Kerbol system period

[mcirish3]

UpDate: some recalculations finished. It would seem the wiki's orbital periods are a bit off.?! Looking for someone to confirm.

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[TD=width: 160]KSP universe period[/TD]

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[TD=width: 160, align: right]4.9605288608E+28[/TD]

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[TD=width: 108]seconds[/TD]

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[TD=width: 160, align: right]8.2675481014E+26[/TD]

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[TD=width: 108]minuts[/TD]

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[TD=width: 160, align: right]1.3779246836E+25[/TD]

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[TD=width: 108]hours[/TD]

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[TD=width: 160, align: right]5.7413528482E+23[/TD]

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[TD=width: 108]days[/TD]

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[TD=width: 160, align: right]1.5729733831E+21[/TD]

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[TD=width: 108]years[/TD]

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[TD=width: 160]Orbital Period (s)[/TD]

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[TD=width: 108]SemiMajor axis (m)[/TD]

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[TD=width: 64]Moho[/TD]

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[TD=width: 160]2215780.7601817600[/TD]

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[TD=width: 108]5263138304[/TD]

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[TD=width: 64]Eve[/TD]

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[TD=width: 160]5658062.9184427500[/TD]

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[TD=width: 108]9832684544[/TD]

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[TD=width: 64]Gilly[/TD]

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[TD][TABLE=width: 160]

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[TD=width: 160]388592.0317515200[/TD]

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[TD=width: 108]31500000[/TD]

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[TD=width: 64]Kerbin[/TD]

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[TD=width: 160]8939380.3759680500[/TD]

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[TD=width: 108]13338240256[/TD]

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[TD=width: 64]Mun[/TD]

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[TD=width: 160]138986.0420959770[/TD]

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[TD=width: 108]12000000[/TD]

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[TD=width: 64]Minmus[/TD]

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[TD=width: 160]1077323.4309866800[/TD]

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[TD=width: 108]47000000[/TD]

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[TD=width: 64]Duna[/TD]

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[TD][TABLE=width: 160]

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[TD=width: 160]17315607.5479440000[/TD]

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[TD=width: 108]20726155264[/TD]

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[TD=width: 64]Ike[/TD]

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[TD=width: 160]65518.6471392642[/TD]

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[TD=width: 108]3200000[/TD]

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[TD=width: 64]Dres[/TD]

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[TD][TABLE=width: 160]

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[TD=width: 160]47893636.8058837000[/TD]

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[TD=width: 108]40839348203[/TD]

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[TD=width: 64]Jool[/TD]

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[TD=width: 160]104662685.7517580000[/TD]

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[TD=width: 108]68773560320[/TD]

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[TD=width: 64]Laythe[/TD]

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[TD=width: 160]52981.5139758690[/TD]

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[TD=width: 108]27184000[/TD]

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[TD=width: 64]Vall[/TD]

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[TD=width: 160]105963.3587308660[/TD]

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[TD=width: 108]43152000[/TD]

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[TD=width: 64]Tylo[/TD]

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[TD=width: 160]211928.8977212430[/TD]

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[TD=width: 108]68500000[/TD]

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[TD=width: 64]Bop[/TD]

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[TD=width: 160]544513.9538282590[/TD]

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[TD=width: 108]128500000[/TD]

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[TD=width: 64]Pol[/TD]

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[TD][TABLE=width: 160]

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[TD=width: 160]901913.4318238570[/TD]

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[TD=width: 108]179890000[/TD]

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[TD=width: 64]Eeloo[/TD]

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[TD][TABLE=width: 160]

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[TD=width: 160]156993928.8618170000[/TD]

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[TD=width: 108]90118820000[/TD]

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Edited August 8, 2013 by mcirish3

[metaphor]

Tylo's orbital period should also be twice Vall's orbital period. Laythe, Vall, Tylo are in a 1:2:4 resonance just like Io, Europa, Ganymede. Also Eeloo is in a 3:2 resonance with Jool. Other than that, there are no resonances between planets/moons in the Kerbal system. That means that the more accurately you measure their period, the longer you have to wait until their orbits match up exactly.

Suggestion: round the periods you measured for each planet up more to the nearest 100-1000 seconds or so (fewer sig figs), and then do the resonance analysis again.

[mcirish3]

Tylo's orbital period should also be twice Vall's orbital period. Laythe, Vall, Tylo are in a 1:2:4 resonance just like Io, Europa, Ganymede. Also Eeloo is in a 3:2 resonance with Jool. Other than that, there are no resonances between planets/moons in the Kerbal system. That means that the more accurately you measure their period, the longer you have to wait until their orbits match up exactly.

Suggestion: round the periods you measured for each planet up more to the nearest 100-1000 seconds or so (fewer sig figs), and then do the resonance analysis again.

Hold up! you can not know that their positions are in conjunction exactly, if you did not use an accurate measurement of their periods, that would be a contradiction.

The Tylo:Vall relationship is close 2:1 but not exact. At the end of one Tylo orbit Vall lags behind 7 min 12 seconds.

I may be able to find some close resonances using your suggestion the question is how useful will those approximations be.

[metaphor]

From the wiki, Laythe's orbital period is 52981, Vall's is 105962 s, Tylo's is 211926 s. So twice Laythe's period is equal to Vall's period, and twice Vall's period is 2 seconds less than Tylo's period.

But those times are rounded to the nearest second. If we assume they are tidally locked to Jool and use the more precise rotation periods instead, Laythe's is 52980.879 s, Vall's is 105962.09 s, Tylo's is 211926.36 s. Twice Laythe's period is 0.331 seconds less than Vall's period, and twice Vall's period is 2.18 seconds less than Tylo's period.

Also from the wiki, Jool's orbital period is 104661432 s, and Eeloo's is 156992048 s. Jool's period times 1.5 is 100 seconds more than Eeloo's period.

I'm not sure where the values on the wiki came from, or how you could measure them accurately. But the bodies might well be in perfect resonance given the possible rounding error.

[mcirish3]

From the wiki, Laythe's orbital period is 52981, Vall's is 105962 s, Tylo's is 211926 s. So twice Laythe's period is equal to Vall's period, and twice Vall's period is 2 seconds less than Tylo's period.

But those times are rounded to the nearest second. If we assume they are tidally locked to Jool and use the more precise rotation periods instead, Laythe's is 52980.879 s, Vall's is 105962.09 s, Tylo's is 211926.36 s. Twice Laythe's period is 0.331 seconds less than Vall's period, and twice Vall's period is 2.18 seconds less than Tylo's period.

Also from the wiki, Jool's orbital period is 104661432 s, and Eeloo's is 156992048 s. Jool's period times 1.5 is 100 seconds more than Eeloo's period.

I'm not sure where the values on the wiki came from, or how you could measure them accurately. But the bodies might well be in perfect resonance given the possible rounding error.

I will check into this.

[mcirish3]

yep of all the bodies I grabbed the wrong orbital period. I checked the numbers and it did not change them by much that two seconds did still mean that it is several centuries before they are exactly in phase however rather than truncating them perhaps I should recalculate the periods to more sigfigs to see just how close they really are. I grabbed my orginal periods from the wiki.

[NovaSilisko]

The game spits out a period value in seconds for each celestial body, directly calculated based on its orbit.

[mcirish3]

The game spits out a period value in seconds for each celestial body, directly calculated based on its orbit.

That was my original assumption, to be sure, and why I was lazy and did not calculate them for myself. So what you are saying is that the numbers for orbital period are exact in the wiki? I hope some one answers quickly before I go through the trouble of calculating them again.

[NovaSilisko]

Not sure how the wiki numbers were gotten, but it should be relatively simple to make a plugin that spits out all the periods for all celestial bodies.

I do suspect the Tylo misalignment is actual, though. There's no way to directly lock a planet to be in resonance, so the period has to be set VERY precisely or else it will slowly drift out of sync. And you can't set the period directly! So, you've gotta set the actual orbital radius to be juuuust right so it has the correct period.

[mcirish3]

Not sure how the wiki numbers were gotten, but it should be relatively simple to make a plugin that spits out all the periods for all celestial bodies.

I do suspect the Tylo misalignment is actual, though. There's no way to directly lock a planet to be in resonance, so the period has to be set VERY precisely or else it will slowly drift out of sync. And you can't set the period directly! So, you've gotta set the actual orbital radius to be juuuust right so it has the correct period.

Well I am a little chagrined. I discovered that using the period formula yields some very different results. one of them being a much much shorter period for the whole Kerbol system, a factor of 10^55 shorter! The new calculations (hopefully better) give a period of 1.6E+21 years rather than 10^76 years. The thing that worries me is that my period calculations for each planet and the ones on the wiki only match for down to the thousandth place, wondering what they used for big G?????

Also according to what I calculated your right about Tylo but it is way down in the fourth decimal place the ratio of Laythe to Tylo is 4.0001:1

Edited August 7, 2013 by mcirish3

[metaphor]

Big G is actually one of the least well measured physical constants since it's so hard to measure.

If Tylo's orbit was 2 seconds off from its rotational period, it would take 350 years for it to show a different face towards Jool. That's almost 3 days straight running at 100,000x time warp. I guess it would be possible to test, but it would take a very long time.

[mcirish3]

Big G is actually one of the least well measured physical constants since it's so hard to measure.

If Tylo's orbit was 2 seconds off from its rotational period, it would take 350 years for it to show a different face towards Jool. That's almost 3 days straight running at 100,000x time warp. I guess it would be possible to test, but it would take a very long time.

Nonetheless It would seem the orbital periods on the wiki are wrong would be nice if someone could confirm I will be posting my calculations here in a minute or two.

[mcirish3]

You're right about Big G not being well known. It is indeed very hard to measure. That is why I wonder what number they used since google list the last two digits as uncertain: the (80). I was wondering if they used them in their calculations or not.