flat rotation curves and 'foam' large scale struct

If we start from the conjecture that 'G' depends on the proximity of other matter, then the fact that the moon earth distance dosn't change consistently with time (i.e. a continual year on year increase, apart from changes already explained) leads us to two possible conclusions.

1) The universe is not expanding

2) The conjecture is wrong.

If the conjecture can be shown to account for the large scale structure of galaxies - i.e. the foam structure possibly caused by 'G' reducing for collapsing superclusters (causing explosions),
then we can conclude that the universe isn't expanding.

John Hunter.

Dear John,

It has been quite a while since we posted here. I am trying to improve a variable-timestep algorithm (just the newtonian part for now). As long as it keeps getting better I will stick to that. The advantage of variable timestepping is the huge dynamic range, useful for calculating close encounters. The disadvantage is the energy leak, this occurs because the area between the calculated triangle and the actual curved orbit differs from the area in a fixed-timestep algorithm.
Fun to work with, but it's timeconsuming.

___

If there is anyone with suggestions on how to incorporate non-newtonian effects, please let us know...

___

I noticed that using the correction

1 / Ge = 1 / G + 2 * m / (r * c ^ 2)

the factor (which arises in GR)

sqr(1 - 2 * G * m / (r * c ^ 2))

can be rewritten as

sqr(1 / (1 + 2 * m * Ge / (r * c ^ 2)))

___

All the best.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Michiel</i>
<br />Dear John,

It has been quite a while since we posted here. I am trying to improve a variable-timestep algorithm (just the newtonian part for now). As long as it keeps getting better I will stick to that. The advantage of variable timestepping is the huge dynamic range, useful for calculating close encounters. The disadvantage is the energy leak, this occurs because the area between the calculated triangle and the actual curved orbit differs from the area in a fixed-timestep algorithm.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Whether your timestep-algorithm is variable or not has nothing to do with the 'energy leak'. In order to minimize the latter, your timesteps must simply be small enough such as to allow a sufficiently accurate representation of the curved orbit.

Thomas

When in a fixed-timestep algorithm the step is not small enough to calculate an elliptical orbit accurately, the orbit will show precession, but will not change size.
In a variable-timestep algorithm, if the base-step is not small enough, the orbit does not precess, but each revolution is a bit smaller than the previous one.
That's what I mean by energy leak. Both methods get better with a smaller timestep, of course.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Michiel</i>
<br />When in a fixed-timestep algorithm the step is not small enough to calculate an elliptical orbit accurately, the orbit will show precession, but will not change size.
In a variable-timestep algorithm, if the base-step is not small enough, the orbit does not precess, but each revolution is a bit smaller than the previous one.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
It depends probably on the method you are using. I used a simple Riemann sum method (i.e. integration of an acceleration- step function with constant intervals) to calculate charged particle orbits in a magnetic field and subject to a time-dependent electric field (see my paper regarding Non-linear Plasma Oscillations ; Chpt.3) and what happened here was that the particle <i>gained</i> energy due to the fact that the approximating step function for the acceleration <i>inscribed</i> the actual acceleration as a function of time (you can see from the numerical result for the associated Energy Change of the particle that the minimum energy slightly increases with time; this effect is simply due to the finite step-width and becomes smaller if one reduces the step-width).

I used the same program also to calculate orbits in 1/r^2 force fields, where the same effect occured i.e. the orbit was getting larger and larger.

So I can't see the energy 'leak' (or 'source' in my case) having anything to do with a variable step width. It is just due to the fact that any numerical approximation of the time dependence of the force will either merely circumscribe or inscribe the latter.

Thomas

[Thomas] "I used a simple Riemann sum method (i.e. integration of a step function with constant intervals) to calculate charged particle orbits in a magnetic field and subject to a time-dependent electric field (see my paper regarding Non-linear Plasma Oscillations; Chpt.3) and what happened here was that the particle gained energy due to the fact that ... "

Does your method make any explicit assumptions about the speed of propagation of the force assocoated with these time dependent electric fields? In particular, do you use c, the speed of light, as the force propagation speed in these calculations?

LB