The Kalendar

[Tfin]

There used to be a Kerbal Calendar mod. I don't know just what it used as its periods.

 

As per the wiki:

Quote

Celestial Body	Parent	Hours	Kerbin
			Days	Months	Years
Kerbin	Kerbol	2556.50	426.08	66.23	1.00
Mun	Kerbin	38.60	6.43	1.00	0.02

The Kerbal Calendar (The Kalendar)

A Kerbin year is 426 days long.
More accurately, it's 426 days, 32 minutes, 24.6 seconds long. (9203544.6 s)

The Mun orbits Kerbin every 6 days, 2 hours, 36 minutes, 24.4 seconds. (138984.4 s)
(Remember for these that a Kerbin day is 6 hours long.)

Kerbals don't have weeks, as they would be less than 2 days long each (an Earth week is ideally one Moon phase, though of course it isn't, quite).

There are 66 (66.22) Munar cycles every year (a month is ideally a Lunar cycle). A Kerbin munth is 6 days long.

Or 7.
In an 11-munth cycle, the length of Kerbin munths would be 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, repeating six times through the year, for 426 days, tracking the Mun as accurately as division into days allows. (Note: starting from 0, the first munth would be the 6 from the end of the last cycle, but this can be satisfied by starting the first-ever cycle 1 munth early.)

For want of a better term, this would create 6 Kerbin seasons of 71 days each. There are no seasonal differences as we know them, due to the 0-degree inclination and axial tilt, and the perfectly circular orbit of the planet.

We can theorize that these are the primary divisions of the year, akin to our months, with munths being similar to weeks.

Leap Day

Earth leap years are every four years, except for years divisible by 100 and not divisible by 400. (This will change slightly in about 784 years.)

There are 1944.6 extra seconds, or 32.41 minutes, in each Kerbin year.
12 of these would be slightly more than a day, by 28.92 minutes.
Since you never want to have a second Leap Day in a year, and it would happen fairly often, the kalendar would be amended with an extra day every 11 years, neatly echoing the 11-munth seasons.

Now there is an extra 0.1 day being added every 110 years.
426 * 110+10 = 46870
426.09 * 110 = 46869.9

So every 1,100th year would skip this Leap Day. There is a small remainder to be dealt with still (numbers were rounded here), but that can be left for Jeb the 11000th to work out.

Alternately, some kerbals prefer leap munths....

 

Unfortunately, I don't think the current time tracking in the game accounts for the leap day. Maybe it needs a mod.

Edited February 12, 2016 by Tfin

[LordKael]

As wonderfully neat as all of your math and reasoning is, I feel like there would be something more akin to an astrological calendar, as opposed to a Munar based one. My reasoning behind this is that the nature of orbits of planets would allow for an essentially even division of a Kerbin year based on which "house" Kerbol was in, as viewed from Kerbin. 

[FancyMouse]

Who cares leap year if Kerbin has 0 eccentricity and 0 axis tilt? I guess kerbals should have a really hard time figuring out year even exists.

[Snark]

5 minutes ago, FancyMouse said:

Who cares leap year if Kerbin has 0 eccentricity and 0 axis tilt? I guess kerbals should have a really hard time figuring out year even exists.

Well, certainly it would be obvious that the sun has a periodic motion against the fixed background of the stars, that takes 426-days-and-change.

Whether they'd attach any particular importance to that, in the absence of seasons, is another question.

[Tfin]

36 minutes ago, FancyMouse said:

Who cares leap year if Kerbin has 0 eccentricity and 0 axis tilt? I guess kerbals should have a really hard time figuring out year even exists.

That was only in reference to the lack of real seasons, because I used the word "season" to refer to a group of munths smaller than a year. The groups only exist due to the 11th-mun skip in the 6-7 munar rythym. As Snark says, they see the motion of objects in the sky. The apparent lack of non-aerospace industry indicates that kerbals are drawn to the sky, so they see these things.

The extra day corrects not just the length of the year, but also the position of the Mun, which these munths try to stick to.

Of course, there's the matter of Kerbol rising a little later every day, until the point, after a year, that a kerbol-rise and -set has been skipped, but since we see that they use a 6-hour day, they must accept that.

Edited February 13, 2016 by Tfin

[SpaceNomad]

Funny. I just recently were also pondering a Kerbal calendar. I also came to the conclusion that the lacking axial tilt, and neither an inclined nor eccentric orbit would make the astronomical year quite irrelevant.

The Mun on the other hand would cause quite substantial tides (given its closeness and the fact that tidal forces scale with 1/r³ instead of 1/r²). It also causes regular eclipses.

So, the calendar I invented was also based on the (Mun-) month.

On 12.2.2016 at 2:29 PM, Tfin said:

The Mun orbits Kerbin every 6 days, 2 hours, 36 minutes, 24.4 seconds. (138984.4 s)

This is the sidereal month. I would expect the synodical month (i.e. full Mun to full Mun) to be more relevant for a calendar. According to my calculation it is 141,115s (6d 3h 11m 55s). The value in the Wiki seems to be slightly off.

Based on that I came up with the following calendar:

• A month is either 6 or 7 (Kerbal) days. It would play the role of the working week.
• A (Mun-)year or Mun-cycle is a cycle of 15 months: A cycle starts with a 7 day months, just alternates between 7 and 6 days and thus also ends with a 7 day month.

This basic pattern gives you an average month of 6d 3h 12m (98 days for 15 months), so just 5s too long.

• Every 288 cycles, the last month would have only 6 instead of 7 days (and this would be called the Month of the Kraken, due to the Stolen Day).
• Thus, we get exactly 6d 3h 11m 55s

Now, what we need is names for the 6/7 days in a week (month) and for the 15 months.

Edited February 13, 2016 by SpaceNomad

[pincushionman]

Well, given the short Munar cycle, one could easily use that as the basis for the week-equivalent. It wiuld also be a stronger and more culturally-universal concept than we have in our world. "Muuk" = 6 days.

As for a month-equivalent, Kerbin has an additional lunar marker we don't to take advantage of.

Minmus.

Minmus' synodic period is 1220132 s = 338.9 h = 56.5 d, approximately. That's a little long, in my opinion, but not out of the question. There's almost exactly 7.5 of these Minmus cycles per Kerbin year.

To make things easier, we might base the "Minth" on Minmus' half-cycle - 28.25 days, or 4.7 6-day Muuks. Now we're in a situation like what we have in the real world, where none of our months match the lunar cycle OR (except February) weeks, but they're close. There are 15.2 Minths (of 28 days) in a Kerbin year. Vary the day-in-a-monthh a little bit, and it's pretty analogous to our situation.

Edited February 13, 2016 by pincushionman

[Tfin]

4 hours ago, SpaceNomad said:

Funny. I just recently were also pondering a Kerbal calendar. I also came to the conclusion that the lacking axial tilt, and neither an inclined nor eccentric orbit would make the astronomical year quite irrelevant.

The Mun on the other hand would cause quite substantial tides (given its closeness and the fact that tidal forces scale with 1/r³ instead of 1/r²). It also causes regular eclipses.

So, the calendar I invented was also based on the (Mun-) month.

This is the month. I would expect the (i.e. full Mun to full Mun) to be more relevant for a calendar. According to my calculation it is 141,115s (6d 3h 11m 55s). The value in the Wiki seems to be slightly off.

Based on that I came up with the following calendar:

• A month is either 6 or 7 (Kerbal) days. It would play the role of the working week.
• A (Mun-)year or Mun-cycle is a cycle of 15 months: A cycle starts with a 7 day months, just alternates between 7 and 6 days and thus also ends with a 7 day month.

This basic pattern gives you an average month of 6d 3h 12m (98 days for 15 months), so just 5s too long.

• Every 288 cycles, the last month would have only 6 instead of 7 days (and this would be called the Month of the Kraken, due to the Stolen Day).
• Thus, we get exactly 6d 3h 11m 55s

Now, what we need is names for the 6/7 days in a week (month) and for the 15 months.

I hadn't considered that, but we have the fact that the kerbals observe sidereal days (sunrise being later every day until a sunrise is skipped) as evidence that they might well not observe synodical months. Even if they don't observe the year with such accuracy, you would expect the same consideration be given to the day as the month.

 

Given the differences observed in Earth calendars (there are a few which observe leap months, note the drifting of the Chinese New Year that just began), I expect both methods might be used by various cultures.

[SpaceNomad]

10 hours ago, Tfin said:

I hadn't considered that, but we have the fact that the kerbals observe sidereal days (sunrise being later every day until a sunrise is skipped) as evidence that they might well not observe synodical months.

Not anymore. It has been that way for a long time. But in 1.0.5 in fact the synodical/solar day was changed to 6 hours. So sunrise is now at the same time every day, at about 4:12 at the KSC (I have repeating Kerbal Alarm Clocks running for sunrise and sunset at KSC). The sidereal day is now a bit shorter (6h 59m 9.4s).

[Tfin]

1 hour ago, SpaceNomad said:

Not anymore. It has been that way for a long time. But in 1.0.5 in fact the synodical/solar day was changed to 6 hours. So sunrise is now at the same time every day, at about 4:12 at the KSC (I have repeating Kerbal Alarm Clocks running for sunrise and sunset at KSC). The sidereal day is now a bit shorter (6h 59m 9.4s).

Ah, so the wiki is VERY wrong.

[SpaceNomad]

3 hours ago, Tfin said:

Ah, so the wiki is VERY wrong.

Not VERY . At least the page on Kerbin states the correct current numbers (it's even mentioned in the "Changes" section). The Wiki is filled with content by users (so you and me ), so if you find a place, where it is still wrong, just fix it!

In defense of the Wiki: At some time Squad claimed it was fixed (0.24 apparently), but it wasn't. And this time they weren't very vocal about it. It's hidden deep in the Changelog and I'm not even sure that the sentence really refers to this change, it's really cryptic:

Quote

========================= First Contract (v0.24.0) =======================================================

- Kerbin's Solar Day is now exactly 6 hours long (sidereal day is now 59 seconds shorter).

=================================== v1.0.5 ============================================================

* Fix issue with solar day length not being calculated correctly when setting Kerbin's rotational period.

 

On another topic: I've actually looked into the Kerbal Alarm Clock source code a few weeks ago to find out how hard it would be to hack another calendar into it. I had assumed it would be quite easy and I just had to add some code converting the number of seconds into a date string. But the date/time code is overly complex and spread over several classes. So, not that trivial.

[Tfin]

7 hours ago, SpaceNomad said:

Not VERY . At least the page on Kerbin states the correct current numbers (it's even mentioned in the "Changes" section). The Wiki is filled with content by users (so you and me ), so if you find a place, where it is still wrong, just fix it!

The numbers I used didn't actually come from the wiki. Where I quoted it in the first post was meant to establish that I wasn't making up the numbers. In fact, the ones I showed don't even quite agree with what I used. Specifically, it shows 66.23 months in a year, while I used 66.22 (66.21998296).

The big difference, where it matters, was the information that 6 hours was a synodic day.

[Tfin]

7 hours ago, SpaceNomad said:

Not VERY . At least the page on Kerbin states the correct current numbers (it's even mentioned in the "Changes" section). The Wiki is filled with content by users (so you and me ), so if you find a place, where it is still wrong, just fix it!

The numbers I used didn't actually come from the wiki. Where I quoted it in the first post was meant to establish that I wasn't making up the numbers. In fact, the ones I showed don't even quite agree with what I used. Specifically, it shows 66.23 months in a year, while I used 66.22 (66.21998296).

The big difference, where it matters, was the information that 6 hours was a synodic day. After you said that, I checked, got full sun-up at 4:13, warped ahead a bunch, and watched a lack of sun at 4:13, and for several minutes after.

 

Because I'd stopped on a sunrise eclipse.