[gem (OP)]

, 'newton proved mathematically that a uniform spherical shell of matter exerts a gravitational force on a particle located outside the shell as if all the shells mass were concentrated at its centre.And also the theorem can also be applied to a situation in which a particle is located inside such a shell,to show the following, a uniform shell of matter exerts no net gravitational force on a particle inside it.

Now i know that this was a mathematical result of newtons showing that all the vector sums added up to prove this theory and i think this theory holds while on the surface of the shell and inside a shell but not when a particle is any great distance from the surface,

i think the variation gravitational acceleration that has being measured shows that it is diminishing faster than the inverse square law predicts while in reasonably close proximity of earth and being detected to be greater than inverse square law predicts when further away at much greater distances.

I think these anomalies are simply because the earths gravitational force that we experience on a daily basis put at roughly 9.81 metres per second squared is just what newton said, a net vector result of every particles attraction in the direction that it is being measured.

 which leads me to conclude that earths gravitational pull on a particle at earths surface is pulling at an approximate average angle of a 90 degree cone which would give a total force equal to close to 14 metres per second squared but with a net vector sum resulting force of 9.81 metres per second squared.

 so when leaving earths surface in reasonably close proximity, the inverse square of the distance changes from the main source of the force out of proportion to the change in the average vector angle.And when at greater distances the vector angle becomes less so allowing the total force a straighter pull on a particle so manifesting in a greater attraction force than predicted in the inverse square law.

 so looking at the Cavendish /Michell experiment and applying the same concerns it would also call into question some of the conclusions drawn.

[gem (OP)]

As no one has found cause to disagree with the logic of the above i will now expand on the areas of concern of conclusions drawn from the Mitchell/Cavendish experiment.

firstly i understand why Cavendish chose lead as his material of mass due to its high density and the fact of its not being affected by magnetism.

However if you look at the vector angles of the interactions between the fixed large spheres and the suspended small spheres they are not the same as the vector angles between the small sphere and the earth.[he compared the attraction of the large and small sphere to the attraction between earth and the small sphere]

giving a result of 5.51 grams cm3 density for the earth, water being 1 gram cm3 and lead 11.34 grams cm3

If for arguments sake you changed the material of the large sphere to one equal to the density of water  and left the small sphere as lead you would change the vector angle of their interaction,indeed if you used a material equal to the density of water in both sets of spheres you could not get their centres as close as in the Mitchell/Cavendish experiment so changing the inverse square of the interaction also.


So if these interactions of homogeneous mass are affected by the space between them  and the choice of material changing the angle of attraction it will also call in to question the value of big G which was later derived from this experiment.

I know newtons mathematical concept to bring everything to the centre simplified things and when you apply it to a homogeneous sphere when on its surface or within it the theory probably holds but when you put space between the two spheres of mass the vector angle of their interaction changes.

[remember in reality every particle attracts every other particle from where they actually are not from the centre]

Given these concerns around a foundation of physics i thought it pertinent to try and bring to the attention of the scientific community.

I look forward to comments

[Ron Hughes]

Are you suggesting that the force on an object at sea level would be less than on an one at say 2KM above sea level?

[graham.d]

gem, as far as I can see you are trying to do the sum of vectors calculation (that normally shows that the force of gravity from a spherically symmetric body can be consider as coming from a point at its centre) and getting it wrong. If g was 14 rather 9.81 I think it would have been noticed!! By claiming that g varies I assume you mean it is G that has been miscalculated because everyone has misunderstood the physics and maths relating to spherical symmetry; clearly g is only 9.81 at the earth's surface. It would affect, for example, the height of a geostationary satellite by a considerable amount and all space flights, especially to the moon, would have failed. There are small errors in the measurement of g because the earth is not a uniform sphere so the acceleration at the earth's surface varies, but it certainly the same to 3 significant figures. I think the various measurements of G, including the Cavendish experiment, agree to at least 5 or 6 significant figures.

[PhysBang]

Since the orbits of the planets place incredibly tight boundaries on Newtonian gravity, I suspect that if one used this proposal to calculate the orbit of one of the planets and account for perihelion shift, then one would soon run into a problem.

I consider the proposal to be mere conjecture until I can see how it calculates an orbit that we have observed in detail.

[gem (OP)]

Thanks for the comments, sorry i haven't replied sooner i have been away for a couple of days.

So i will try to answer the points raised, Ron to be clear earths gravitational acceleration when on the surface will be stronger than 2KM away from the mass of the earth.

Graham i am not saying that g acceleration is close to fourteen metres per second i am saying if you look at the average angle of attraction on a body at earths surface earths mass is pulling with a force equal to an acceleration of just under          14 mps. 9.81 mps is the vector result.

PhysBang the Mitchell/Cavendish experiment was done after newton died, and as far as i understand it newton and other astronomers were predicting and plotting the motion of the planets with out the values that this experiment gave.

As regards when this extra force will manifest its self it will have to be at much greater distance than say the 400km that a space shuttle orbits at because the vector angle between the masses hardly changes.

And when you factor in earths movement around the Bary centre,variation of the moon and suns distance, earths tides land and sea there are lots of variables to contend with already.

So this begs the question how to detect wether earths mass [or any other planets mass] is pulling greater than inverse square law predicts when at a distance from the mass that diminishes the vector angle of attraction down to a much straighter interaction. Maybe the bending of light. 

I have just had a reply from a person that does experiments to test G on another topic in this forum, i will bring this post to his attention and see if he will bring his expertise to bear on these issues

[graham.d]

Geo-stationary satellites are at 35,786 km and the altitude is very precisely known, as is the rotation speed (obviously). This would simply be in contradiction to your assertion. NASA would also have missed the moon and mars by a long way during space missions.

[gem (OP)]

Geostationary satellites are at 35,786 km and the altitude is very precisely known, as is the rotation speed (obviously). This would simply be in contradiction to your assertion. 

A relevant point which has to be considered.

So to try and put some values of Ag at this altitude
a rough approximation of the value of the predicted strength of the acceleration applied to a Geo stationary satellite is 225 millimetres a second squared,however if you factor in just earths orbit around its barycentre this causes this value to vary by around 40 millimetres per second squared with out factoring in any other variables.

Then if you consider what i am suggesting you have to allow for the fact half of earths volume is within the last 1315 kilometres of earths radius so the vector angle may not have diminished as much as may be first thought.

But that said it is thought that earths core is much denser than the rest of the planet, which is most likely and will have a direct effect on resulting attraction,Indeed it would change the results of the 13.8 metres per second squared for the 90 degree average interaction on earth to a lesser figure but this does not change the basic principle to which i am alluding.

So these things considered [angle of attraction given the satellites distance and the fact that earth is not a homogeneous sphere]So to just put some rough figures to give a example, that the mass acceleration resulting force at earths surface equal to 12.4 metres per second squared giving a force on the satellite equal to an acceleration of 283 millimetres per second squared.

So only about 20 millimetres PS2 different to the variable that is predicted by the inverse square law as it is presently applied when considering earths orbit around its barycentre, and as there are other variables to allow for it may be within the tolerances of the station keeping that is designed in to these satellites.

There are other points of concern that call in to question using the inverse square from the centre, for example if you take point mass at the centre and two  point masses any where else but equal distance from a body [say a satellite] the distance between the masses not at the centre do not increase in the same way as the distance between the point mass at the centre and the satellite.

[remember in reality every particle attracts every other particle from where they actually are not from the centre]


I look forward to comments

[gem (OP)]

It seems that experimental results show inverse square law violation also.

It appears  when looking at the data of experiments made since 1894 they show a dependence on mass separation.

this is a introduction to a paper published in 2009 by R newman E berg P boynton

1 Introduction
In 1974 Daniel Long published a paper Why do we believe Newtonian gravitation at laboratory
dimensions? (Long 1974), comparing measurements of G made since 1894 with
various mass separations r. His plot of G values as a function of r strongly suggested a
dependence on mass separation. Two years later, Long reported an experiment of his own
(Long 1976) which used a torsion balance to compare the forces produced by source masses
at distances of 4.5 cm and 29.9 cm. Long’s experiment used ring-shaped source masses,
exploiting the fact that the force on a test mass at a certain point on the axis of a ring source
mass is at an extremum and thus is quite insensitive to error in its position relative to the ring. Daniel Long reported that the ratio of the torque produced by the more distant ring to
that produced by the nearer ring exceeded the Newtonian prediction by (0.37 ± 0.07)%, a
result consistent with the distance dependence found in his analysis of G measurements........

And this is a summary by D long


D. R. Long1

(1)  Eastern Washington University, 99004 Cheney, Wash.

Received: 27 October 1980   

Summary  A number of works has now been completed in an effort to check on my earlier work showing a variation of the gravitational constant with mass separation. The precise null experiment of Speroet al. turns out to be ambiguous because vacuum polarization processes probably cannot be observed in a null experiment. To date all of the experiments which measureG(R) directly as a function ofR have had large errors, but almost all of those data tend to support my result......


So it seems that my assertion may already have been detected at very weak levels of attraction.

One note of concern is the current experiments have started to move away from using torsion balances and mass spheres as they were getting to many inverse square law violation results.   

[Ophiolite]

Where was this paper published? I find it surprising that you have omitted that information. Moreover I find the lack of any mathematical treatment disappointing. Can you rectify these two points?

[gem (OP)]

These are the sites that link to the published content if you want to view D longs paper in full you have to purchase

http://www.springerlink.com/content/u5j4724173336606/

(see http://physics.uci.edu/gravity).

Note i was unaware of these apparent inverse square law violations when i started this post i became aware of them when Eric berg kindly answered a question posted on this site and provided the above link.

It was my opinion that the difficulty of detecting such weak forces on the scale of apparatus in a laboratory would be to weak to detect, as what i am alluding to would manifest its self as radius distance increases where a very weak attraction force is diluted down by the multiplication of its radius and would be beyond the sensitivity of these experiments

That's why i thought it would be easier to detect on the scale of the planets and the bending of light as the forces are much greater

[gem (OP)]

To expand on this separate point as to why using inverse square law from the centre of a mass may fail when calculating the strength of gravitational attraction on a separate issue other than the variation in angle of vector interaction.  quote below
 

There are other points of concern that call in to question using the inverse square from the centre, for example if you take point mass at the centre and two point masses any where else but equal distance from a body [say a satellite] the distance between the masses not at the centre do not increase in the same way as the distance between the point mass at the centre and the satellite.

[remember in reality every particle attracts every other particle from where they actually are not from the centre
[/quote]


I have attached a diagram to demonstrate this point, the diagram shows three identical masses one at the centre point, C  and two others at points, B
these three masses are point masses enclosed within a homogeneous sphere [radius of 6400k/m] and contribute to the gravitational attraction applied to a mass at points A.


Now when mass A is at the position of zero on the surface of the homogeneous sphere the centre to centre distance between mass A and mass C is 6400k/m and the centre to centre distance between mass A and masses B is to 9000k/m. giving a difference in distance of 2600k/m

And when mass A is away from the homogeneous sphere in space at a distance of 20000k/m the centre to centre distance between mass A and C is 26400k/m and the centre to centre distance between mass A and masses B is 27200k/m. giving a difference in distance of only 800 k/m.

So it would seem the distance between mass at any point not at the centre does not decrease in accordance with the way gravitational attraction is calculated at present.

I would be interested to have some one defend the way the strength of gravitational force is calculated.

Note you have to click on the attachment to view

[gem (OP)]

Einstein used the results from these experiments in his theory of general relativity in the form of the gravitational constant big G .

http://en.wikipedia.org/wiki/General_relativityhttp://

If these experiments were flawed for the reasons given above it would explain why Einsteins theory's give a closer prediction to what is observed in reality compared to newton because he was factoring in a greater value for gravitational attraction than newton.

So do Einsteins  theory's have a inherent flaw in them.

I say again, I would be very interested to have some one defend the way the strength of gravitational force is calculated given the issues above.

[gem (OP)]

        By claiming that g varies I assume you mean it is G that has been miscalculated because everyone has misunderstood the physics and maths relating to spherical symmetry;

yep


The fact that G [big G ] is giving results closer to what is observed is due to the fact it came to a higher value for gravitational attraction by accident.