New measurement of Kerbin's sidereal day (not 6 hours)

[OhioBob]

But what I wonder more is how did that get your attention and why bother to work all that out?

I'm just weird.

Seriously though, I was just thinking about how the Kerbin days are all messed up being based on the sidereal day rather than the solar day. I started checking to see how much later the sun rose each day and I started to notice some descrepencies. One thing led to another and before you know it I discovered the 42-second year-to-year difference in the rising time of the sun. I knew something was out of whack so I checked the sidereal time using a reference star. I then worked out the math and the rest is history.

What does knowing this tell us?

As far as playing the game goes, nothing. It's just a curious side note. I find this kind of stuff interesting because it just makes the game feel more real to me. The fact that we can make observations and perform experiments to learn things about these fictional worlds as if there were real planets I think is pretty cool.

[hoojiwana]

Seriously though, I was just thinking about how the Kerbin days are all messed up being based on the sidereal day rather than the solar day. I started checking to see how much later the sun rose each day and I started to notice some descrepencies. One thing led to another and before you know it I discovered the 42-second year-to-year difference in the rising time of the sun. I knew something was out of whack so I checked the sidereal time using a reference star. I then worked out the math and the rest is history.

What if the day is just 1 flat second shorter than we think it is? That fits the ~42 second difference with 426 days, doesn't it? So we have a backwards leap second every day.

[Geschosskopf]

Kerbin never had a 24-hour day. When Kerbin began rotating in 0.12, it had a 6-hour sidereal day, and it's year was about 106 Earth days, as it is now.

The MET Clock and other game times did initially count in 24-hour days and 365-day years, however.

I know that Kerbin's day/night cycle has always been 6 hours and that the game clock used to count in 24-hr days.. Which has never been the issue---the actual period of time involved the same number of hours, minutes, and seconds regardless of what you arbitrarily call a "day".

The question I have is with the year length, in hours. Kerbin's orbital velocity around the sun doesn't seem to have changed so either the 365x 24-hr years had too many hours or the 426x 6-hr days have too few. I had always thought, without bothering to do the math, that the 365x 24hr year was the true solar year, there being no need for KSP's "hours" in game time to be the exact same length as Earth's hours. But now that I think about it, I realize that there's no way toy-sized Kerbin could have a 365-day year or it would necessarily be as far from the sun as Earth.

So thanks to all for setting me straight.

. Either the 365x 24hr day year was too long, or the current 426x 6-hr day year is too short.

[mikegarrison]

Well, I'm sure all this is terribly important to the many Kerbal farmers who have to worry about making sure their planting calendars match up with the seasons -- except Kerbin doesn't have any seasons. Or any farmers, either.

(It's a shame we can't land our ships in the middle of a wheat field or a city park or a school playground.)

Edited July 28, 2015 by mikegarrison

[regex]

But now that I think about it, I realize that there's no way toy-sized Kerbin could have a 365-day year or it would necessarily be as far from the sun as Earth.

You're partially correct; Kerbin would be further away but because Kerbol doesn't mass the same as the Sun it wouldn't be as far away as the Earth.

E: It would have to be between the orbits of Duna and Dres to have an Earth year long orbit.

Either the 365x 24hr day year was too long, or the current 426x 6-hr day year is too short.

The 426-ish day year with 6 hour days is correct by orbital math. Edited July 29, 2015 by regex

[OhioBob]

Geschosskopf said:

The question I have is with the year length, in hours. Kerbin's orbital velocity around the sun doesn't seem to have changed so either the 365x 24-hr years had too many hours or the 426x 6-hr days have too few. I had always thought, without bothering to do the math, that the 365x 24hr year was the true solar year, there being no need for KSP's "hours" in game time to be the exact same length as Earth's hours. But now that I think about it, I realize that there's no way toy-sized Kerbin could have a 365-day year or it would necessarily be as far from the sun as Earth.

So thanks to all for setting me straight.

. Either the 365x 24hr day year was too long, or the current 426x 6-hr day year is too short.

The length of Kerbin's sidereal year is calculated using orbital mechanics. It is based on the gravitational parameter of the sun (constant of gravitation * mass) and Kerbin's semimajor axis (mean distance from sun). It uses the following equation,
 

P² = 4*pi²*a³/GM

where P is the period, a is the semimajor axis, and GM is the gravitational parameter.
 

For Kerbin this number computes to 9,203,545 seconds, or 426.09 6-hour days.
 

Of course this only takes into account the mass of the Sun. The more correct method also considers the mass of the planet. Since the mass of the planet is so small in comparison to the sun, the difference is small but not insignificant. The corrected formula is,
 

P² = 4*pi²*a³/(G(M+m))
 

where m is the mass of the planet.
 

Using this method, the period computes to 9,203,531 seconds. I'm not 100% certain which method is used in KSP, though it seems it is likely the first method. At least this is what the writers of the Wiki articles believe because all the periods of revolution seem to be based on the first formula. It makes sense that the KSP team would want to simplify the computation by ignoring the mass of the secondary body when its effect on the result is so small.
 

Interestingly, my method of computing the sidereal year based on observations of the sun and stars works out to 9,203,554 seconds. This is closer to the first method, though either of the above solutions are within my margin of error. I'm just delighted that I got so close. If I were to extend my observations out to 100 years, rather than 10 years, I could gain another decimal point of accuracy, however that's more work than I'm willing to do.
 

Edited March 3, 2017 by OhioBob

[Tw1]

So,

Sidereal day = 5.999976 hours?

Solar day = 6.01409 hours?

I'm sure I've seen the debug log say something about the day being 5.99 hours long.

[problemecium]

45 seconds after a whole year?

I'm on Day 181 and the Sun is rising over an hour past 0:00, and it falls a few seconds farther behind every day. The "warp to next morning" still works as designed, but the clock isn't following the actual day length very well.

Interestingly, I don't think the Sun is supposed to rise at 0:00 to begin with (e.g. when starting a new game), but for a time mine did, which is what first clued me in to the "drift." I thought SQUAD said they had patched this o_O

[Findthepin1]

OP, where did you measure the sunrises from? Anywhere above sea level (with water just to the east) the time between sunrises will be longer, because at sea level you're exactly 600 km away from the core of Kerbin. At KSC's altitude you're 600.07 km from the core. Since you're on land at KSC, and well above sea level, and the sea is to the east from KSC, there is not a level surface blocking light at KSC. When the sun rises there, it only has to cross the 0-elevation boundary to shine, but when the sun sets it has to cross a higher elevation boundary (and therefore earlier) because the west is land. This same effect causes mountain peaks to remain sunlit for a while after/before the sun sets/rises at their bases, or planes reflecting sunlight as seen from below after sunset and before sunrise. A related scenario is how the Moon still reflects sunlight and is visible at night.