**
**

From Arthur I.Miller's, Albert Einstein's Special Theory of Relativity, page (*xxx):

- Logic demands that (1) applies to all srt variables.
- No observable fact (2) can be assigned to inertial frames.
- "Logical weakness" (3) is a 'very weak' statement for the non-existence of a fundamental part of the srt.
- The frequent use of the word 'observer' (3) suggests some reality and is particularly misleading when used in non-existing frames.
- The srt is right and consistent as pure mathematics but not as applied-mathematics!
- A successful experiment is
**confirmation**not proof for a theory.

All experiments with high-energy particles --the only 'tangible results' of the srt-- are conducted in the presence of gravity. The machinery for gravity*, however, is still unknown, and so are its effects on moving bodies. This suggests that the observed reduced acceleration is caused by gravity. This should be investigated. Since professionals do not do this, DIY is resorted to, as is the normal course of action when professionals let you down.

This is **not** an attempt to prove or disprove existing methods or
theories or to provide new ones. The understanding of the mechanics that cause
the various phenomena, is the objective. That this is possible at all, is based
on a strongly held belief that the basics, the fundamental rules are simple and
can be shown to be so, especially when the explanations are presented in the
simplest possible form.

These explanations are not meant for people who know it all already and think that understanding the mathematics is the same as understanding the -supposedly- underlying physics it 'describes'. They are meant for the genuinely, reasonably intelligent, interested layman as a pilot scheme.

The result may or may not be the correct model, but it does show that a model
can provide **insight** where that was impossible before. It shows that it is
indeed worth the effort to try and find the underlying machinery and transfer
thereby **existing** recipes into real theories.

Before jumping to conclusions, consider the following:

- Michelson&Morley found no difference in the velocity of light on their granite slab, full stop. The rest are interpretations of that fact.
- "oil drop" Millikan divided his results in good- and bad ones, the good ones confirmed his ideas, the bad ones did not.
- Eddington measured the bending of light. Nothing else. Not that light has mass, not that it follows the curvature of space, or anything else.
- The 'Harvard experiment" showed that the wavelength of light changes with the strength of gravity. No more, no less.
- If the height for a pendulum clocks changes they 'run' fast or slow. The same happens with atomic clocks. When these clocks are moved -horizontally- through gravity, the frequency of the 'ticks' also changes. A demonstrated fact and open to various interpretations, but, in the presence of gravity, excluding srt.

These examples are apparently used as proof according to preconceived ideas and/or convictions.

* And not only gravity misses a foundation, the fundamental properties of light, that play such an important role, are still a mystery.

Newton: "It is nonsense to think that one body can affect an other body at distance, and only a fool would do so". This was his opinion about gravity. He could, however, not find a suitable foundation to explain his theory. Hence, his -often wrongly quoted- remark about hypotheses.

One often reads that 'Newton' fails at certain velocities, but it is very
difficult to find out precisely how and why. It is for instance difficult to
understand, with Newton's fools in mind, how **empty** space, curved or
otherwise, can cause the observed phenomena.

With the above in mind I devised a particle model for gravity instead of the
current 'gespenster' or phantom field. Something that exists in nature or, that
at least, **could exist** and can assist in explaining gravity. Without some
-realistic- idea of the mechanism it is impossible to understand gravity and
that in turn may well be the cause of 'Newton's failure'. Newton's formula is
used as a starting point for this attempt to solve this, three centuries old,
problem.

Derivation of the necessary formulae --in HTML notation-- marked **GM-1**
etc.

Consider, in 'deep' space, two bodies with a mass of one kilogram each, at a
distance of one meter. The bodies exert forces on each other that are, in
accordance with 'Newton', equal to G (Newton). Spreading one kg -in very small
particles- over one square meter of a sphere with a one meter radius and one kg
at the centre, gives a pressure of G (N / m^{2}). That pressure acting
on the entire surface, results in a total -inward- force of four pi times G
(Newton).

It is easy to show that this force -with that mass per square meter- remains
the same for all diameters. This indicates that a model with particles, evenly
distributed, will produce the inverse square law. It is obvious that such an
arrangement will collapse unless there are **-opposing-** balancing forces on
the particles.

Imagine therefore, space filled with two types of entities: +N and -N. The
mass of the N's to be very small*, so small that some properties of the N's are
comparable to those of the neutrino. While the **mass** is the same for the
two types of N's, the **weights** differ: +W for +N and -W for -N.

The N's are arranged so that the forces on the N's balance. Space, all space (even that between electron and nucleus!), 'filled' with such particles will produce gravitational effects as described by Newton. It is then a simple matter to derive his formula. With matters so designed, that is no surprise. That it can be done is of little consequence, except, that there is now a machinery for gravity and a basis for the formula, it is no longer just a recipe.

It also provides better insight. With the N's we do not have an attractive
force operating at distance through empty space. Bodies are not pulled- but
**pushed** together. This solves** the hardy problem of action at a
distance.

* Subsequent calculations suggest a mass of about 4.85 x
10^{-35 }kg.

** Reduces that problem to sub-atomic level.

__
__

The above does not indicate where 'Newton' fails, but it does suggest that it
may have something to do with motion. Moving bodies alter the local strength of
gravity. A moving body signals ahead to increase the strength and to decrease it
in the other direction. These adjustments cannot be instantaneous. They take
some time. Newton's theory does not allow for this **and this is where 'Newton'
fails.**

It seems reasonable to take the maximum velocity, that of light (c), for the
signalling velocity. The body, in the **corresponding time**, moves a certain
distance. There is a shortening of distances in the forward- and a lengthening
in the opposite direction.

The body is therefore not in the centre of its gravity spheres and the forces on it are no longer in equilibrium. To compensate for this, part of the accelerating force is used.

A modification of Newton's second law is necessary. Multiplication of the
accelerating force by a correcting factor **(1 - v²/c² = cos ^{2}a),**
is required.

This factor is -for the resulting velocity- similar to the factors of Fitz-Gerald and the srt. It is, however, quite different in application. It can only be used -but without limitations- to adjust the velocity. It does not require, or provide proof for, the special effects of the srt on mass, time or length.

The correction ought to be applied to acceleration (and deceleration) in general, but it only produces an observable difference with higher velocities as in Mercury's orbit.

As an example: the dotted line in the figure shows the reduction to U' = 0.43 of a velocity U = 0.50* (50% of the light velocity). This figure is unsuitable for more common velocities. The triangles shown, even for Mercury's velocities, would lie completely within the thickness of the baseline.

* The velocity attained with Newton's second law.

GM-2__
__

This 'new' correction-factor is, in contrast to the srt factor, applicable to the velocities of Mercury. The velocity decreases slightly in the accelerating part of the orbit, and the satellite 'falls' to a lower orbit. This 'falling' to a lower orbit increases the velocity.

This increase in velocity brings the satellite back to the same elliptical orbit but with the axes rotated through a small angle (the increase in energy is twice the reduction).

In the decelerating part of the orbit, something similar occurs but now there is a small decrease in velocity and a reduced orbital velocity.

This also explains why a reduction-factor can produce an advance. Using simple mathematics produces for Mercury the observed advance of 43 seconds per century.

GM-3

__
__

__
__

Light in water moves at about three-quarter of the velocity of light in air, but in air again it continues at the original velocity. This indicates, and proves, that light does not behave as, and is not, a simple projectile going from A to B.

It seems that moving between and through the water molecules (temporarily) checks the velocity, or has that effect*. The only substance present between -and inside- the molecules, are the N's.

Assume that it is the strength (average strength) of the N's in water that reduces the velocity. Comparing the ratio of the lengths light travels, in the same time, in water and in vacuum, produces a ratio for the respective strengths.

Comparing two horizontal lengths, at different radii, relates this to gravity and produces a simple formula for the dependence of the light velocity on gravity. At maximum strength the velocity is zero and at minimum strength maximum (c). As shown this gives a very simple expression for this relationship. (r = 2.G.M / c^2)

At a distance of less than one meter (.88 m, 100 times r), from a concentrated earth mass, the velocity is already 99% of its maximum. It then approaches the maximum velocity asymptotically, making it nearly constant. For the earth, r is only 8.8 mm. This means that the graph shows a distance of about 18-cm from the centre of a concentrated earth. At the surface of the earth, the distance is more than 700.000.000 times r.

The difference in velocity, at the surface of the earth, is only -0.41 m/s. For the sun it is -1265 m/s, and this is large enough to have detectable consequences.

The speed of light is no longer a constant and the **c** in the
gamma-factor is a variable. For Mercury the effect is very small and is ignored,
for the binary PSR 1913+16 it causes the decaying of the orbit by about 3 mm per
orbit. The calculations become more complicated, but understanding "what is
going on" is still clear.

* Other explanations must also clarify why light, in water, maintains its coherence.

__
__

The **reduction in velocity** is bending light. We have, into this
--continually changing-- medium, an angle slightly larger than 90°. At the
tangent, near the sun, it is a right angle. The normal for the strength of
gravity turns through a right angle!

The velocity increases again for the journey to the earth and so forms a, practically, symmetrical path. Applying Snell's law gives an angle of 1.74 seconds, in agreement with observations.

LM-2__
__

The local strength of gravity effects the **energy** of the emitted light.
Thereafter the **velocity** adjusts everywhere to the local strength. Light
emitted at the bottom, (of e.g. the Harvard tower), has a frequency (energy)
that is different from that emitted, by the same source, at the top.

The velocity is slightly greater at the top. This increase, by the same energy, means that the wavelength has increased. The velocity, over this relatively small distance, can be considered as uniformly accelerated.

That allows the ratio, increase in wavelength to wavelength, to be easily
calculated. The result is 2.44 × 10^{-15}. This converts to 2.63
millimetres per hour (for the Mossbauer crystal), the velocity found in the
Harvard experiment.

The velocity measured in this experiment also determines the difference in the light velocity. That difference, 5.26 mm per hour, is extremely small but a difference it is --contradicting srt-- and it provides confirmation for the dependence of the light velocity on the strength of gravity.

LM-3__
__

This famous experiment was to measure the difference in the velocity of
light, due to the orbital motion of the earth through the aether. The experiment
showed, in a **horizontal plane** (R is constant!), no difference. The
conclusion was, in conflict with the current theories, that the velocity of the
earth did not effect the velocity of light.

To accept that result, without changing existing theories, several solutions were suggested. One, by Fitz-Gerald, said --seriously-- the difference is there, but measuring it is impossible. Lengths contract and precisely so that the difference disappears. A set of empirical formulae supported that idea.

The srt produced the same formulae and because of its hypothesis of the constancy of the light velocity, there are even two solutions for the M-M problem. One can choose either, there is no difference because that is a law of nature, or, with the same formulae, work again with obliging lengths etc. (with the idea of an aether still intact!).

A simple explanation is possible with the N's. The N's near the earth adjust to the presence of the moon, the sun, the solar system and so on and on. The earth moves through the sun's gravity etc, but carries its own adjustment, its own change, with it.

It is this particular local, and locally dominant, adjustment that determines
the velocity of light, and it is this **adjustment**, and that **adjustment
only**, that is carried along and is responsible for the Michelson-Morley
results. Nothing **material** is carried along! It also means that **all**
light from a distant- or from a local source will adjust to the same
velocity.

Note that M-M measures the light velocity in a horizontal plane only and can therefore state only that there was no detectable difference in the light velocity in horizontal planes that are at rest relative to the earth.

There is still the rotation of the earth to consider. An -almost- perfectly symmetrical earth rotates within its own set of gravitational spheres. (Foucault's pendulum etc.) With an accuracy comparable with e.g. the Harvard experiment, a difference in the light velocity should be detectable.

The elementary force, between two **N'**s, is delta-**F** (Newton) and
with **n ^{2}** particles per square meter is that in (

For equilibrium, each shell must be in balance with its neighbours. **P**
--the sum of delta-**P** over the spherical area-- is, ignoring the
direction, a constant. This force **C** at **R** is (**N**ewton)

Or for the elementary force at **R** in (**N**ewton)

With two bodies we have: every **N** in one body attracts every **N**
in the other and vice versa. Mass is the product of the number of **N**'s in
the body and the mass of one **N**. The force **F** between two masses
**M** and **m** is therefore

With the all constants gathered in **G**

Resulting in (**N**ewton)

**
**

This is Newton's well-known empirical formula as a first and necessary indication of the usefulness of this devised model.

Consider a body **m** moving with a velocity **v** relative to -local
dominant- gravity. The reaction-distance **R = ct,** of any gravity-radius ,
reduces, in the forward direction, to **(c-v)t** and increases, in the
reversed direction, to **(c+v)t**.

A factor **(c-v)/c** reduces
**all** distances forward, and **(c+v)/c** increases **all** distances
in the opposite direction. This is a (virtual) movement of **m**, by a
distance **s.** With **v / c **equal to **u** is that

It is as if the body has moved within its own gravitational spheres. The
resultant at **m** is therefore no longer zero. This means that the strength
**a'** at **s** is the ratio **s / R **times the strength **a** at
**R**

The distance **s** is measured from the centre. Part of the force **F**
is used to overcome this opposing force. With the ratio, **s / R** equal to
**u** and applying this, we have

And from this the forces

Giving an (algebraic!) correction of

And a corrected velocity

__
__

The corrected velocity, for **u<<1, **can be written --with
acceptable accuracy-- as (two terms only)

Giving a corrected acceleration of

With a difference in acceleration of

For a **circular orbit** is the change in **a, (a =
u ^{2} / R),** for a small change in

And the -proportional- change in terms of the radius

The change in **gravity** for a small change in R is

Multiplying with **t/R** and setting **gt / R = u / R = ß** and
**u ^{2} = h / R **, gives for the small change in orientation in the
usual form

Summation over one orbit gives

Per orbit in radians

__
__

Comparing the distance covered, in the same time, through e.g. water and
vacuum makes it possible to find an expression that links length to strength.
Take **l _{w}** and

The strength is proportional to

Division gives

The connection with gravity follows from the horizontal lengths
**l _{R}** and

For gravity we have

From this follows

The general formula must satisfy the following conditions:

Suggesting for the velocity of light at

__
__

The dependence, of the light velocity on gravity, gives for the sun an index
**N** of

Applying Snell's law gives

Or

The angle is, through symmetry, twice that to an observer on earth, resulting in

Which is the observed value.

__
__

Light emitted at **B** (**B**ottom) and received at **T**
(**T**op) has the local velocity but an energy (frequency) that differs from
light emitted by the same source at **T** (**R**_{T} =
**R**_{B }+ delta-**R**).

The light velocity at **B** is

A small change in **R** gives for the proportional change in velocity

This change causes a decrease (or increase) in the wavelength of the light.
This increase, for a red shift, is not constant, but zero at
**R**_{B} and proportional to **dc** at **(R**_{B}+
delta-**R.)** The acceleration can, over that 'small' distance, be considered
uniform.

The average velocity is then

And with

The wavelength ** l** becomes

And the proportional change

At the Harvard experiment **dR = 22.5 m**

And the measured 'velocity'

In agreement with the experiment and indicating that the light velocity
**increased **by about **5 mm / hr !**

INTERESTING FOLLOW-UPDe :j.s.brandsma (j.s.brandsma@hccnet.nl) Objet :Re: Note to Chris Hillman. Crackpots again. View: Complete Thread (8 articles) Original Format Groupes de discussion :sci.physics.relativity Date :2001-07-15 10:44:22 PST Re: Note to Chris Hillman. Crackpots again. I was wrong. I really thought that Chris Hillman was one of the more reasonable experts. A lot of time spent in name-calling, ridiculing and jumping to conclusions, none in refuting. Why react in this viperous way? There is no competition. You are the professor of mathematics. Nobody doubts that, or your competence in that field. What is in doubt, for instance, is where in this universe one can FIND an inertial frame (NB preferably with OBSERVERS!), other than in the pure mathematics of the srt. That the mathematics is applicable as applied-mathematics, turning it into physics, is the problem. A highpoint is of course where a quote from AE is dismissed. He did not know either! If I was to partake in this juvenile name-calling I would say emerge from your manifold before you are called an idiot savant. Naturally I am not doing this. The srt is indeed used in the grt 'infinitesimal little cubes' to get e.g. the velocity correction factor, a.k.a. the Lorentz-transformation, into the calculations. It introduces the factor 3, which is crucial for the final result -the same factor Dirk van den Moortel is asking about. This makes doubting the srt very difficult. Vested interests are of course loath even to consider the possibility that the Kaufmann betha-ray (1901) experiments etc. may have a different explication, one that gives the same correction and does not need the srt. It is typical of the knee-jerk type reaction that he stopped reading. He simply KNOWS that whatever I have to say CAN NOT have been augmented by any mathematics, however simple. A very scientific approach, no arguments needed! I do indeed not understand the subtleties of that. About understanding: The precession of Mercury. The satellite is in an elliptical orbit around the sun and adjusts its velocity accordingly and the velocity correction has its effect. The satellite loses (or gains) kinetic energy. This means a lower (or higher) orbit that compensates -at double the rate- the loss or gain. Summing this over the orbits in a century is calculated (with maths c.h!) as 43". I challenge Chris Hillman to explain the PHYSICS better for the INTENDED AUDIENCE. Details supporting this in: http://home.hccnet.nl/j.s.brandsma/gravity.html Let this be enough for Hillman et al. To Dirk van den Moortel: =| GM-3 The perihelion advance of Mercury. =| =| The corrected velocity, for u<<1, can be written =| --with acceptable accuracy-- as (two terms only) =| =| u' = u (1 - u^2 / 2)......[ 1 ] =| =| Giving a corrected acceleration of =| =| a' = a (1 - 3 u^2 / 2)....[ 2 ] =How is that? =How do you obtain this result? [ 1 ] (1 - u^2 / 2) The first two terms of the Taylor series for sqrt (1 - u^2) [ 2 ] The derivative of [ 1 ] a' = du' / dt etc. Thanks for all proper replies. I am still waiting for adjudication or founded refutation. Comments a la juvenile delinquents are apparently easier. jsb De :Dirk Van de moortel (dirkvandemoortel@ThankS-NO-SperM.hotmail.com) Objet :Re: Note to Chris Hillman. Crackpots again. View: Complete Thread (8 articles) Original Format Groupes de discussion :sci.physics.relativity Date :2001-07-15 11:22:33 PST "j.s.brandsma"wrote in message http://groups.google.com/groups?selm=9isknq%24afj%241%40news.hccnet.nl... > [snip] > About understanding: The precession of Mercury. > The satellite is in an elliptical orbit around the sun and adjusts its > velocity accordingly and the velocity correction has its effect. The > satellite loses (or gains) kinetic energy. This means a lower (or higher) > orbit that compensates -at double the rate- the loss or gain. Summing this > over the orbits in a century is calculated (with maths c.h!) as 43". > > [snip] > To Dirk Van de moortel: [corrected my name - DVdm] > > =| GM-3 The perihelion advance of Mercury. > =| > =| The corrected velocity, for u<<1, can be written > =| --with acceptable accuracy-- as (two terms only) > =| > =| u' = u (1 - u^2 / 2)......[ 1 ] > =| > =| Giving a corrected acceleration of > =| > =| a' = a (1 - 3 u^2 / 2)....[ 2 ] > > =How is that? > =How do you obtain this result? > > [ 1 ] (1 - u^2 / 2) The first two terms of the Taylor series for sqrt (1 - > u^2) > > [ 2 ] The derivative of [ 1 ] a' = du' / dt etc. Okay, you know what a derivative is. Just a test. (Had a bad experience with mr. Androcles) | GM-3 The perihelion advance of Mercury. | | The corrected velocity, for u<<1, can be written | --with acceptable accuracy-- as (two terms only) | | u' = u (1 - u^2 / 2) | | Giving a corrected acceleration of | | a' = a (1 - 3 u^2 / 2) | | With a difference in acceleration of | | a - a' = da = 3 a. u^2 / 2 | | For a CIRCULAR orbit is the change in a, | (a = u^2 / R), for a small change in R | | da = - a . dR / R = 3 a . u^2 / 2 You just said that: > About understanding: The precession of Mercury. > The satellite is in an ELLIPTICAL orbit around the sun and adjusts its > velocity accordingly and the velocity correction has its effect. (uppercasing is mine) Circular or elliptic? If it is a circle, what would be precessing? De :j.s.brandsma (j.s.brandsma@hccnet.nl) Objet :Re: Note to Chris Hillman. Crackpots again. View: Complete Thread (8 articles) Original Format Groupes de discussion :sci.physics.relativity Date :2001-07-16 05:34:37 PST Reply to Dirk Van de moortel. =Okay, you know what a derivative is. Just a test. =(Had a bad experience with mr. Androcles) =| GM-3 The perihelion advance of Mercury. snip =| For a CIRCULAR orbit is the change in a, =| (a = u^2 / R), for a small change in R =| da = - a . dR / R = 3 a . u^2 / 2 =You just said that: => About understanding: The precession of Mercury. => The satellite is in an ELLIPTICAL orbit around the sun and adjusts its => velocity accordingly and the velocity correction has its effect. =(uppercasing is mine) =Circular or elliptic? =If it is a circle, what would be precessing? Apology. My notes are just that, notes and with the translation into HTML a small, but important section, was inadvertently omitted. My apologies to the only person who, at least, tried to follow my arguments and who apparently has no serious objections to the parts G 1 and G 2. With the omitted lines: "And for the elliptical orbit" "Betha = 6 . pi . h / a ( 1- e^2 )" added, the anomaly disappears. The circular orbit is only used, in an intermediate phase, to simplify the mathematics and has no other function or meaning. I will adjust my notes on the site accordingly and check everything again.. Thanks. jsb De :Dirk Van de moortel (dirkvandemoortel@ThankS-NO-SperM.hotmail.com) Objet :Re: Note to Chris Hillman. Crackpots again. View: Complete Thread (8 articles) Original Format Groupes de discussion :sci.physics.relativity Date :2001-07-16 10:01:28 PST "j.s.brandsma" wrote in message http://groups.google.com/groups?selm=9ium7e%24e8e%241%40news.hccnet.nl... > Reply to Dirk Van de moortel. > [snip] > =| For a CIRCULAR orbit is the change in a, > =| (a = u^2 / R), for a small change in R > > =| da = - a . dR / R = 3 a . u^2 / 2 > > =You just said that: > => About understanding: The precession of Mercury. > => The satellite is in an ELLIPTICAL orbit around the sun and adjusts its > => velocity accordingly and the velocity correction has its effect. > > =(uppercasing is mine) > =Circular or elliptic? > =If it is a circle, what would be precessing? > > Apology. > My notes are just that, notes and with the translation into HTML a small, > but important section, was inadvertently omitted. My apologies to the only > person who, at least, tried to follow my arguments and who apparently has no > serious objections to the parts G 1 and G 2. > > With the omitted lines: "And for the elliptical orbit" > "Betha = 6 . pi . h / a ( 1- e^2 )" added, the anomaly disappears. > > The circular orbit is only used, in an intermediate phase, to simplify the > mathematics and has no other function or meaning. > > I will adjust my notes on the site accordingly and check everything again.. > Thanks. No problem. Apology accepted ;-) I'll have another look at the reasoning when: 1) all references (explicit and implicit) to circles are completely gone. 2) infinitesimal differences (dR, da, dg, db) appear on both sides of all equations or are written as real derivatives (total or partial). 3) you show in detail where the 42.7" comes from. i.e. provide the complete mathematically correct derivation of the final formula, and list all the constants that are used to obtain the numeric result. Please email me when these modifications are made? Bye for now, Dirk Vdm De :Dirk Van de moortel (dirkvandemoortel@ThankS-NO-SperM.hotmail.com) Objet :Re: Note to Chris Hillman. Crackpots again. View: Complete Thread (8 articles) Original Format Groupes de discussion :sci.physics.relativity Date :2001-07-16 10:02:57 PST "j.s.brandsma" wrote in message http://groups.google.com/groups?selm=9ium7e%24e8e%241%40news.hccnet.nl... > Reply to Dirk Van de moortel. > > > =Okay, you know what a derivative is. Just a test. > =(Had a bad experience with mr. Androcles) > > =| GM-3 The perihelion advance of Mercury. > > snip > > =| For a CIRCULAR orbit is the change in a, > =| (a = u^2 / R), for a small change in R > > =| da = - a . dR / R = 3 a . u^2 / 2 > > =You just said that: > => About understanding: The precession of Mercury. > => The satellite is in an ELLIPTICAL orbit around the sun and adjusts its > => velocity accordingly and the velocity correction has its effect. > > =(uppercasing is mine) > =Circular or elliptic? > =If it is a circle, what would be precessing? > > Apology. > My notes are just that, notes and with the translation into HTML a small, > but important section, was inadvertently omitted. My apologies to the only > person who, at least, tried to follow my arguments and who apparently has no > serious objections to the parts G 1 and G 2. I must admit, I haven't looked at G1 and G2 or anything else. Only GM-1, GM-2 and GM-3. GM-1 I didn't understand, but I'll accept the result F = G * M * m / R^2 > With the omitted lines: "And for the elliptical orbit" > "Betha = 6 . pi . h / a ( 1- e^2 )" added, the anomaly disappears. > > The circular orbit is only used, in an intermediate phase, to simplify the > mathematics and has no other function or meaning. > I will adjust my notes on the site accordingly and check everything again.. > Thanks. De :j.s.brandsma (j.s.brandsma@hccnet.nl) Objet :Re: Note to Chris Hillman. Crackpots again. View: Complete Thread (8 articles) Original Format Groupes de discussion :sci.physics.relativity Date :2001-07-17 12:24:29 PST Reply to Dirk Van de moortel. [ 3 ] You wrote: =I'll have another look at the reasoning when: =1) all references (explicit and implicit) to circles are completely gone. =2) infinitesimal differences (dR, da, dg, db) appear on both sides of =all equations or are written as real derivatives (total or partial). =3) you show in detail where the 42.7" comes from. =i.e. provide the complete mathematically correct derivation of the =final formula, and list all the constants that are used to obtain the =numeric result. =Please email me when these modifications are made? =Bye for now, Writing mathematical formulae in HTML is a rather clumsy affair. My reaction was to keep it as short as possible. It appears I may have overdone it. The well-known expression for the square of the velocity in an elliptical orbit can be modified to: u ^ 2 / R = g (2 - R / a ) = g . k With k = ( 2 - ( 1 - e ^ 2 ) / ( 1 + e cos b )) Differentiating g = ( u ^ 2 ) / R . k ( with b constant ) Gives dg = - 2 g . dR / R = 3 a . ( u ^ 2 ) / 2 as before. The final formula with the available data gives as a result: Betha = 6 x 3.14159 x 1477 / ( 57.9 x 10 ^ -9 ) x ( 1 - 0.2056 ^ 2 ) = 0.499 x 10 ^ -6 radians. For 100 years: Betha x 206265" x 100 x 365.25 / 87.96 = 42.7 " I agree with you that it would have been better to write e.g. delta-a for a - a', or better still DELTA-a for capital delta, but things are clumsy enough as it is. The d stands, occasionally, also for small, not just for infinitely small. The mathematics is not intended to provide a rigorous proof, but is only used as a tool to get some quantitative results. Please, also keep in mind/consider that all I am trying to do is understand physics, or rather, trying to understand nature. I still feel I had some success with that. jsb De :Dirk Van de moortel (dirkvandemoortel@ThankS-NO-SperM.hotmail.com) Objet :Re: Note to Chris Hillman. Crackpots again. View: Complete Thread (8 articles) Original Format Groupes de discussion :sci.physics.relativity Date :2001-07-17 14:15:14 PST "j.s.brandsma" wrote in message http://groups.google.com/groups?selm=9j234a%24g4%241%40news.hccnet.nl... > Reply to Dirk Van de moortel. [ 3 ] > > You wrote: > > =I'll have another look at the reasoning when: > =1) all references (explicit and implicit) to circles are completely gone. > =2) infinitesimal differences (dR, da, dg, db) appear on both sides of > =all equations or are written as real derivatives (total or partial). > =3) you show in detail where the 42.7" comes from. > =i.e. provide the complete mathematically correct derivation of the > =final formula, and list all the constants that are used to obtain the > =numeric result. > > =Please email me when these modifications are made? > =Bye for now, > > Writing mathematical formulae in HTML is a rather clumsy affair. My reaction > was to keep it as short as possible. It appears I may have overdone it. > > The well-known expression for the square of the velocity in an elliptical > orbit can be modified to: > > u ^ 2 / R = g (2 - R / a ) = g . k > > With k = ( 2 - ( 1 - e ^ 2 ) / ( 1 + e cos b )) > > Differentiating g = ( u ^ 2 ) / R . k ( with b constant ) > > Gives dg = - 2 g . dR / R = 3 a . ( u ^ 2 ) / 2 as > before. > > The final formula with the available data gives as a result: > > Betha = 6 x 3.14159 x 1477 / ( 57.9 x 10 ^ -9 ) x ( 1 - 0.2056 ^ 2 ) = > 0.499 x 10 ^ -6 radians. > > For for 100 years ..Betha x 206265" x 100 x 365.25 / 87.96 = 42.7 " > > I agree with you that it would have been better to write e.g. delta-a for > a - a', or better still DELTA-a for capital delta, but things are clumsy > enough as it is. > The d stands, occasionally, also for small, not just for infinitely small. > The mathematics is not intended to provide a rigorous proof, but is only > used as a tool to get some qualitative results. > > Please, also keep in mind/consider that all I am trying to do is understand > physics, or rather, trying to understand nature. I still feel I had some > success with that. Yeah well... you should understand what I'm trying to do here. Since you come up with the General Relativity precession formula, I'm looking for the shortcut you have taken somewhere - deliberately or not - I'll leave that in the middle ;-) I should also tell you that I didn't have a close look at your parts G-1 and G-2. Just jumped in on GM-2 and frowned a bit on GM-3. Perhaps it *would* be a good idea to modify the HTML after all like I suggested. It's isn't that difficult to enter formulae with for instance FrontPage... Going abroad as from Thursday morning, so I'll check the site when I get back... meanwhile I'll go and get my GR course from 25 years ago from the attic - the old courses are beginning to pile up here in the living room. Love the refreshment :-) See you... Dirk Vdm