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I've been working on an orrery for the Kerbol system and I've run into a couple of issues with regard to the length of Kerbin's year. Using values from the wiki and extracted from the game (suppposedly) using HyperEdit, I've managed to calculate this year length: Parameter Symbol Value Source Gravitational Constant G 6.67408 ∙ 10-11 m3/(kg ∙ s2) From patch notes Acceleration at Kerbin SL g0 9.80665 m/s2 From patch notes Acceleration at Sun surface (in g’s) gS,g 1.7462500333786 ∙ g0 Extracted with HyperEdit Acceleration at Sun surface (m/s2) gs 17.1248629 m/s2 gs,g ∙ g0 Radius of Sun rs 2.616 ∙ 108 m From wiki / verified in game Sun gravitational constant GMs 1.171932456926 ∙ 1018 m3/s2 gs = GMs/rs2 Kerbin SMA rk 13599840256 m Extracted with HyperEdit Kerbin orbital period Tk 9205116.471 s T = 2π√(rk3/GMs) This works out to a Kerbin year of 426 d, 0 h, 58 m, 36.471 s. And there are two problems with this value. First, I can't replicate this in-game. I placed a satellite into a 13599840256 m orbit around the Sun using the debug menu orbit editor and compared the apoapsis and periapsis of this orbit, and I get a difference of 213 d, 0h, 16 m, for an orbit of 426 d, 0 h, 32 m. You'll notice my math gives a different result by some 27 minutes, give or take a minute (.0173%). This may not seem like much, but given the precision needed for successful small-body encounters in KSP, accuracy to the game's physics is key. So one of two things is happening: either my math is wrong or the values I'm using for my calculations are. Please check my math, and if anyone knows any methods to determine these values correctly, I'm all ears. Second, you'll notice this isn't an integral number of days, no matter which one is used. So, like Earth, there should be leap years. Given my math above, the sequence would be one extra day every six years, except for the 258th year of each cycle (like how on Earth we have one extra day every four years EXCEPT for years divisible by 100 (like 1900) UNLESS it's also divisible by 400 (like 2000)). But given the year length in-game is a little more than 426 d 1/2 h, it would be one extra day every 12 years, except on the 180th year of the cycle. Or something odd like that. But I've timewarped for 15 years and saw no evidence of a leap day in any of those years. Does the game simply do 426-day years and let the "new year" point drift backward by 1/2 hour each year? Now, I do understand that the math as it is now is going to be dang close. However, objects in-game are moving faster than in my model. I'd like to be able to plot user-defined trajectories as well as the planet positions, and if the orbital motions are off by even a small amount, the data the tool gives about encounters is going to be bad information. Plus I'm a little obsessive about accuracy. Either way, I'd like to avoid this kind of error if I can. Thanks in advance for your help!
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There used to be a Kerbal Calendar mod. I don't know just what it used as its periods. As per the wiki: 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.