:41
2034-03-20 13:13 2034-06-21 06:48 2034-09-22 22:42 2034-12-21 19:30
2035-03-20 19:02 2035-06-21 12:35 2035-09-23 04:31 2035-12-22 01:20
2036-03-20 00:51 2036-06-20 18:23 2036-09-22 10:19 2036-12-21 07:09
2037-03-20 06:40 2037-06-21 00:11 2037-09-22 16:08 2037-12-21 12:59
2038-03-20 12:29 2038-06-21 05:59 2038-09-22 21:56 2038-12-21 18:48
2039-03-20 18:18 2039-06-21 11:47 2039-09-23 03:44 2039-12-22 00:38
2040-03-20 00:07 2040-06-20 17:35 2040-09-22 09:33 2040-12-21 06:28
2041-03-20 05:56 2041-06-20 23:23 2041-09-22 15:21 2041-12-21 12:17
2042-03-20 11:45 2042-06-21 05:11 2042-09-22 21:10 2042-12-21 18:07
2043-03-20 17:34 2043-06-21 10:59 2043-09-23 02:58 2043-12-21 23:56
2044-03-19 23:23 2044-06-20 16:47 2044-09-22 08:47 2044-12-21 05:46
2045-03-20 05:12 2045-06-20 22:35 2045-09-22 14:35 2045-12-21 11:35
2046-03-20 11:01 2046-06-21 04:23 2046-09-22 20:24 2046-12-21 17:25
2047-03-20 16:50 2047-06-21 10:11 2047-09-23 02:12 2047-12-21 23:14
2048-03-19 22:39 2048-06-20 15:59 2048-09-22 08:01 2048-12-21 05:04
2049-03-20 04:28 2049-06-20 21:47 2049-09-22 13:49 2049-12-21 10:53
2050-03-20 10:17 2050-06-21 03:35 2050-09-22 19:38 2050-12-21 16:43
2051-03-20 16:06 2051-06-21 09:23 2051-09-23 01:26 2051-12-21 22:33
2052-03-19 21:55 2052-06-20 15:11 2052-09-22 07:15 2052-12-21 04:22
2053-03-20 03:44 2053-06-20 20:58 2053-09-22 13:03 2053-12-21 10:12
2054-03-20 09:33 2054-06-21 02:46 2054-09-22 18:52 2054-12-21 16:01
2055-03-20 15:22 2055-06-21 08:34 2055-09-23 00:40 2055-12-21 21:51
2056-03-19 21:11 2056-06-20 14:22 2056-09-22 06:29 2056-12-21 03:40
2057-03-20 03:00 2057-06-20 20:10 2057-09-22 12:17 2057-12-21 09:30
2058-03-20 08:49 2058-06-21 01:58 2058-09-22 18:06 2058-12-21 15:19
2059-03-20 14:39 2059-06-21 07:46 2059-09-22 23:54 2059-12-21 21:09
2060-03-19 20:28 2060-06-20 13:34 2060-09-22 05:43 2060-12-21 02:58
2061-03-20 02:17 2061-06-20 19:22 2061-09-22 11:31 2061-12-21 08:48
2062-03-20 08:06 2062-06-21 01:10 2062-09-22 17:20 2062-12-21 14:38
2063-03-20 13:55 2063-06-21 06:58 2063-09-22 23:08 2063-12-21 20:27
2064-03-19 19:44 2064-06-20 12:46 2064-09-22 04:57 2064-12-21 02:17
2065-03-20 01:33 2065-06-20 18:34 2065-09-22 10:45 2065-12-21 08:06
2066-03-20 07:22 2066-06-21 00:22 2066-09-22 16:34 2066-12-21 13:56
2067-03-20 13:11 2067-06-21 06:10 2067-09-22 22:22 2067-12-21 19:45
2068-03-19 19:00 2068-06-20 11:58 2068-09-22 04:11 2068-12-21 01:35
2069-03-20 00:49 2069-06-20 17:46 2069-09-22 09:59 2069-12-21 07:24
2070-03-20 06:38 2070-06-20 23:34 2070-09-22 15:48 2070-12-21 13:14
2071-03-20 12:27 2071-06-21 05:22 2071-09-22 21:36 2071-12-21 19:03
2072-03-19 18:16 2072-06-20 11:09 2072-09-22 03:25 2072-12-21 00:53
2073-03-20 00:05 2073-06-20 16:57 2073-09-22 09:13 2073-12-21 06:42
2074-03-20 05:54 2074-06-20 22:45 2074-09-22 15:02 2074-12-21 12:32
2075-03-20 11:43 2075-06-21 04:33 2075-09-22 20:50 2075-12-21 18:22
2076-03-19 17:32 2076-06-20 10:21 2076-09-22 02:39 2076-12-21 00:11
2077-03-19 23:21 2077-06-20 16:09 2077-09-22 08:27 2077-12-21 06:01
2078-03-20 05:10 2078-06-20 21:57 2078-09-22 14:16 2078-12-21 11:50
2079-03-20 10:59 2079-06-21 03:45 2079-09-22 20:04 2079-12-21 17:40
2080-03-19 16:48 2080-06-20 09:33 2080-09-22 01:53 2080-12-20 23:29
2081-03-19 22:37 2081-06-20 15:21 2081-09-22 07:41 2081-12-21 05:19
2082-03-20 04:26 2082-06-20 21:09 2082-09-22 13:30 2082-12-21 11:08
2083-03-20 10:15 2083-06-21 02:57 2083-09-22 19:18 2083-12-21 16:58
2084-03-19 16:04 2084-06-20 08:45 2084-09-22 01:07 2084-12-20 22:47
2085-03-19 21:53 2085-06-20 14:33 2085-09-22 06:55 2085-12-21 04:37
2086-03-20 03:42 2086-06-20 20:21 2086-09-22 12:44 2086-12-21 10:26
2087-03-20 09:31 2087-06-21 02:09 2087-09-22 18:32 2087-12-21 16:16
2088-03-19 15:20 2088-06-20 07:57 2088-09-22 00:21 2088-12-20 22:05
2089-03-19 21:09 2089-06-20 13:45 2089-09-22 06:09 2089-12-21 03:55
2090-03-20 02:59 2090-06-20 19:32 2090-09-22 11:58 2090-12-21 09:45
2091-03-20 08:48 2091-06-21 01:20 2091-09-22 17:46 2091-12-21 15:34
2092-03-19 14:37 2092-06-20 07:08 2092-09-21 23:34 2092-12-20 21:24
2093-03-19 20:26 2093-06-20 12:56 2093-09-22 05:23 2093-12-21 03:13
2094-03-20 02:15 2094-06-20 18:44 2094-09-22 11:11 2094-12-21 09:03
2095-03-20 08:04 2095-06-21 00:32 2095-09-22 17:00 2095-12-21 14:52
2096-03-19 13:53 2096-06-20 06:20 2096-09-21 22:48 2096-12-20 20:42
2097-03-19 19:42 2097-06-20 12:08 2097-09-22 04:37 2097-12-21 02:31
2098-03-20 01:31 2098-06-20 17:56 2098-09-22 10:25 2098-12-21 08:21
2099-03-20 07:20 2099-06-20 23:44 2099-09-22 16:14 2099-12-21 14:10
2100-03-20 13:09 2100-06-21 05:32 2100-09-22 22:02 2100-12-21 20:00
The full century is shown regardless of whether you cosider centuries to begin with '00 years of '01 years.
|
|
Posted by Charlie
on 2021-07-06 11:47:55 |
a solution
