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Lunar Recession and the Slowing of the Earth's Rotation


Introduction

One area of Geophysics that gets little attention for its degree of importance is the recession of moon. Yes the moon is slowly moving farther away and slowing the Earth’s rotation in the process. This was first discovered following the Apollo moon landings by bouncing laser off reflectors left behind by astronauts. The reflectors were designed to accurately measure the Earth-Moon distance. The measurements showed that the moon is getting further away at a rate of 1.5 inches or 3.82 cm per year. Furthermore a day is getting longer by 1.7 milliseconds per day per century.  Both affects are a result of tidal forces between them these same forces are responsible for the high and low tides experienced trice a day. 

Lunar recession has been used as evidence against the old Earth model for several decades now. Those claiming an old Earth have made an effort to respond to the calculations some have been a challenge while others have been pathetic. The pathetic efforts generally involve projecting current rates back in a linear fashion with no regard to the actual forces involved, this naturally fails because gravity is not linear. More challenging efforts involve complex calculations involving the affect of continental positions on the tides.

What follows is the result of a objective study on whether or not Lunar recession is a limiting factor on the age of the Earth and whether or not it is compatible with the claim that the Earth is 4.5 billion years old. One way in which this study is different from most previous ones is that it only considers the forces acting on the two bodies. Most other studies simplify the calculations by assuming  that angular momentum is conserved in the Earth - Moon system. This study considered the possibility that some of the angular momentum could be lost from the Earth by other means such as frictional heating or other factors. The results show exactly what it would take for Lunar recession to have been going on for 4.5 billion years as well as whether or not it agrees with other data.

WARNING! The next six sections contain a lot of math, if you don't understand it feel free to ignore it since you can understand the rest without it. The math is needed to set the back ground on which that material is based and is for those that can understand it.


Reason for Tides

Tides occur because the gravitational force exerted by one body on another changes with the distance between them. As a result of this and the fact that physical objects are not points but are extend over a volume different parts of an object will experience different gravitational forces. Since planets are not absolutely rigid these differences produce a small bulge facing the object and one of equal size on the opposite side of the planet. 

The pull of the moon's gravity on the center of the Earth is proportional to  1 / R2

The pull of the moon's gravity on the Earth's tidal bulge is proportional to  1 /( R-r)2

 The difference is:    

               1               1            
 ----------  - -------
      ( R-r)2        R2        

          Now the mass of  the tidal bulge  (Mb) would be proportional to this difference resulting in:

                                 1               1            
Mb = c2   ----------  - -------
              ( R-r)2        R2   

The mass of the tidal bulge would be proportionally higher simply because the size of the tidal bulge would be proportionally bigger. This is because that the closer the moon gets to the Earth the stronger the gravitational forces between them become.


Geometry of tidal Forces

 

The key element in tidal geometry is the tidal phase angle θ which is the angle that results from the delay of the mass in the tidal bulge reacting to the gravitational pull of the moon. This delay causes high tide to be slightly ahead of the moon since the Earth rotates faster than the moon orbits the Earth. If on the other hand the moon orbited the faster than the Earth rotated  then θ would be negative. If the moon orbited at the same rate the Earth's rotation then θ = 0.

θ = C1 wE - w L

The tidal phase angle q is proportional to the difference in the angular velocity of the Earth's rotation and the angular velocity of the moon's orbit. Now it is possible that as the moon gets closer and the size and mass of the tidal bulge gets bigger that the reaction time would actually be longer but that would only  increase θ reducing the time over which Lunar recession can have been going on.

θ' = p - θ

If θ is in radians

θ' = 180 - θ

If θ is in degrees

θ' = 200 - θ

If θ is in gradians

The angle of the opposite bulge (θ') is exactly a half circle behind θ

Unless stated other wise all angles are in radians.


 

            VL
wL = -------
          R

wL = The angular velocity of the moon in its orbit.

R = The distance between the Earth and the moon.

VL =  The linear velocity of the moon in its orbit.


          VE
wE = -------
          r

wE = The angular velocity of the Earth's rotation.

r = The radius of the Earth .

Ve =  The linear velocity of the Earth's rotation at its surface.


R'2= r2 + R2 - 2rR cos(θ)

R''2 = r2 + R2 - 2rR cos(θ')

R''2 = r2 + R2 - 2rR cos(p - θ)

R''2 = r2 + R2 + 2rR cos(θ)

R' = (r2 + R2 - 2rR cos(θ))-2

R'' = (r2 + R2 + 2rR cos(θ))-2


              R2 + R'2 - r2
a = cos-1 ------------------
          2 R R'

              R2 + R''2 - r2
b = cos-1 ------------------
          2 R R''


f = 2p - θ - a

f' = 2p - θ' - b

f' = 2p - (p - θ) - b

f' = 2p - p + θ- b

f' = p + θ - b


At this point we have the full geometry of tidal interactions not only between the Earth and the Moon but for any two bodies. However the case before us is about the Earth / Moon system and these calculations are set up specifically to analyze that system. This now allows us to calculate the actual forces for both the Earth and Moon.


Forces on the Moon

Here we have the forces that result on the moon from the Earth's tidal bulges. These forces are the gravitational forces of the Earth as a whole as well as both tidal bulges. Being gravitational forces all three get exponentially larger as the moon get closer to the Earth.

        G ME ML
g =  ---------------
       R2

This is the formula for the gravitational force between the Earth and Moon. 

G is the gravitational constant.

ME is the mass of the Earth.

ML is the mass of the Moon.

R is the radius of the Moon orbit.

g is the force of gravity between the Earth and the Moon.


        G Mb ML
g' =  ---------------
       R'2

This is the formula for the gravitational force between the Earth's forward tidal bulge and Moon. 

G is the gravitational constant.

Mb is the mass of the Earth's tidal bulge.

ML is the mass of the Moon.

R' is the distance between the Moon and the Earth's near tidal bulge.

g' is the force of gravity between the Moon and the Earth's near tidal bulge.


        G Mb ML
g'' =  ---------------
       R''2

This is the formula for the gravitational force between the Earth's far tidal bulge and Moon. 

G is the gravitational constant.

Mb is the mass of the Earth's tidal bulge.

ML is the mass of the Moon.

R'' is the distance between the Moon and the Earth's far tidal bulge.

g'' is the force of gravity between the Moon and the Earth's far tidal bulge.


Now it needs to be noted that the values of both R' and R'' are dependent on the value of the tidal phase angle (θ) as shown on the previous page. This means that θ is a critical factor for determining both g' and g'' in fact θ is the most critical factor of Lunar recession. 


Fn' = g' sin (α)

This is the force applied to the Moon by the Earth's near tidal bulge along its orbit causing the Moon to accelerate and spiral out. Its is actually stronger than the observed net force because it is countered in part by a smaller force from the Earth's far tidal bulge. α is the angle between R' and R as shown on  the previous page.

Ff' = g'' sin (β)

This is the force applied to the Moon by the Earth's far tidal bulge along its orbit causing the Moon to decelerate. It is smaller than the force from the Earth's near tidal bulge and counters in part that larger force from the Earth's near tidal bulge. This is because the far tidal bulge is farther from the Moon than the near tidal bulge.  β is the angle between R'' and R as shown on  the previous page.

Ft' = Fn' - Ff'

This gives the net force on the moon along its orbit causing the Moon to accelerate and slowly spiral out. Since both α and β and  are related to θ,  θ is shown to be even more important.

tL = Ft' * R

This is the Torque applied to Earth from the net tidal force

IL= ML R2

This is the moon's moment of inertia in its orbit.

           tL
ΔωL = ----
           IL

        This is the rate of change in the moon's angular velocity.


This set of formulas derives the relationship between  the moon's angular velocity and the radius of its orbit.

 

R =  VL/  g

g =  G ME/ R2

R =  VL2/ ( G ME/ R2 )

VL  = wL R

  R =  wL2 R2/ ( G ME/ R2 )

 R =  wL2 R4 / (G ME)

      G MEwL2 R4 / R

 G MEwL2 R3

wL2 R3  =  G ME

This now give us the relationship between the moon's angular velocity and the radius of its orbit.

          G ME
 w L2 =  -----------
          R3

          (G ME)1/2
 w L =  ---------------
         R3/2

  Use this  formula to get the moon's angular velocity from the radius of its orbit.

     

         G ME
R3  =  -----------
         w L2

 ( G ME )1/3
R =  ---------------
         w L2/3

 Use this  formula to get the radius of the moon's orbit from its angular velocity.


Forces on the Earth

Here we have the forces that result on the Earth's tidal bulges from  the moon.  These forces are the gravitational forces that act on the Earth as a whole as well as both tidal bulges. Being gravitational forces all three get exponentially larger as the moon get closer to the Earth.

        G ME ML
g =  ---------------
       R2

This is the formula for the gravitational force between the Earth and Moon. 

G is the gravitational constant.

ME is the mass of the Earth.

ML is the mass of the Moon.

R is the radius of the Moon orbit.

g it the force of gravity between the Earth and the Moon.


        G Mb ML
g' =  ---------------
       R'2

This is the formula for the gravitational force between the Earth's forward tidal bulge and Moon. 

G is the gravitational constant.

Mb is the mass of the Earth's tidal bulge.

ML is the mass of the Moon.

R' is the distance between the Moon and the Earth's near tidal bulge.

g' is the force of gravity between the Moon and the Earth's near tidal bulge.


        G Mb ML
g'' =  ---------------
       R''2

This is the formula for the gravitational force between the Earth's far tidal bulge and Moon. 

G is the gravitational constant.

Mb is the mass of the Earth's tidal bulge.

ML is the mass of the Moon.

R'' is the distance between the Moon and the Earth's far tidal bulge.

g'' is the force of gravity between the Moon and the Earth's far tidal bulge.


Now it needs to be noted that the values of both R' and R'' are dependent on the value of the tidal phase angle (θ) as shown on a previous page. This means that θ is a critical factor for determining both g' and g'' in fact θ is the most critical factor of Lunar recession. 


σ is the angle between the radial force on the near tidal bulge and g'.

σ = φ - π/2

σ' is the angle between the radial force on the far tidal bulge and g''.

σ' = π/2 -φ'


Fn = g' cos (σ)

This is the force applied to the Earth's near tidal bulge by the Moon along the rotation of the Earth. Its is actually stronger than the observed net force but it is countered in part by a smaller force between the Moon and the Earth's far tidal bulge. 

Ff = g'' cos (σ')

This is the force applied to the Earth's far tidal bulge by the Moon along the rotation of the Earth. It is smaller the force that between the Moon and the Earth's near tidal bulge counters in part that larger force. This is because the far tidal bulge is farther from the Moon than the near tidal bulge.

Ft = Fn - Ff

This gives the net force on the Earth along its rotation causing the Earth's rotation to slow. Since both σ and σ' and are related to θ, θ is shown to be even more important.

τE = Ft * r

This is the Torque applied to Earth from the net tidal force


If the Earth were a perfect solid sphere its moment of Inertia would be:

IE = (2/5)ME r2

However the Earth is not a perfect solid sphere so the above moment of Inertia produces a slowing rate of 5.28 ms/cy when the correct value is  2.3 ms/cy correcting the error requires multiplying the above moment of Inertia by 5.28/2.3.

IE = (5.28/2.3)(2/5)ME r2

IE = (10.56/11.5)ME r2    


This produces a slowing of the Earth's rotation  of:  

         tE
ΔωE = ----
           IE


Measured Quantities

ML =  7.3477 1022 kg    

R = 384,399,000 m

δR = 3.84 cm/year = 0.0384 m/year

ME =  5.9742 1024 kg    

r = 6,371,000 m

ω = 2π / 23 hr 56 min 4.1 sec = 2π / 86,164.1 s = 7.29115 x 10-5 s-1

ΔωE  = 1.7 milliseconds day-1 century-1 = 0.0017 s day-1 cenury-1 = 4.56215 x10-22 s-2 

High tides lags 12 minutes behind the Moon

θ = 0.05236 = 3o

Average ocean tide height 1.6 feet = 0.48768 meters

Largest Tsunami 1720 feet = 524.25600 meters

G = 6.67300 10-11 m3 kg-1 s-2


Initial calculated Quantities

Recall the following from the section on the forces on the Moon:

 

        G Mb ML
g' =  ---------------
       R'2

        G Mb ML
g'' =  ---------------
       R''2

 G Mb ML
Fn' =  --------------- sin (α)
   R'2

        G Mb ML
Ff' =  --------------- sin (β)
       R''2

Ft' = Fn' - Ff'

Combining these results in:

              G Mb MLsin (α)           G Mb MLsin (β)        
Ft' =  -------------------- -  -----------------------
                R'2                                         R''2                      

              G MLsin (α)           G  MLsin (β)        
Ft' / Mb =  -------------------- -  -----------------------
                R'2                                         R''2              

                    G MLsin (α)           G  MLsin (β)        
K0 =  -------------------- -  -----------------------
                R'2                                R''2             

Ft' / Mb =  K0

Ft'  =  K0 Mb

Ft' / K0 =  Mb

Mb =  Ft' / K0

Ft'  is calculated by converting the lunar recession rate (ΔR) to the change in Moon angular velocity (ΔωL)

This can be done with the formulae provided in the section on the forces on the Moon

 

The mass of the Earth's tidal bulge is related to the difference distance between the Earth's center and the Moon; and  distance between the Earth's surface nearest the Moon and the Moon.

This fact results in the following relationship.

 

                 1               1            
k =   ----------  - -------
        ( R-r)2        R2  
  

Mb = c2 * k

Mb /  k = c2

c2= Mb /  k


Limiting Factors

θ > π/2

If  θ > π/2 then the Earth rotation would accelerate and it could never drop below or even reach θ = π/2. 

With θ < π/2 then the Earth rotation slows and it can never get above or even reach θ = π/2.

 

The Earth's surface rotational velocity must be less than orbital velocity of about 4.5 mile per second. (Rotation period 1.5 hours)

If the Earth's surface rotational velocity were equal to or greater than orbital velocity then it could not form by collapse by natural means.

If the Earth's surface rotational velocity were greater than orbital velocity the outward stress on the planet would eventually tear it apart.

 

The Moon's orbital radius must be greater than the Earth's Roche limit for the Moon. (15,562 km km)

If the Moon's initial orbital radius were less than the Roche limit then the Moon could not have formed from gravitational collapse as a result it original orbital radius had  to have been more than the Roche limit.

The Moon's orbital radius at time t must be greater than geostationary orbital radius at time t.

If the Moon's orbital radius were less than geostationary orbital radius then it would spiral in towards the Earth and not away from it.

If the Moon's orbital radius were equal to geostationary orbital radius then the Earth and Moon would be tidally locked and no change would occur.

Note that with a faster rotation rate the geostationary orbital radius would be smaller and could at some time in the pasts be less than the Roche limit.


Backwards Projection

The following section shows four backwards projections of lunar recession data based on four different conditions. The first is a strait forward backwards projection with no tweaks. The others projections were made to deal with common mistakes made on the issue.  Some times these mistakes are made by accident but other times they are made to hide the problems this data makes for a 4.5 billion year old Earth.

A strait forward backwards projection


This a backwards projection of the number of days in a year based on forces  acting on Moon and Earth.


This a backwards projection of the distance of the moon based on forces  acting on Moon and Earth.

This is a strait forward backwards projection of the relative proper secular breaking of the Earth's rotation and lunar recession data made without any tweaks. The current data is simply plugged into the math. as shown earlier. The result is that the Moon would have been at the Earth's Roche limit of 15,562 km 1.171 billion years ago. This is far short of the 4.5 billion years commonly given for the age as the Earth. This suggests that the Earth Moon system can not be any where near 4.5 billion years old. These results are similar to other calculations done by Dr. Walt Brown and others showing these calculations are valid.

A backwards projection based on the observed slowing of the Earth's rotation 


This a backwards projection of the number of days in a year based on forces  acting on Moon and Earth.


This a backwards projection of the distance of the moon based on forces  acting on Moon and Earth.

This is a backwards projection of the relative proper secular breaking of the Earth's rotation and lunar recession data made assuming that the current relative proper secular acceleration of the Earth's rotation continued back.  The relative proper secular acceleration is the difference between the relative proper secular breaking and the observed net breaking of the Earth's rotation. The reason given for this difference is the process of Earth rounding out following the Ice age. Once again the current data is simply plugged into the math. as shown earlier. The result is that the Moos would have been locked in Geosynchronous orbit around the Earth at  16,000km 1.25 billion years ago. This is far short of the 4.5 billion years commonly given for the age of the Earth. This suggests that the Earth Moon system can not be any where near.4.5 billion years old.

Backwards projection assuming  a constant breaking of the Earth's rotation


This a backwards projection of the number of days in a year based on a constant breaking pf the Earth's Rotation.


This a backwards projection of the distance of the moon based on forces  acting on Moon and Earth based on a constant breaking pf the Earth's Rotation.

This is a backwards projection of the number of days in a year and lunar recession data made assuming a constant breaking of the Earth's Rotation.  This is not a  reasonable assumption but it is a common mistake. The result is that the Moon would have been locked in Geosynchronous orbit around the Earth 1.36 billion years ago. So even this extremely generous assumption produces a result that is far short of the 4.5 billion years commonly given for the age of the Earth. This suggests that the Earth Moon system can not be any where near 4.5 billion years old.

Backwards projection assuming the Earth's rotation is constant


This is a backwards projection of the number of days in a year assuming a constant breaking of the Earth's rotation.


This a backwards projection of the distance of the moon based on forces  acting on Moon and Earth assuming a constant breaking of the Earth's rotation.

This is  a backwards projection of the number of days in a year and lunar recession data made assuming that the Earth's rotation is constant . This is not a  reasonable assumption in fact it is totally contrary to observation. The result is that the Moon would have been locked in Geosynchronous orbit around the Earth 1.55 billion years ago at 42,164 km. So even this extremely generous assumption produces a result that is far short of the 4.5 billion years commonly given for the age of the Earth. This suggests that the Earth Moon system can not be any where near 4.5 billion years old.

These results show that the forces on the moon are far more important than those on the Earth in determining a maximum age for the Earth Moon system. The fact that you don't even get half way to 4.5 billion years even when keeping the Earth's rotation rate constant is strong evidence for the Earth Moon system not being any were near 4.5 billion years. We could potentially stop here but  several arguments have been raised against such calculations and we need to deal with those arguments.


Paleontological Data

Old Earth proponents often point to paleontological data as evidence  that the previous backward projections are wrong. The claim will often includes a few examples that are often dated as millions of years apart. However this claim does not consider all of the fact about this data including alternative interpretations that do have any thing to do with lunar recession and the length of an Earth day.

This paleontological data comes in the form of fossil bivalves and coral, fossil "stromatolites", and fossil "tidal rhythmites." Bivalves and coral are animals that tend to live about a year and show daily growth rings on their hard exteriors. Stromatolites are produced by the activity of cyanobacteria. Tidal Rhythmites are produced by tidal action.

Stromatolites

Stromatolites are produced by the activity of cyanobacteria and living colonies produce 365 layers in year. Fossil "colonies” have been found with 450-800 layers in apparent agreement with the slowing of the Earth rotation through the geologic ages.

The main problem is that fossil stromatolites may not have formed from cyanobacteria. Some contain no evidence of the cyanobacteria and carbonate precipitation can result in some very stromatolite like structures, rendering the number of layers meaningless. However even if they are legitimate fossil stromatolites it could just means that the colonies lived longer than a year in the past.

Tidal Rhythmites

Tidal Rhythmites are produced by tidal action, so called fossil tidal rhythmites are assumed to indicate the moon's position and the number of days in a month or year in the past. Now getting this data out of rock patterns is not a simple process. It is based on the fact that there are two high tides in a day and it changes over a month from different positions of the moon. Figuring out the number of days in a month or year in the past requires comparing patters in the rocks with patterns expected to be produced by the moon.

The main problem with this is that it requires making assumptions about where the moon was at the time, resulting in a degree of circular reasoning. In addition there are factors that distort the tidal rhythmites producing erroneous patterns. There is also an additional problem since the types of same patterns occur in varves. This leads to the question of  whether or not these are rhythmites or varves? It turns out the even experts have a hard time telling them a part in the geologic record. If they are varves then the patterns are meaningless for determining past lunar positions or the number of days in a year.

Bivalves and Coral

Coral and bivalves normally produce one growth ring per day, normally it is 365. Do to the slowing of Earth rotation coral would have had more rings in the past on an old Earth .  Fossil coral and bivalves have been found with 357-450 growth rings. The extra growth rings are assumed to indicated more day per year. However they could mean that these corals and bivalves lived more than a year. Further more in some cases what are being examined are monthly growth rings with the number of day in a year being calculated based on an assumption of more than twelve shorter lunar months. In those cases it is assuming that both days and lunar months were shorter making it circular reasoning to use it as evidence for the same.


Made from data from
the Present is Key to Past, 365 Topics in Historical Geology,
by Hugh Rance (revised July 2012)
http://geowords.com/histbookpdf/L13.pdf

 

Stromatolites, (green)  fossil tidal rhythmites, (blue) and fossil bivalves and coral (orange) all have indicators interpreted as showing more days  in a year in the past. However when one looks closely at this data, the claim is shown not to be so certain. The first clue is the fact that the degree of scattering in the data is not what would be expected if it were really the result of lunar rescission.

 

It should produce a clear curve like as seen above but it does not. Now scattering often occurs in data, but in this case there is no reason for this degree of scattering. If there were a clearer line with a little scattering the scattering could be early deaths. However The actual degree of scattering does not indicate this.

From a creation science perspective the scattering of the fossil bivalves and coral (orange) could easily be a result of hydrological sorting during the Genesis Flood since those with more growth rings would be larger and there by end up buried lower, and the scattering results from hydrological sorting being an imperfect t process. The Stromatolite data shows four pairs of data points. The "older" two pairs could be pre-Flood and may even been formed during the creation week. The other two pairs seem to be an early Flood deposits. The relationship within each pair shows no trend. However there is a trend among the pairs, and in particular among the three older pairs. This could simply represent a change in precipitation patterns.

The basic assumption of this data that makes it meaningful to lunar recession is the dates. If the dates are wrong and  these fossils and features were a result of  the Genesis Flood or a recent creation then it would not be expected to fit a lunar recession model consistent with a 4.5 billion year old Earth. From an old Earth perspective this data represents real data on the slowing of the Earth's rotation. Thus any viable Old Earth model needs to fit with this data. If the old Earth model does not fit this paleontological data it is a failed model.


Trying to save the 4.5 billion years time scale

Naturally Old Earth proponents have tried to defend it from laws of physics. Most responses to the lunar recession issue found on anti-creationist websites are little more than copy and paste jobs from a main anti-creationist web site. The argument is based on a paper by Kirk S Hansen.

Secular Effects of Oceanic Tidal Dissipation on the Moon's Orbit and the Earth's Rotation

Reviews of Geophysics and Space Physics (Reviews of Geophysics) 20(3): 457-480, August 1982.

The main argument is based on the notion that  in the past the phase angel (θ) between the Earth's lunar tidal bulge and the moon was smaller than the current 3o. In the abstract to his paper Hansen states the past calculations leading to a 1-2 billion year maximum age for the Earth - Moon system assume a "constant frictional phase lag angle". To reduce the phase angle he claims that the current continental position has produced an unusually high phase angel. He further proposed that when there was a single super continent the phase angel was smaller than today. However subsequent calculations including that done by Walt Brown and the current study make no such assumption showing that the phase angel (θ) is a function of the rotation rate of the Earth and the orbital rate the Moon resulting in a tendency of it to be higher in the past unless the moon is near geosynchronous orbit. 

The conclusion given is that the Moon started at a distance of 151,000 miles with a 12hr day on Earth, though often the 12hr day is omitted. However when this claim is studied more closely it does not work without specific tweaking to get the current Earth - Moon system from these starting conditions. 

A parliamentary backwards calculation shows that a phase angel of less than 1o is needed for most of the Earth's history for the Earth - Moon system to be 4.5 billion years old. In this backwards calculation no geologic bases is used to get the 1o phase angel it is just what is mathematically necessary to save the 4.5 billion year figure from the laws of celestial mechanics.

When this 1o phase angel is used to  project the number of days in a year backwards and compare it with old Earth proponents' own paleontological data it fall far short of that paleontological data. This shows that such a slow slowing of the Earth's rotation is not workable simply because it does not agree with other data that it must agree with to be accurate.

When the starting conditions of this claim of a lunar distance of 151,000 miles and a 12hr Earth day are plugged into the math along with a phase angle of 0.942351o the resulting lunar distance today is today's value of  384,399 km.

However the number of hours in a day at present comes to 26.44 hours which is significantly above the present-day value  of 24.

It also produces a days in a year projection totally below old Earth proponents' own paleontological data. This is so bad that it even goes below a fossil indicating just 350 days.

In an effort to be as fair as possible I added a fudge factor to the Earth's rotation rate so as to get it in line with the observed present-day value. This fudge factor was originally designed to deal with the  current relative proper secular acceleration of the Earth's rotation which is thought to result from the Earth rounding out following the Ice age. However since this fudge factor is the percentage of the torque on the Earth from the Moon that actually slows the Earth's rotation it can hence substitute for any unknown factor that reduces the slowing of the Earth's rotation without acting on the Moon. The phase angle was adjusted to 0.939o and the fudge factor was set to 91.5%. There is no known geological basses for this fudge factor, it is simply required to make this model fit reality.

By making these adjustments we once again get today's lunar distance of  384,399 km.

An we also manage to get a 24 hour day.
 

However the projection of the number of days in a year still falls far short of old Earth proponents' own paleontological data.  Thus this model fails this critical test as well.

It gets even worst for this model since it starts with 729 days in a year which is actually less than at least two of old Earth proponents' own paleontological data points.

However the final nail in this model's coffin is that it runs afoul of the currently accepted and presented as truth theory of the Moon's origin. According to this now currently accepted model the moon resulted from an impact between Earth and a Mars size planet 4.5 billion years ago. It also has the Moon forming at one tenth the distance from the Earth as the model we have been examining. As a result this attempt to save the 4.5 billion year figure from the laws of celestial mechanics fails every test that can be thrown at it.


Evaluating the Giant Collision Hypothesis of the Origin of the Moon

The Giant Collision Hypothesis of the origin of the Moon proposes that the Moon formed as a result of collision between the Earth and a Mars size body referred to as Theia. This is the latest in a long line of theories and it will probably be taught in schools as fact only to be replaced in a few decades by a new theory that will be taught as fact. One evolutionist illustrated the difficulty they have in explaining the Moon by purely natural means by jokingly saying that the best explanation for the Moon is observational error.


Use under GNU Free Documentation License.
Lecture 12: The Moon and Mercury
Credit: User:Marvel wikimedia commons

As shown here Theia forms at Earth's L5 point with the sun and eventually drifted into an impact. The L5 point is one of 5 points  between the Earth and the sun where a small body can have a relatively stationary position with respect to the Earth and the Sun. The Moon is thought to have formed after being hit by the hypothetical protoplanet Theia. The Name Theia comes from Greek mythology, and was the  name of the Titan goddess who was the mother of the Moon goddess Selene.

The question before us is can you get the current Earth-Moon System from this in a manner consistent with the observed data. What follows is an analysis of the reseeding of Moon and slowing of the Earth's rotation to test the feasibility of this model with regards to the laws of celestial mechanics. These results are then compared to old Earth proponents' own paleontological data to see if they fit.

This model has a set if starting conditions for the Earth-Moon system resulting from the hypothetical impact. The model has a 5 hour day on Earth when the moon formed. It further starts with the Moon just 14,000 miles (22,526 km) from Earth. These starting conditions allow us to calculate this model forward to the present to see how it fits reality.

The first forward calculation of this model simply involved plugging the starting conditions into the simulator with no fudge factors. It produced an initial phase angel (θ) of 6.93o which is more than twice the current value of 3o.

The result was a present Earth day of 44.9 hours and a lunar distance of 440476 km both of which are significantly larger than their current values.

The next forward calculation of this model plugged the starting conditions into the simulator but forced a phase angel (θ) of 0.99o and an additional fudge factor 94.3% of the torque from the Moon actually applying to slow the Earth's rotation rate. The additional factors were not based on any geological or other factor that would suggest it but was simply what was required to get the current Earth Moon system from the starting conditions.

Now this simulation did produce the current Earth-Moon system but only by tweaking two factors of the simulation specifically to get that result.

However the projection of the number of days in a year falls far short of old Earth proponents' own paleontological data. As a result the Giant Collision Hypothesis of the Origin of the Moon fails the reality test. Yes if tweaked just right you can get the current Earth-Moon system but it dose not fit other data.

The conclusion is that Giant Collision Hypothesis of the origin of the Moon dose not naturally produce the current Earth-Moon system and only does so by deliberately tweaking  the phase angel and the percentage of torque from the Moon that is actually applied to the slowing of the Earth's rotation rate to do so. There is no scientific bases for this tweaking other than forcing the simulation to produce the current Earth-Moon system. Furthermore it does not fit with the paleontological data from old Earth proponents' own theoretical system of geology, thus this model fails.


Best possible fit to Paleontological Data

In an effort to be thorough and to give the 4.5 billion year figure every possible chance a simulation was run specifically so as to match the Paleontological Data. However the results only make matters worst for the  4.5 billion year figure because it not only fails to save the figure but actually raises more problems for it.

This chart shows how this backward projection goes for the number of days in a year as compared the old Earth proponents' own Paleontological Data. While it obviously fits that data it happens by artificially adjusting the phase angel (θ) specifically to fit it and not based on any actual geological bases.

Time  in years

% of  calculated
phase angel used

0

100%

50,000,000

170%

450,000,000

30%

1,100,000,000

25.5%

Changing the phase angel to these percentages at these times in the simulation produced this graph. Now let's look at the Moon's distance from the Earth.

When we look at the backwards projection of Moon's distance from the Earth it is found to be at the Roche limit about 2.067 billion years ago. This once again indicates that the Earth-Moon system can not be 4.5 billion years old. The Moon just moves too quickly to get the current Earth-Moon system by any realistic means by starting 4.5 billion years ago.

Finally to allow it to reach the 4.5 billion years required adding an additional phase angel adjustment to 0.92% in the simulation at 1.975 billion years. The result was to reduce the phase angel to 0.06-0.10 degrees.  Like before this was done for no other reason than to make it reach the 4.5 billion year mark.

The fact that it takes unrealistic phase angels to reach this result is enough to invalidate the 4.5 billion year figure. However beyond 4.26 billion years ago the phase angel becomes totally impossible since the Moon’s gravity is not strong enough to pull any thing the required distance that fast. Further more based on the observed current value of 3 degrees it is probably physically impossible to the Earth it’s oceans to react to the Moon’s gravity quickly enough for the needed phase angels of 1/10th of a degree and less. As a result even this last ditch effort to salvage the  4.5 billion year figure fails.


Conclusion

The conclusion of this study on Lunar recession, tides and the Age of the Earth is that there is no legitimate model of Lunar recession that fits with a 4.5 billion year old Earth. The simple fact is Lunar recession limits the age of the Earth to way less than 4.5 billion years. True it dose not prove the Earth is 6-7 thousand year old but it proves beyond a reasonable doubt that it is considerably younger than 4.5 billion years.

Old Earth proponents clearly understand that they have a problem here since their ultimate response seems to be that the Earth-Moon system is too complicated to get accurate results form such calculations. Even if that is true this study went to every length to fit the model to data so as to get accurate results and it still shows that the Earth-Moon system can’t be 4.5 billion years old.  So even in their efforts you rebut the Lunar recession age limit they only show that it is a problem for them.

Now this does not prove beyond any doubt that the Earth-Moon system can’t be 4.5 billion years old. After all you can never prove anything beyond an unreasonable doubt. However believing that the Earth-Moon system is 4.5 billion years old requires an act of faith that there is a solution out there some place that has yet to be discovered.


 

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