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You can get the rotation periods of any planet from the map screen or tracking station and clicking the planet and openning the info tab.
All the data you could need and some you don't need is displayed there.
The formulas for orbital radii finding are...
T = ((4*Pi^2*R^3)/(G*m))^(1/2)
R = ((G*m*T^2)/(4*Pi^2))^(1/3)
T is your orbital period in seconds.
Pi is Pi and your calculator should have a button for this.
R is radius in meters measured from the center of the orbit, NOT from the surface of the planet.
G is newtons gravitational constant. It's about 6.67*10^-11 but you don't need it for this.
m is the mass of your planet.
G and m are refered to as Mu and this value is given to you in the game where all the other planetary information is on the map screen.
1 full Kerbin rotation around its axis isn't.
You have to keep in mind Kerbin not just rotates around its own axis. It also moves on solar orbit all the time. Which makes the Sun "move" along too. And since that extra Sun time moves counterclockwise (with the Kerbin rotation), it extends the daylight and night time by a few minutes every day compared to one exact Kerbin rotation around its own axis.
The same is true for Earth. While we have 24h clocks for light reasons, our home actually does full circle form A to A in less than that (my guess by ~1 / 365.24 from 24h).
The same counts for earth too. A solar day is 24:00:00 while the rotation period relative to the stars is just 23:56:04.09 hours
as the wikipedia article explains, a sidereal day on earth is ~23 hours 56 minutes rather than the 24 hours of a solar day
KSP really has to start implementing some of these. And the sun's orbit around that center is really tiny.
Your talking about simulating real N-body physics? That would take an entire re-write of the KSP physics engine. (Not to mention melt the majority of CPU's)
I wouldn't hold your breath, maybe in KSP 2.
Sure, anything could happen.
On a side note; if you are interested in N-body physics, I've got a great game recommendation for you:
http://store.steampowered.com/app/230290/Universe_Sandbox/