## Sunday, 13 July 2014

### The length of the antediluvian month and year

If the earth's spin increases then the days in a year increases. The year—as measured in a stable time metric, such as atomic-seconds—is unchanged because it is dependant on the distance from the sun, but the year as measured in days does change because the length of the day is dependant on the spin. The same can be said about the month.

If we define the year length to be y in unchanging units; the day to be da for the antediluvian day and dp for the postdiluvian day; na is number of days in an antediluvian year and np the number of days in a postdiluvian year; then

da × na = y = dp × np

da = dp × np/na

dp/da = na/np

Many ancient calendars use 360 days for a year. Perhaps these are stylised, especially as these calendars are postdiluvian; but what if they were based on memory of an antediluvian year of such a length? In such a case the length of an antediluvian day would have been

da = 24 hours × 365.25/360 = 24 hours 21 minutes.

We will define a month to be m in unchanging units and the number of days in an antediluvian month ka; then

da × ka = m = dp × kp

ka = kp × dp/da = kp × na/np

dp/da = ka/kp = na/np

If a (synodic) month is now 29.53 days (new moon to new moon)

dp = 24 hours, kp = 29.53 days

then the antediluvian month (assuming a 360-day year) was

ka = 29.5 days × 360/365.25 = 29.1 days

Now consider instead if the antediluvian month was 30 days in length

ka = 30 days, kp = 29.53 days

then the antediluvian day was

da = dp × kp/ka = 24 × 29.53/30 = 23 hours 38 minutes

and the antediluvian year was

na = np × ka/kp = 365 × 30/29.53 = 371 days

These calculations assume no change in distance from the earth to the sun or the moon.