The Gravitation Constant

[James R]

Hmm... Without working it out directly, I think the answer to the integral is

F = GmM / [4Lx (x² + L²)^1/2]

Note that if the mass m is a long distance away from the cylinder, the cylinder looks like a point mass with mass M, as far as the test mass m is concerned. For this situation, x is much larger than L, so we can ignore the L² term in the bracket, to get:

F = GmM / (4Lx²)

Notice that in this case the force falls off as the inverse square of the distance x, as we would expect for two point masses.

On the other hand, look what happens when the test mass m is very close to the cylinder, so that x is much less than L. In that case, we ignore the x² term in the bracket, to get:

F = GmM / (4L² x)

Since L is constant, the force drops off as the inverse of the distance x, when the test mass is close to the cylinder, rather than as the inverse square of the distance.

Hope this helps.

 

[mhobbs_bbt]

>>You will find that the small point masses produce the same net force in combination as a single point mass located at the centre of the large sphere, with mass equivalent to the sum of all the masses of the constituent point particles.

I agree

>> There is no such thing as a black hole in Newtonian physics

from my analysis there are not such things as 'black holes'. The field spin to create such an object would be too large for reality.

>> maths...

I have posted these formula. I assume that an orbiting object is weightless (ie has no unbalanced forces acting upon it), therefore it is inertial... it is basically at rest. So the tangential velocity is the velocity component of the field spin/drift/curl. Mass is removed from the equations and the mode of action is a 'push' from spin.... centripetal force.... so gravity is a 'push' reaction. This applies to any specified geomagnetic body (in a poloidal field spin)[secondary field] in an already spinning field, the toroidal field [primary field].

Each field (toloidal field is now a poloidal field) is differentially driven by other toroidal fields, so all fields are interlinked. This field is composed of the orthogonally induced electric and magnetic vectors created by matter.

Each spin field spin has a specific constant ( Gcentral spin). The value is drawn from the difference in toroidal spin (velocity vector) created by the size of the field the orbiting body's mass induces in that toroidal field,( this can be calculated from the distance of Lagrangian points either side of the orbiting body). The product of the distance vector and the velocity vector^2 is a constant..... so rv^2 is a constant and so it defines all inertial states in that poloidal field, and it defines the reaction to non inertial motion as gravity

my understanding, written up in "Electrodynamic Spin Gravity" and "Solar System Parameters from Gcentral spin".


James R we are each talking different 'models'.
Rational and accurate results can be obtained with simple and easily verified physical principles, I see no reason to resort to contortions of reality.

QM provides an excellent electrodynamic model of atomic structure. The only missing link in that model is 'why atoms are stable in their long term configerations'.

This binding force is basically the cause of gravity, an electric-magnetic reactive spinning field, based upon the concept of the Poynting energy vector. It is a resonance that defines 'inertial'. All matter has a field and any field not in resonance will induce a reaction... it is not inertial and attracts a centipetal reaction. Bit like precession seen in spinning tops, except it is electrodynamic in the case of gravity and is manifest in three dimensions, .. and it is independant of time.

All the physics of the above is observable, why resort to contivance to assume control of the reality? IMO


The gravitation constant G, is the relation of the amount of energy field a quantity of matter has ( 1 kg mass )

Zarcov,

An interesting new twist. I was under the impression that nobody really knew what gravity was. You're saying that it is known and the maths all works out okay ?

Is there a beginners guide to 'Electrodynamic Spin Gravity' and 'Solar System Parameters from Gcentral spin' ? Or do you need a degree in Physics / Maths to understand it anyway ?


Mike.

 

[mhobbs_bbt]

Mike:



Ok. Let's take a relatively simple example. Suppose I have a cylinder of length L with total mass M and radius R. Assume, for simplicity, that we only want to know the gravitational force on a point mass m, which sits next to the cylinder at distance x from centre of the cylinder. I am talking about a situation where the point mass is at position x on the x axis, and the axis of the cylinder lies along the y axis, with the centre of the cylinder at y=0. (You should draw a diagram to follow what is below).

Consider the force on m due to a small section fo the cylinder of length dy and mass dM, located at position y. The mass of the the small cylinder section dM is its density times the volume of the section. That is:

dM = p pi R² dy

where p is the density of the cylinder.

The force on on the mass m due to this small section is given by:

dF = Gm dM / r²

where dm is given above, and r is the distance of this section from the point mass m. Using Pythagoras's theorem, we have:

r² = x² + y²

so

dF = [Gm p pi R² / (x² + y²)] dy

Now, consider another small section of the cylinder, at position -y on the y axis. The force dF from this small section is the same as the force for the section at position +y. However, force is a vector. Taking the forces from both these sections and adding them together resutls in the vertical components cancelling out, and the horizontal components adding together. Therefore, the only part of dF from any one section of the cylinder which contributes to the net force on the mass m is the horizontal component of dF, which is equal to

dF × x / (x² + y²)^1/2

Hence, from a small section of mass dM, the effective force on the mass m is:

dF(effective) = [Gm p pi R² x / (x² + y²)^3/2] dy

the density is equal to the total mass over the volume, or:

p = M / (pi R² L)

so

dF(effective) = [Gm(M/L) x / (x² + y²)^3/2] dy

To get the total gravitational force, we need to integrate this expression for the range of y values from y=-L/2 to y=L/2.

The integral is a bit tricky (looks like I picked a somewhat difficult problem).

Perhaps somebody else here can do it. If not, I'll get back to you a little later on with the solution.

Anyway, that's how to set up a problem like this.

James,

Thanks. Printing it off to look through later.


mike.

 

[Zarkov]

>> Is there a beginners guide to 'Electrodynamic Spin Gravity' and 'Solar System Parameters from Gcentral spin' ? Or do you need a degree in Physics / Maths to understand it anyway ?

I have written both articles and am compiling into a small book. The maths and logic are extremely user friendly. All the derivations are algebra based.

I have written both articles as a "student edition".
I have not completely finalised one small part, however this part is only window dressing.

 

[mhobbs_bbt]

Okay. It's been a while so working through the maths took some time. (The power of 3/2 foxed me for a while). All makes sense until the integration part ? Not sure how you 'integrate for the ranges of y from y= -L/2 to y=L/2 ?

I notice that the final figure still divides by some factor of x ?? Wouldn't this still give infinity at x = 0 ?

Another small point. All of the calculations assume that the mass is concentrated at the centre of the cylinder, the same as the calculations for G with spheres. For this to work, wouldn't the centre of the cylinder / sphere have to represent the average distance from the other object ? Whilst this is close enough for objects at large distances, it's not true for close objects ?

From my tests, the average distance between two spheres of radius 1000 units at a distance (from centres) of 2000 units, is not 2000 units but approx. 2200 units ?? Is this right ?? If true, I'm assuming that there's a similar issue with the cylinder example ?

( In fact the average distance between two objects of radius 1000 units at zero distance, ie. overlapping, is approx. 1020 units !! ?? )

 

[Neurocomp2003]

its the force between two large bodies ....pick up any astrophysics(carroll and ostlie) book and it will explain it. The more famous F = mg is actually a form of this one where the mass of the sun is taken to be on eof the Masses and g = GM/R^2

also about the quark and atom charges its only a scale....whose to say we have the right scale and the electron is -1? maybe the rudimentary value is set at the quark and the value that is called +/- 1/3 is actually +/- 1 and the electron would have...shit can't remember teh quark values but i think it would add to -3

 

[James R]

Mike:

Okay. It's been a while so working through the maths took some time. (The power of 3/2 foxed me for a while). All makes sense until the integration part ? Not sure how you 'integrate for the ranges of y from y= -L/2 to y=L/2 ?

How much integral calculus do you know?

I notice that the final figure still divides by some factor of x ?? Wouldn't this still give infinity at x = 0 ?

Yes, but the solution does not apply to x=0. It only applies when the mass m is outside the cylinder. If you want to handle the inside, that's a separate calculation.

Another small point. All of the calculations assume that the mass is concentrated at the centre of the cylinder, the same as the calculations for G with spheres. For this to work, wouldn't the centre of the cylinder / sphere have to represent the average distance from the other object ? Whilst this is close enough for objects at large distances, it's not true for close objects ?

I was a little sloppy. It is possible to do a more complicated calculation which takes the varying distances of the parts of each "slab" of the cylinder into account, too. The answer you get if you do that is the same, since certain effects average out.

From my tests, the average distance between two spheres of radius 1000 units at a distance (from centres) of 2000 units, is not 2000 units but approx. 2200 units ?? Is this right ?? If true, I'm assuming that there's a similar issue with the cylinder example ?

I'm not clear on how you reached that conclusion about the spheres.

 

[mhobbs_bbt]

The average distance between points in spheres was just an estimate based on a computer simulation generating thousands of random points and then averaging out the distances.

I've also run a simulation to pick random points and calculate the forces in all 3 dimensions between two spheres and they do, as you pointed out, cancel out leaving just the x components. Once these are averaged over a large number of calculations they do indeed cancel out back to F=GMm/r^2. Quite surprised but can now see why.

The problem with objects inside other objects is presumably that the values of x become both positive & negative, balancing out to an average of 0 as the centres of the objects meet, giving a Force that does indeed tend toward zero as suggested.

Think that about convinces me. It was an interesting journey but now I think I've caught up.

Thanks to everyone, especialy James, for their help.


Mike.