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Useful formulae and constants (IE may not work) (Read 9201 times)
abyssoft
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Re: Useful formulae and constants (IE may not work
Reply #15 - 01/20/12 at 14:40:31
 
Minimum time to tide lock with parent body
     T≈(a^6 ωIQ)/(3Gm_p^2 k_2 R^5 )
ω is the initial rotation period of the primary body in rad/s
a is the semi-major axis of the secondary body
G is the gravational constant
m_p  is the mass of the primary body
m_s  is the mass of the secondary body
R is the radius of the secondary body
I is the moment of inertial for the secondary body
     I≈0.4m_s R^2
Q is the dissipation function of the secondary body  
(typically between 50 and 500)  see http://en.wikipedia.org/wiki/Fluctuation_theorem#Dissipation_function for equation
     k_2≈1.5/(1+(19μ/2ρgR))  
     ρ is the density of the secondary body
     μ is the rigidity of the secondary body in terms of crushing pressure;
     This can be taken as 3×10^10  Nm^(-2) for rocky objects and 4×10^9  Nm^(-2)  
     for icy ones as an estimation,if you want to refine determine what pressure
     is needed per square meter to deform the normal crystal lattice  
     of the substance averaged over the composition of the body.
 
g is the surface gravity of the secondary body
     g≈(Gm_s)/(R_V^2 )
     R_v  is the mean volumetric radius of the secondary body
 
I believe this to be related to Obliquity Erosion when a planet looses it tilt over time but more research is needed.
 
Due to complexity I'm going to go about this one a bit differently for the image
 

 
Combined as 1 Formula
 

 
Simplified
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« Last Edit: 03/13/12 at 00:04:35 by abyssoft »  
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abyssoft
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Posts: 302
Re: Useful formulae and constants (IE may not work
Reply #16 - 03/13/12 at 13:22:01
 
Updated the posts with images still working on the Kirkwood gaps and peaks, the analysis is take a bit longer then I had hoped but I'm trying to make sure I have at least a 5 sigma confidence.
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