Question 10.

(MAYAN TIME)

A = BT^2 = 7.1683012 × 10^16 ms

X = 7.1683012

a. What are the magnitudes of T^1, T^-1, T^2 and T^-2?

b. What are the values of B and t?

c. Using t, what are the whole numbers of the Mayan baktun, katun, tun, uinal and kin? (Show the equivalent Western time).

a.

T^1 = √(A/B) = 10^3 ms

T^-1 = √(B/A) = 10^-3 ks

T^2 = A/B = 10^6 ms²

T^-2 = B/A = 10^-6 ks²

b.

B = A/T^2 = X × 10^16 / 10^6 = X × 10^10 ks

t = BT^1 = X × 10^10 × 10^3 = X × 10^13 s

To convert the total seconds (t) to baktun, katun, tun, uinal and kin format we can use this formula.

Note: 28800/73, 1440/73 and 72/73 etc are conversion factors, as in 1 Mayan baktun is 28800/73 Western Years.

Note: we are not using months for this exercise.

Note: a Mayan time is given then the equivalent Western time, and so on.

c.

baktun – katun/20 = t / 12441600000 – katun/20 = 5761

y – d/365 = baktun × 28800/73 – d/365 = 227053

katun – tun/20 = katun/20 × 20 – tun/20 = 11

y – d/365 = katun × 1440/73 – d/365 = 220

tun – uinal/18 = tun/20 × 20 – uinal/18 = 3

y – d/365 = tun × 72/73 – d/365 = 3

d – h/24 = tun × 360 – h/24 = 1290

uinal – kin/20 = uinal/18 × 18 – kin/20 = 10

d – h/24 = uinal × 20 – h/24 = 210

kin – h/24 = kin/20 × 20 – h/24 = 10

h – m/60 = h/24 × 24 – m/60 = 17

m – s/60 = m/60 × 60 – s/60 = 46

s – cs/100 = s/60 × 60 – cs/100 = 40

NOTE: obviously we do NOT literally minus the decimal such as katun/20 on the calculator, we simply minus the whole number and multiply the decimal by 20 or 18 etc. We do not write or type long numbers. We only have to type the first division below such as baktun – katun/20 and ‘lift’ the whole number, the rest is done by the calculator.

For example:

Note: you do not need to write the below, it is all done on the calculator.

baktun – katun/20 = 71683012000000 / 12441600000 – katun/20 = 5761

y – d/365 = 5761.55896347737 × 28800/73 – d/365 = 227053

katun – tun/20 = (5761.55896347737 – 5761) × 20 – tun/20 = 11

y – d/365 = 11.1792695473196 × 1440/73 – d/365 = 220

tun – uinal/18 = (11.1792695473196 – 11) × 20 – uinal/18 = 3

y – d/365 = 3.58539094639127 × 72/73 – d/365 = 3

d – h/24 = 3.58539094639127 × 360 – h/24 = 1290

uinal – kin/20 = (3.58539094639127 – 3) × 18 – kin/20 = 10

d – h/24 = 10.5370370350429 × 20 – h/24 = 210

kin – h/24 = (10.5370370350429 – 10) × 20 – h/24 = 10

h – m/60 = (10.7407407008577 – 10) × 24 – m/60 = 17

m – s/60 = (17.7777768205851 – 17) × 60 – s/60 = 46

s – cs/100 = (46.6666092351079 – 46) × 60 – cs/100 = 40

Then insert the whole numbers into the baktun/katun/tun/uinal/kin format:

t = 5761 baktun 11 katun 3 tun 10 uinal 10 kin 17:46:40

Hand written example: