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