Hi,
I think that I must say a pair of additional things.
First, I'm very grateful to Miles Mathis for his many insights, and for
his clarity, freedom and generosity in openly sharing his ideas. He is a
great source of inspiration and original ideas.
Second, the only way to produce progress and novelty in a field, is by
being wrong a good number of times. We have that right. The right of
being wrong, if you excuse the pun. In the long term, we must only try
that our hits surpass our misses, in number and particularly in importance.
And talking about being wrong, it turns out that there is something
wrong in the formulas below. And that that is interesting in itself.
Let's see:
I've made the intensity of the gravitational field directly proportional
to the mass of the "emitting" body alone. This, one would presume, is
the logical thing to do. But with a field like that, lighter objects
fall faster than heavier objects. Due to inertia, and given the same
field intensity, it's easier to accelerate a less massive object than a
more massive one. Newton's second law.
But(and here I'm indebted again to Miles Mathis), the gravitational
field is a very particular field; a field so particular that the former
does not happen. The gravitational field, in the centripetal direction,
counteracts inertia, so to speak. It defies Newton's second law. That's
why the gravitational force, in Newton's universal gravitational
formula, is directly proportional to the *product* of the masses. If I
multiply the numerator by the mass of the second body, that will later
exactly cancel out the dividing mass in a=f/m, and we will have equal
centripetal accelerations independently of the masses of the second body.
The right formula for the magnitude of the force is then:
f=-star.mass*planet.mass/pow(r.length(), exponent);
But the problem is now that this formula defies mechanics. This product
in the numerator means that, if we stick to the idea of a force field,
the emitting body must emit different intensities depending on the mass
of the receiving body. And that does not make sense.
This is probably also why GR speaks of space curvature. That way, it is
dispensed with the need to explain this very particular behavior of the
gravitational field.
But there must be another explanation. An explanation that does not hide
in geometry, and which also makes physical sense.
The candidates I can come up are:
1) A given gravitational field is proportional to the mass of the
emitting body, but is "processed" or "felt" differently by a receiving
body, according to the body's mass, in a form that exactly cancels out
the inertia of the body. That is, the intensity of a gravitational field
"felt" by a body is directly proportional to its gravitational mass. So
a=f/m no longer holds for the gravitational field. We instead have a=f,
or better, a=f*mg/mi. mg in the numerator is the gravitational mass, and
mi, the inertial mass. Normally, mg=mi.
2) A gravitational field is the result of an interaction of bodies, not
an emission of any given body on its own. The intensity of this
interaction is proportional to the product of the gravitational masses
of the interacting bodies. The interaction itself works in ways that we
don't understand yet.
1) looks more mechanically tractable, whereas 2) looks more "wave like",
or "flow like". An approach like 2) can also probably explain dark
matter, and gravitational anomalies.
Notice also that 1) implies a kind of "amplification" effect.
Particularly in the case of a greater body being influenced by a smaller
one, the influence will depend on the mass of the second body. Which is
strange, to say the least.
Particularly in 1), to augment the gravitational interaction, we'll have
to increase the body's gravitational mass(without increasing its
inertial mass), to decrease its inertial mass(without decreasing its
gravitational mass), or both. How to do it is left as an exercise for
the reader at the moment :-)
Mauro
On 10/16/2010 09:28 PM, Mauro Lacy wrote:
> On 10/14/2010 08:06 AM, Mauro Lacy wrote:
>> On 10/11/2010 01:50 PM, OrionWorks - Steven Vincent Johnson wrote:
>>>
>>> A question for you, Mauro:
>>>
>>>
>>>
>>> I would nevertheless love to computer simulate a so-called authentic
>>> elliptical orbit that is more accurately based on Miles' three-part
>>> gravity model, one that incorporates both the attractive 1/r^2 force
>>> and the repulsive E/M 1/r^4 forces. At present I'm at loss as to how
>>> I might do that -- that is without my computer simulations reverting
>>> back to nothing more than another mechanistic heuristic exercise.
>>> Maybe that's all one can really do in our so-called "mechanistic" world.
>>>
>>
>> You're right, and I'm doing exactly that at the moment. A celestial
>> mechanics simulator based on first principles. I'll try to use the
>> smallest number of principles. So far, I've identified four:
>> - Newton's first law (uniform movement law, i.e. inertia)
>> - Newton's second law (f=ma => a=f/m)
>> - A spherically(circularly, in two dimensions) radiating force field,
>> with one (or more than one) transform(i.e. propagation) terms (1/r^0,
>> 1/r^1, 1/r^2, ...)
>> - Force fields act only in the centripetal direction, that is, they
>> have no influence orthogonally.
>>
>> With that and a small enough interval, I think I can build an orbit
>> simulator to test for laws using only first principles. More about
>> this later, probably.
>
> Well, I've built a two-body, two-dimensional orbit simulator based in
> these four principles. It turns out it was very easy to program using
> vectorial arithmetics, so here's the method. It uses vector
> substraction, addition, invertion, normalization, and vector
> multiplying by an scalar.
> Let me know if you discover something that is incorrect.
>
> // inverse square law
> int exponent = 2;
>
> // vectors planet.pos and star.pos have the actual positions of
> the bodies.
> r=planet.pos-star.pos; // the radius vector is the vectorial
> substraction of the position of the bodies
>
> float f; // magnitude of the force
>
> f=-(star.mass/pow(r.length(), exponent)); // minus means
> attractive attractive force. r.length() gives us the
>
> // magnitude of the radius vector.
>
> planet.ac=r.normalized()*(f/planet.mass); // centripetal
> acceleration acts in the radius vector direction. r.normalized() gives
> us the unit vector.
>
> planet.velocity=planet.velocity + planet.ac; // vectorial addition
> of velocity and centripetal acceleration
>
> // now do the same for the star
> f=-(planet.mass/pow(r.length(), exponent)); // force of the planet
> on the star
>
> star.ac=-(r.normalized())*(f/star.mass); // centripetal
> acceleration produced on the star. In the opposite direction
>
> star.velocity=star.velocity + star.ac;
>
> // now calculate the new positions
> planet.pos=planet.pos + planet.velocity;
> star.pos=star.pos + star.velocity;
>
> That's it. Except for a=f/m and the force field transform, there are
> no other formulas.
> Suffice it to say that it produces elliptical orbits, which depend on
> the initial positions, velocities, masses and distance between the bodies.
> I've used Qt4 QVector2D implementation, but any vector class or
> library that implements basic vector operations will do.
>
> Regards,
> Mauro
