# The Naked Scientists Forum

### Author Topic: Calculating the Gravitational Constant  (Read 1272 times)

#### jeffreyH

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##### Calculating the Gravitational Constant
« on: 15/03/2014 23:29:32 »
If we take the calculation for g = -GM/r^2 and take the radius as 1 metre and the value of g as 1 we can rearrange as gr^2/M = G. The gif below shows the straight line plot along which the actual value of G will be found. When values are determined experimentally they will be invalid if they do not fall along this line.

#### jeffreyH

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##### Re: Calculating the Gravitational Constant
« Reply #1 on: 16/03/2014 02:29:13 »
I have managed to calculate the gravitational constant using known values. The value is 6.6738377255129193273770687936191e-11. This was done using Planck values from earlier research. As the Planck values are themselves uncertain this should be considered uncertain. If the Planck values could be refined this method would produce an exact value.

The plot below shows the upper and lower values obtained by experimentation. The above value falls between these bounds.

This produces a revised Planck length of
1.6161989838715412097141201268384e-35
« Last Edit: 16/03/2014 03:13:55 by jeffreyH »

#### jeffreyH

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##### Re: Calculating the Gravitational Constant
« Reply #2 on: 16/03/2014 15:00:08 »
If we now take the calculation for the Planck length lp = SQRT(hbar*G/c^3) and make lp = 1 metre. We can rearrage the equation to solve for G. This gives us a value for G of 2.5549710508300273660790803864996e+60. Using this in the calculation for g and taking the radius as 1 and the mass of the earth we arrive at a value of g of 1.5258287115556923430224268068172e+85. Dividing this by 9.78 gives 1.5601520568054113936834629926554e+84. Dividing our value of G for the 1 metre pl by this result gives 6.6738400000000000000000000000003e-11 as our value for the gravitational constant. Some clever use of this type of method could arrive at a mathematically accurate value for G that would not need experimental measurement to confirm as all values would be known with a low degree of uncertainty.

NOTE The rearrangement of the equation gives initially lp^2 = (hbar*G)/c^3 then G =(lp^2*C^3)/hbar. As lp was in natural units and = 1 we have simply G = C^3/hbar.
« Last Edit: 27/03/2014 03:32:09 by jeffreyH »

#### jeffreyH

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##### Re: Calculating the Gravitational Constant
« Reply #3 on: 16/03/2014 16:49:28 »
In the graph above the gradient does vary by very small decrements so this is not a straight line. Inserting the value for G calculated above into the plot data does in fact fit well into this gradient with a high degree of accuracy. This value also corresponds with the current value as stated on wikipedia although I have not looked up the current SI definition.

#### jeffreyH

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##### Re: Calculating the Gravitational Constant
« Reply #4 on: 16/03/2014 17:07:23 »
The previous value of G did not return 1g when used in calculations so does not fit within the gradient. A new modified value of G
(6.7966579035498995311453449430688e-12)
returns a value of
0.99999999999999999999999999999988g
This value is higher than has ever been determined but fits precisely into the gradient of G over mass. This value was determined by using a radius equal to the earths radius rather than the 1 metre radius used earlier.

Update: When plugging this into the equation to calculate g for the earth using the radius and mass of earth this value returns exactly 1g. Therefore this has to be wrong. The point of interest is the fact that this value returns exactly 1g. The relationship between using 1 metre and earth radius in the calculations requires some further study.
« Last Edit: 16/03/2014 17:13:44 by jeffreyH »

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##### Re: Calculating the Gravitational Constant
« Reply #4 on: 16/03/2014 17:07:23 »