Short Comings of the Planetary Spin-Orbit Coupling Model

SIMPLE TIDAL TORQUING MODEL

(UPDATED 20/03/2012)

Imagine that Venus and Earth are aligned directly above a point A that is on the surface of the Sun. The combined tidal force of Venus and Earth produced two tidal bulges upon the surface of the Sun located at A and B.

Jupiter is located at an angle θ to the line joining the two tidal 

bulges at A and B. Let Rs be the radius of the Sun = OA = OB.

Now by the cosine rule:

JB² = RJ² + Rs² – 2 × RJ × Rs × cos(θ)                         and

JA² = RJ² + Rs² – 2 ×RJ × Rs × cos(π - θ)

      = RJ² + Rs² + 2 ×RJ × Rs × cos(θ)                                                             

Let angle JAO = φ 

and angle JBO = ψ                                                                  

then by the sine rule:

RJ / sin (φ) = JA / sin (π – θ)                                           and

RJ / sin(ψ) = JB / sin (θ)

therefore:

sin (φ)  = (RJ / JA) × sin (π – θ)

sin (ψ) = (RJ / JB) × sin (θ)

 By Newtons Law of Universal Gravitation

Ff = G M_J M_S / JA² = const / JA²                 const = G M_J M_S

Fn = G M_J M_S / JB² = const / JB²

Now

Ffp  = Ff × sin(φ)

hence:

Ffp  = (const / JA²) × (RJ / JA) x sin (π  − θ) 

       = (const’ / JA³) × sin (θ)       

                                                                   const’= const × RJ

and

Fnp = Fn × cos (ψ – π/2) 

       = Fn × cos (-(π/2 – ψ)) 

       = Fn × cos (π/2 – ψ) 

       = Fn × sin (ψ))

hence:

Fnp = (const / JB²) × (RJ /JB) × sin (θ) 

      = (const’ / JB³) × sin (θ)

Finally:  ΔF = The net tangential force of Jupiter's 

gravitational on the Sun's tidal bulges 

ΔF = Fnp – Ffp 

     = const’ × [(1 / JB³) – (1 / JA³)]  × sin (θ)

ΔF = const’ × {(1 / [RJ² + Rs² – 2 × RJ × Rs × cos(θ)]^3/2) 

         − (1 / [RJ² + Rs² + 2 ×RJ × Rs × cos(θ)]^3/2)} × sin(θ)

The following graph shows the net tangential acceleration of the  

Sun's surface due to Jupiter's gravitational force acting upon the 
tidal bulges that are induced by Venus/Earth upon the Sun's surface 
as a function of Jupiter's angle θ (please refer to diagram above). 
Note: It is assumed that Jupiter's force only acts upon one percent 
of the mass of the convective zone of the Sun (=0.0002 % of the 
mass of the Sun). 

Even under these ideal assumptions, the maximum peak acceleration 

only reaches ~ 3.0 micro-metres per second^2. 

Assuming that half this peak acceleration is applied to 0.02 % of the 
Sun's mass for one full day at each of the roughly seven alignments 
of Venus and Earth over the 11.07 years it takes for θ to change from 
0 to 90, the net change to to the Sun's velocity should be 


acceleration x delta time ~1.5x10^(-6) x 7 x 24 x 3600 ~ 0.91 m/sec

Given these highly optimistic assumptions, it could be argued that 
if Jupiter's gravitational force only had to change the rotational
velocity of one % of the mass of the convective zone of the Sun 
(~ 0.02 % of the mass of the Sun) it would produce a significant
change rotational velocity of this small amount of mass.


Of course, the assumptions used in these calculation require 
that the one % of the Sun's convective layer mass that is affected 
by Jupiter's gravity is dynamically decoupled from the remaining 
0.998 % of the Sun's mass. At this stage, there is no region of 
the Sun's convective layer that is known to be effectively 
dynamically decoupled from the rest of the Sun. In addition, 
even if such a region did exist within the Sun's convective zone, 
we have no idea of its relative mass. 


Given these large uncertainties, all we can say is that the 
0.91 m/sec change in rotational velocity is most likely a 
loose upper bound to the real value.   


(N.B. All the arguments given above assume that there are 
no other induced asymmetries in the spherical shape of the Sun 
other than those produced by the combined tidal forces of 
Venus and Earth at the time of alignment).

CONCLUSION

The simple planetary spin-orbit coupling model does not

appear to produce a significant change in the velocity of 

rotation in the outer layers of the Sun.

Hence, in order for it to taken seriously, the planetary 
spin-orbit coupling model would require a considerable 
and as yet unknown amplification mechanism .     

One possible amplification mechanism is discussed here:

http://astroclimateconnection.blogspot.com.au/2010/05/mechanism-for-amplifying-planetary.html