Você Sabia? - 17/03/2019
Cálculo do Dia da Páscoa, Carnaval e Corpus Christi
Páscoa Dia da Páscoa, por definição, é o
primeiro Domingo após a lua cheia que ocorre após o equinócio vernal, e pode cair entre 22 de Março e 25 de Abril.
A seqüência dos dias de Páscoa se repete em ciclos de aproximadamente
5.700.000 anos.
As fórmulas existentes calculam o que se convencionou chamar de "
Cálculo Eclesiástico", quando em 325 o
Concílio de Nicea assim definiu.
O
Carnaval acontece 47 dias antes da Páscoa. Logo o Carnaval pode acontecer de 4 de fevereiro a 9 de março.
Corpus Christi acontece 60 dias depois da Páscoa. Logo Corpus Christi pode acontecer de 21 de maio até 24 de junho.
Existem diversas fórmulas para a determinação do Domingo de Páscoa, entretanto uma das mais simples é a fórmula de Gauss, descrita a seguir:
CarnavalPara calcular o dia da Páscoa (Domingo), usa-se a fórmula abaixo (
Fórmula de Gauss em 1750), onde o ANO deve ser introduzido com 4 dígitos. O operador MOD é o resto da divisão. A fórmula vale para anos entre 1901 e 2099. A fórmula pode ser estendida para outros anos, alterando X e Y conforme a tabela a seguir (criada por Gauss até 1999 e estendida pelo autor até 2299):
faixa de anos X Y
1582 1599 22 2
1600 1699 22 2
1700 1799 23 3
1800 1899 24 4
1900 2019 24 5
2020 2099 24 5
2100 2199 24 6
2200 2299 25 7
Para anos entre 1901 e 2099:
Corpus Christi
X=24
Y=5
a = ANO MOD 19
b= ANO MOD 4
c = ANO MOD 7
d = (19 * a + X) MOD 30
e = (2 * b + 4 * c + 6 * d + Y) MOD 7
Se (d + e) > 9 então DIA = (d + e - 9) e MES = Abril
senão DIA = (d + e + 22) e MES = Março
Há dois casos particulares que ocorrem duas vezes por século:
• Quando o domingo de Páscoa cair em Abril e o dia for 26, corrige-se para uma semana antes, ou seja, vai para dia 19;
• Quando o domingo de Páscoa cair em Abril e o dia for 25 e o termo "d" for igual a 28, simultaneamente com "a" maior que 10, então o dia é corrigido para 18.
Neste século estes dois casos particulares só acontecerão em 2049 e 2076.
Para calcular a Terça-feira de
Carnaval, basta subtrair 47 dias do Domingo de Páscoa.
Para calcular a Quinta-feira de
Corpus Christi, soma-se 60 dias ao Domingo de Páscoa.
Exemplos:
Para o ano de 2019:
a=2019 MOD 19 = 5
b=2019 MOD 4 = 3
c=2019 MOD 7 = 3
d=(19 * 5 + 24) MOD 30 = 29
e=(2 * 3 + 4 * 3 + 6 * 29 + 5) MOD 7 = 1
(d + e) = 29 + 1 = 30
Logo, o Domingo de Páscoa é 21/Abril/2019
Carnaval: 05/03/2019
Corpus Christi: 20/06/2019
Para o ano de 2020:
a=2020 MOD 19 = 6
b=2020 MOD 4 = 0
c=2020 MOD 7 = 4
d=(19 * 6 + 24) MOD 30 = 18
e=(2 * 0 + 4 * 4 + 6 * 18 + 5) MOD 7 = 3
(d + e) = 18 + 3 = 21
Logo, o Domingo de Páscoa é 12/Abril/2020
Carnaval: 25/02/2020
Corpus Christi: 11/06/2020
Para o ano de 2021:
a=2021 MOD 19 = 7
b=2021 MOD 4 = 1
c=2021 MOD 7 = 5
d=(19 * 7 + 24) MOD 30 = 7
e=(2 *1 + 4 *5 + 6 * 7 + 5) MOD 7 = 6
(d + e) = 7 + 6 = 13
Logo, o Domingo de Páscoa é 04/04/2021
Carnaval: 16/02/2021
Corpus Christi: 03/06/2021
Para o ano de 2022:
a=2022 MOD 19 = 8
b=2022 MOD 4 = 2
c=2022 MOD 7 = 6
d=(19 * 8 + 24) MOD 30 = 26
e=(2 * 2 + 4 * 6 + 6 * 26 + 5) MOD 7 = 0
(d + e) = 26 + 0 = 26
Logo, o Domingo de Páscoa é 17/04/2022
Carnaval: 01/03/2022
Corpus Christi: 16/06/2022
Para o ano de 2023:
a= 2023 MOD 19 = 9
b= 2023 MOD 4 = 3
c= 2023 MOD 7 = 0
d=(19 * 9 + 24) MOD 30 = 15
e=(2 * 3 + 4 * 0 + 6 * 15 + 5) MOD 7 = 3
(d + e) = 15 + 3 = 18
Logo, o Domingo de Páscoa é 09/04/2023
Carnaval: 21/02/2023
Corpus Christi: 08/06/2023
Para o ano de 2024:
a= 2024 MOD 19 = 10
b= 2024 MOD 4 = 0
c= 2024 MOD 7 = 1
d=(19 * 10 + 24) MOD 30 = 4
e=(2 * 0 + 4 * 1 + 6 * 4 + 5) MOD 7 = 5
(d + e) = 4 + 5 = 9
Logo, o Domingo de Páscoa é 31/03/2024
Carnaval: 13/02/2024
Corpus Christi: 30/05/2024
Para o ano de 2025:
a= 2025 MOD 19 = 11
b= 2025 MOD 4 = 1
c= 2025 MOD 7 = 2
d=(19 * 11 + 24) MOD 30 = 23
e=(2 * 1 + 4 * 2 + 6 * 23 + 5) MOD 7 = 6
(d + e) = 23 + 6 = 29
Logo, o Domingo de Páscoa é 20/04/2025
Carnaval: 04/03/2025
Corpus Christi: 19/06/2025
Para o ano de 2026:
a= 2026 MOD 19 = 12
b= 2026 MOD 4 = 2
c= 2026 MOD 7 = 3
d=(19 * 12 + 24) MOD 30 = 12
e=(2 * 2 + 4 * 3 + 6 * 12 + 5) MOD 7 = 2
(d + e) = 12 + 2 = 14
Logo, o Domingo de Páscoa é 05/04/2026
Carnaval: 17/02/2026
Corpus Christi: 04/06/2026
Para o ano de 2027:
a= 2027 MOD 19 = 13
b= 2027 MOD 4 = 3
c= 2027 MOD 7 = 4
d=(19 * 13 + 24) MOD 30 = 1
e=(2 * 3 + 4 * 4 + 6 * 1 + 5) MOD 7 = 5
(d + e) = 1 + 5 = 6
Logo, o Domingo de Páscoa é 28/03/2027
Carnaval: 09/02/2027
Corpus Christi: 27/05/2027
Para o ano de 2028:
a= 2028 MOD 19 = 14
b= 2028 MOD 4 = 0
c= 2028 MOD 7 = 5
d=(19 * 14 + 24) MOD 30 = 20
e=(2 * 0 + 4 * 5 + 6 * 20 + 5) MOD 7 = 5
(d + e) = 20 + 5 = 25
Logo, o Domingo de Páscoa é 16/04/2028
Carnaval: 29/02/2028
Corpus Christi: 15/06/2028
Para o ano de 2029:
a= 2029 MOD 19 = 15
b= 2029 MOD 4 = 1
c= 2029 MOD 7 = 6
d=(19 * 15 + 24) MOD 30 = 9
e=(2 * 1 + 4 * 6 + 6 * 9 + 5) MOD 7 = 1
(d + e) = 9 + 1 = 10
Logo, o Domingo de Páscoa é 01/04/2029
Carnaval: 13/02/2029
Corpus Christi: 31/05/2029
Para o ano de 2030:
a= 2030 MOD 19 = 16
b= 2030 MOD 4 = 2
c= 2030 MOD 7 = 0
d=(19 * 16 + 24) MOD 30 = 28
e=(2 * 2 + 4 * 0 + 6 * 28 + 5) MOD 7 = 2
(d + e) = 28 + 2 = 30
Logo, o Domingo de Páscoa é 21/04/2030
Carnaval: 05/03/2030
Corpus Christi: 20/06/2030
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