L’Equazione del Tempo
Nella seguente tabella ciascun valore quotidiano dell’equazione del tempo è il risultato della media aritmetica dei veri valori calcolati in un periodo di 400 anni, dal 2001 al 2400 (durata media anno: 365.2425d ), riferiti alle 11:00 TD di ogni giorno.
I valori dell’equazione vengono espressi sia nel formato minuti-secondi sia in quello minuti.decimali
La scelta di considerare il periodo di 400 anni, anziché di 10, 20 o 100 ecc. non è certo casuale: com’è noto 400 sono gli anni dopo i quali si ripete il ciclo alla base dell’attuale calendario gregoriano, che con 365.2425d di media all’annod ) in maniera tutto sommato ragionevolmente semplice e precisa
La scelta di riferire il periodo agli anni 2001-2400, invece, deriva unicamente dal trovarci attualmente in quest’epoca, con lo sguardo al futuro…
Valori quotidiani
GEN FEB MAR APR MAG GIU LUG AGO SET OTT NOV DIC 1 +2m 58s +2.97m +13m 06s +13.10m +12m 03s +12.05m +3m 49s +3.81m −2m 45s −2.74m −1m 49s −1.82m +4m 18s +4.30m +6m 43s +6.72m +0m 15s +0.25m −10m 15s −10.25m −16m 32s −16.54m −11m 20s −11.33m 2 +3m 26s +3.44m +13m 14s +13.24m +11m 52s +11.86m +3m 32s +3.53m −2m 51s −2.85m −1m 39s −1.65m +4m 29s +4.49m +6m 39s +6.64m −0m 05s −0.08m −10m 35s −10.58m −16m 34s −16.56m −10m 57s −10.95m 3 +3m 54s +3.90m +13m 21s +13.36m +11m 40s +11.66m +3m 14s +3.24m −2m 57s −2.95m −1m 29s −1.49m +4m 41s +4.68m +6m 34s +6.56m −0m 24s −0.41m −10m 54s −10.90m −16m 34s −16.57m −10m 34s −10.57m 4 +4m 22s +4.36m +13m 28s +13.46m +11m 27s +11.45m +2m 57s +2.96m −3m 02s −3.04m −1m 19s −1.31m +4m 51s +4.86m +6m 28s +6.47m −0m 44s −0.74m −11m 13s −11.22m −16m 34s −16.57m −10m 11s −10.18m 5 +4m 48s +4.81m +13m 33s +13.55m +11m 14s +11.24m +2m 41s +2.68m −3m 07s −3.12m −1m 08s −1.13m +5m 02s +5.03m +6m 22s +6.37m −1m 05s −1.08m −11m 31s −11.52m −16m 33s −16.56m −9m 46s −9.77m 6 +5m 15s +5.25m +13m 38s +13.63m +11m 01s +11.01m +2m 24s +2.40m −3m 11s −3.19m −0m 57s −0.95m +5m 12s +5.20m +6m 15s +6.26m −1m 25s −1.42m −11m 50s −11.83m −16m 32s −16.53m −9m 22s −9.36m 7 +5m 41s +5.69m +13m 42s +13.70m +10m 47s +10.78m +2m 07s +2.12m −3m 15s −3.25m −0m 46s −0.76m +5m 22s +5.36m +6m 08s +6.13m −1m 46s −1.77m −12m 07s −12.12m −16m 29s −16.49m −8m 56s −8.94m 8 +6m 07s +6.11m +13m 45s +13.75m +10m 33s +10.55m +1m 51s +1.85m −3m 18s −3.30m −0m 34s −0.56m +5m 31s +5.52m +6m 00s +6.00m −2m 07s −2.11m −12m 25s −12.41m −16m 26s −16.43m −8m 31s −8.51m 9 +6m 32s +6.53m +13m 47s +13.79m +10m 18s +10.31m +1m 35s +1.59m −3m 21s −3.34m −0m 22s −0.37m +5m 40s +5.67m +5m 52s +5.86m −2m 28s −2.47m −12m 42s −12.70m −16m 22s −16.36m −8m 04s −8.07m 10 +6m 56s +6.94m +13m 49s +13.82m +10m 03s +10.06m +1m 19s +1.32m −3m 23s −3.38m −0m 10s −0.16m +5m 49s +5.81m +5m 43s +5.71m −2m 49s −2.82m −12m 58s −12.97m −16m 16s −16.27m −7m 38s −7.63m 11 +7m 21s +7.34m +13m 50s +13.83m +9m 48s +9.80m +1m 04s +1.07m −3m 24s −3.40m +0m 02s +0.04m +5m 57s +5.94m +5m 33s +5.55m −3m 11s −3.18m −13m 14s −13.24m −16m 10s −16.17m −7m 11s −7.18m 12 +7m 44s +7.73m +13m 50s +13.83m +9m 33s +9.55m +0m 49s +0.81m −3m 25s −3.41m +0m 15s +0.25m +6m 04s +6.07m +5m 23s +5.38m −3m 32s −3.53m −13m 30s −13.50m −16m 04s −16.06m −6m 43s −6.72m 13 +8m 07s +8.11m +13m 49s +13.82m +9m 17s +9.28m +0m 34s +0.56m −3m 25s −3.42m +0m 28s +0.46m +6m 11s +6.19m +5m 12s +5.20m −3m 54s −3.89m −13m 45s −13.75m −15m 56s −15.93m −6m 15s −6.25m 14 +8m 29s +8.48m +13m 48s +13.79m +9m 01s +9.01m +0m 19s +0.32m −3m 25s −3.41m +0m 41s +0.68m +6m 18s +6.30m +5m 00s +5.01m −4m 15s −4.25m −13m 59s −13.99m −15m 48s −15.79m −5m 47s −5.78m 15 +8m 51s +8.84m +13m 46s +13.76m +8m 45s +8.74m +0m 05s +0.09m −3m 24s −3.40m +0m 53s +0.89m +6m 24s +6.40m +4m 49s +4.81m −4m 37s −4.62m −14m 13s −14.22m −15m 38s −15.64m −5m 19s −5.31m 16 +9m 12s +9.19m +13m 43s +13.71m +8m 28s +8.47m −0m 09s −0.14m −3m 22s −3.37m +1m 07s +1.11m +6m 30s +6.50m +4m 36s +4.60m −4m 59s −4.98m −14m 27s −14.45m −15m 28s −15.47m −4m 50s −4.83m 17 +9m 32s +9.53m +13m 39s +13.65m +8m 11s +8.19m −0m 22s −0.37m −3m 20s −3.34m +1m 20s +1.33m +6m 35s +6.58m +4m 23s +4.39m −5m 20s −5.34m −14m 40s −14.66m −15m 17s −15.28m −4m 21s −4.35m 18 +9m 51s +9.86m +13m 35s +13.58m +7m 54s +7.90m −0m 35s −0.59m −3m 18s −3.30m +1m 33s +1.55m +6m 40s +6.66m +4m 10s +4.16m −5m 42s −5.70m −14m 52s −14.86m −15m 05s −15.09m −3m 52s −3.86m 19 +10m 10s +10.17m +13m 30s +13.50m +7m 37s +7.62m −0m 48s −0.80m −3m 15s −3.25m +1m 46s +1.77m +6m 44s +6.73m +3m 56s +3.93m −6m 04s −6.07m −15m 03s −15.06m −14m 53s −14.88m −3m 22s −3.37m 20 +10m 29s +10.48m +13m 24s +13.40m +7m 20s +7.33m −1m 00s −1.00m −3m 11s −3.19m +1m 59s +1.99m +6m 47s +6.79m +3m 41s +3.69m −6m 26s −6.43m −15m 14s −15.24m −14m 39s −14.65m −2m 53s −2.88m 21 +10m 46s +10.77m +13m 18s +13.30m +7m 03s +7.04m −1m 12s −1.20m −3m 07s −3.12m +2m 12s +2.21m +6m 50s +6.83m +3m 26s +3.44m −6m 47s −6.79m −15m 25s −15.41m −14m 25s −14.41m −2m 23s −2.39m 22 +11m 03s +11.04m +13m 11s +13.18m +6m 45s +6.75m −1m 23s −1.39m −3m 02s −3.04m +2m 26s +2.43m +6m 52s +6.87m +3m 11s +3.18m −7m 09s −7.15m −15m 35s −15.58m −14m 10s −14.16m −1m 54s −1.90m 23 +11m 18s +11.31m +13m 03s +13.06m +6m 27s +6.46m −1m 34s −1.57m −2m 57s −2.95m +2m 39s +2.64m +6m 54s +6.90m +2m 55s +2.92m −7m 30s −7.50m −15m 44s −15.73m −13m 54s −13.90m −1m 24s −1.40m 24 +11m 34s +11.56m +12m 55s +12.92m +6m 10s +6.16m −1m 45s −1.75m −2m 51s −2.86m +2m 52s +2.86m +6m 55s +6.92m +2m 39s +2.65m −7m 51s −7.86m −15m 52s −15.87m −13m 37s −13.62m −0m 55s −0.91m 25 +11m 48s +11.80m +12m 47s +12.78m +5m 52s +5.87m −1m 55s −1.92m −2m 45s −2.75m +3m 04s +3.07m +6m 56s +6.93m +2m 22s +2.37m −8m 13s −8.21m −16m 00s −15.99m −13m 20s −13.33m −0m 25s −0.42m 26 +12m 02s +12.03m +12m 37s +12.62m +5m 34s +5.57m −2m 04s −2.07m −2m 39s −2.64m +3m 17s +3.29m +6m 56s +6.93m +2m 05s +2.09m −8m 34s −8.56m −16m 06s −16.11m −13m 01s −13.02m +0m 05s +0.08m 27 +12m 14s +12.24m +12m 27s +12.46m +5m 17s +5.28m −2m 13s −2.22m −2m 31s −2.52m +3m 30s +3.50m +6m 55s +6.92m +1m 48s +1.80m −8m 54s −8.91m −16m 13s −16.21m −12m 42s −12.71m +0m 34s +0.57m 28 +12m 26s +12.44m +12m 17s +12.28m +4m 59s +4.98m −2m 22s −2.37m −2m 24s −2.40m +3m 42s +3.70m +6m 54s +6.90m +1m 30s +1.50m −9m 15s −9.25m −16m 18s −16.30m −12m 23s −12.38m +1m 03s +1.05m 29 +12m 38s +12.63m +12m 06s +12.10m +4m 41s +4.69m −2m 30s −2.50m −2m 16s −2.26m +3m 54s +3.91m +6m 52s +6.87m +1m 12s +1.19m −9m 35s −9.59m −16m 23s −16.38m −12m 02s −12.04m +1m 32s +1.54m 30 +12m 48s +12.80m +4m 24s +4.40m −2m 38s −2.63m −2m 07s −2.12m +4m 06s +4.10m +6m 50s +6.83m +0m 53s +0.88m −9m 55s −9.92m −16m 27s −16.44m −11m 41s −11.69m +2m 01s +2.02m 31 +12m 57s +12.96m +4m 06s +4.11m −1m 58s −1.97m +6m 47s +6.78m +0m 34s +0.57m −16m 30s −16.50m +2m 30s +2.50m
GEN FEB MAR APR MAG GIU LUG AGO SET OTT NOV DIC
Spiegazioni sulla natura, sul significato e sull’uso dell’equazione del tempo in astronomia ed in gnomonica non vengono qui fornite, dandole per note. Tutte le informazioni possono facilmente essere reperite altrove. Qui se ne offrono solo i risultati di calcolo.
I decimali sono 2, garantendo perciò una precisione almeno uguale a quella del formato minuti-secondi , in effetti maggiore (quasi doppia).
365d/a ·400a +400a ·1d /4a −3d =146000d +100d −3d =146097d , cioè i “normali” 365 giorni all’anno più 97 “extra” (cioè i 100 che deriverebbero dalla regola giuliana di considerarne sempre 1 ogni 4 anni, meno i 3 esclusi dagli anni secolari non divisibili per 400, secondo la regola gregoriana), da cui 146097d /400a =365.2425d/a .
L’esatta durata dell’anno tropico, attualmente, è di 365.2421988d , che, se rimanesse costante, porterebbe i 3 decimillesimi di giorno residui che si accumulano ogni anno a costituire un intero giorno di scarto dopo 3320 anni, suggerendo perciò ulteriori ritocchi al calendario gregoriano, come, ad esempio, l’adozione di un più ampio ciclo di 4000 anni che, a partire dal 4000, renda comuni quegli anni (4000, 8000, 12000…) altrimenti bisestili secondo la regola corrente.
Riferiti alle 11:00 TD di ciascun giorno.
