Earth rotation period is 23h, 56m, 4s or 86164s

Earth orbital period is 365.256363004 days or 31558149.7635456s

In the time of one rotation, Earth's orbit advances by 0.2730325%

0.2730325% of Earth's rotation period is 235.2557233s

Adding that to the rotation period gives 86399.2557233s, or 23.999793256 hours, which is within margin of error of the observed 24h day length.

Because of this difference between true rotation period and observed length of day, one year isn't exactly 365 observed days, but about 365.25. This error adds up to a full day every 4 years, leading to a leap year.

There is actually some reason as to why days are 24 hours, hours are 60 minutes and minutes are 60 seconds. Old calendars would show the year as having 360 days, and both 24 and 60 divide this numbers, meaning you can cleanly divide each year into these smaller portions of time.

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Avalon's rotation period is 127h, 44m, 25.5s or 459,865s (aprox). It is tidally locked, so this is equal to its orbital period.

Valaya's orbital period is 13 years, 19 days, 15h, 15m, 26.8s or 411,952,066s (aprox).

In the time of one rotation of Avalon, Valaya's orbit advances by 0.11163084793045729%

0.11163084793045729% of Avalon's rotation period is 513.3518511879132s

Adding that to the rotation period gives 460,378.93623492046s, or 127h, 52m, 58.936234920460265s. This the length of one perceived day (day/night cycle) on Avalon.

This means that the length of one full year in Avali-time is 894.8108473547217 Avali-days. Their calendar most likely rounds this to 895 days. This introduces an error of about 0.189 Avali-days per year. This rounds up to a full day every 5 Avali years. But since it is extra time, it leads to a day getting skipped in the calendar, rather then added.

In human time, this "skip year" occurs about every 65 human years. Despite the longer natural lifespan of the Avali (about 100 human years), this is probably still a once in a lifetime occasion for the Avali, and might thus hold cultural significance.

However, this skip year doesn't fully correct the error in the calendar, but its the same for the leap year on Earth. So the remaining little error might be corrected on a technical level, similar to the UTC Leap Second on Earth, or by skipping two days every few Avali-decades, instead of one.

Early Avali calendars most likely used 900 as the number of days in a year, similar to how early calendars on Earth counted 360 days in a year, instead of 365. And, just like on Earth, the Avali most likely chose divisors of that number as the factors by which to divide the length of each day into smaller fractions. On Earth, 24 and 60 are used as both divide 360.

Because of the longer days on Avalon, Avali might instead use 36 as the length of a day (which is conveniently also equal to 100 in base-6), and 90 as the length of an hour and minute. This provides the seemingly best mathematical convenience.

Using these numbers, we can calculate the length of each Avali-hour to be 12788.303784303345s.

The Avali-minute is then equal to that divided by 90, which is 142.09226427003716s.

And finally, we arrive at a unit for the Avali-second (sA), being 1.5788029363337464s.


1sA = 1.5788029363337464s
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