gravitation dilemma

[miguel]

WHAT ABOUT THAT UNIVERSAL CONSTANT OF "G"

We are aware that a celestial orbital condition involves the mutual rotation of the two bodies around a common center of rotation (or center of gravity if you insist) with equal angular velocity. We are also aware that the ratio of the radii must be mathematically identical to the ratio of the tangential velocity, and inversely proportional to the ratio of the "mass" values: That is R1:R2 = V1:V2= M2:M1.

 

Now let us apply that knowledge. We will assign a fixed mathematical value of 1 to the "mass", tangential velocity, and radius of rotation to the first of two celestial bodies. Then we shall assume a range of possible mathematical values for the "mass" of the second body. Let the range of "mass" of the second body vary from M1 to many, many times M1.

 

When the two bodies have equal mass (M2=M1) then M2:M1=1 and it must follow that R2:R1=1. We have a condition analogous to two equal weight children playing on a see-saw. At this condition, we shall "freeze the postion of the mutual center of rotation relative to M1.

 

Now let the value of M2 begin to increase, while M1, R1, and the location of the center of rotation remain fixed. As M2 increases, the value of R2 must decrease. This is analogous to a heavy child moving inward (toward the pivot point) on a playground see-saw board to offset the effect of his excess weight over that of the lighter child.

 

 

Now apply the current scientific concept that the centripetal force exerted by the celestial bodies (MV^2/R) is the cause of the "mass attraction" between the two bodies which causes them to remain in orbit. Mathematically, Fc = Fg = GM1M2/(R1+R2)^2.

 

We are aware that the mathematical value of the centripetal force exerted on both bodies must be identical. Then the mathematical equation of equality is M1V1^2/R1 = M2V2^2/R2 = GM1M2/(R1+R2)^2. To simplify, we know that the centripetal force must be simply M1V1^2/R1= 1*1^2/1 = 1. It must follow that GM1M2/(R1+R2)^2 = 1.0, and since M1 and R1 are 1.0, this reduces to 1.0=G*M2/(1+R2)^2.

 

Substitute M2=M1*(R1/R2) = 1*(1/R2) = 1/R2 in the preceding equation to get G=1/M2+2/M2^2+1/M2^3. Let M2 then vary from 1 (when M2=M1), to infinity (when M2 >>M1). The conclusion is that the mathematical value of that "universal constant" of G must actually be a variable. For example, when M2 = 1, then the value of G is 4.0. When the value of M2 is 2, then the value of G is 1.125. When the value of M2 is 10 the value of G must be 0.121.

 

As we continue to increase the value of M2, the value of "G" must continue to decrease, until eventually it approaches simply 1/M2. (Due to the predominance of the 1/M2 term in the equation in relation to the other terms.)

 

We are forced to the one of two conclusions. Either the currently accepted concept which forms the basis of "mass attraction" is false, or else "G" is not a "universal constant". If both those "accepted" concepts are valid, then the distance between every pair of mutually rotating celestial bodies throughout the universe would have be be identical. For example, the distance between Earth and moon would have to be identical to the distance between Earth and Sun.

[Royston]

But, all you seem to be doing is changing the mass and the distance, so why would that effect the constant G. Obviously F will change, but as that's reliant on the values of mass and distance, it stands to reason...and why would the mass of one body decrease, if the other increases, that doesn't make sense.

 

EDIT: You seem to be confusing weight with mass...as you're using the analogy of a see-saw.

[swansont]

Now let the value of M2 begin to increase, while M1, R1, and the location of the center of rotation remain fixed. As M2 increases, the value of R2 must decrease. This is analogous to a heavy child moving inward (toward the pivot point) on a playground see-saw board to offset the effect of his excess weight over that of the lighter child.

 

I think this is the problem. The center of rotation will not remain fixed. You have overconstrained the problem, which forces G to be a variable.

[D H]

Now let us apply that knowledge. We will assign a fixed mathematical value of 1 to the "mass", tangential velocity, and radius of rotation to the first of two celestial bodies. Then we shall assume a range of possible mathematical values for the "mass" of the second body. Let the range of "mass" of the second body vary from M1 to many, many times M1.\

 

The problem with your analysis starts here. Your analysis assumes circular orbits. The quoted text is not valid. The circular orbit velocity is a function of the masses and the distance between the masses. When you change M2 (and R2), you also change V1.

[D H]

I think this is the problem. The center of rotation will not remain fixed. You have overconstrained the problem, which forces G to be a variable.

 

 

He can hold the center of rotation fixed by make R2 a function of the second objects mass, R2 = M1R1/M2. With M1=1, and R1=1, R2 = 1/M2.

[swansont]

He can hold the center of rotation fixed by make R2 a function of the second objects mass, R2 = M1R1/M2. With M1=1, and R1=1, R2 = 1/M2.

 

Yes. But as you note, when R2 varies, V1 will also vary. So it is overconstrained. It's somewhat arbitrary at this point to decide which parameter needs to be freed. V1 or CoM.