The core of my heuristic-based CM simulations can be represented by the
following algorithm. The code has been simplified for your viewing pleasure.
The code/algorithm is represented in Visual Basic .NET (2008). I've also
performed MC simulations using C#. But VisualBasic, in many ways is an
easier language to use particularly since it automatically takes care of a
lot of clerical details that can end up consuming much of a programmer's
time. Using VB helps me focus on the primary task at hand. Using Microsoft's
.NET architecture to generate graphics has also turned out to be a
powerfully useful tool.
******************************************************************
******************************************************************
******************************************************************
'===========================================================================
==================
'Perform Basic Orbit Calculations: A FEED-BACK LOOP!
'===========================================================================
==================
For i = 1 To itterationCount Step 1
'Move current coordinates into previous vector settings
'in preparation to generate next itterative step in loop.
prevXPos = currXPos
prevYPos = currYPos
prevXVec =.currXVec
prevYVec = currYVec
'Determine current radius length/distance... based on distance starting
at (0,0) origin.
currAttractRadius = util.length(0.0, 0.0, currXPos, currYPos)
'Determine current attractive force, based on current determined
distance, i.e. F = 1/r^2 etc...
currAttractForce = util.force(currForceConstant, currAttractRadius,
attractionPower)
'Generate current vector coordinates
currXVec += (-1) * currAttractForce * (CurrXPos / currAttractRadius)
currYVec += (-1) * currAttractForce * (CurrYPos / currAttractRadius)
'Feed current vectors back into x,y coordinates
currXPos += CurrXVec
currYPos += CurrYVec
'DO OTHER STUFF HERE...like plot the coordinate on an (x,y) graphic,
generate statistics, etc...
Next
******************************************************************
******************************************************************
******************************************************************
Again, the above code has been stripped to its core & simplified. For
example I don't explicitly show how I determine distance or the current
Attractive Force. I placed the inner workings of that code in a "utility"
class. Nevertheless, this is an accurate representation of what much of my
research has been based on. I've been playing around with stuff like this
for years. I've also experimented with oodles of interesting permutations
and hybrid formulas, just to see what pops up. Occasionally I have been
surprised, if not totally baffled.
Regards
Steven Vincent Johnson
www.OrionWorks.com
www.zazzle.com/orionworks
From: Mauro Lacy [mailto:[email protected]]
Sent: Thursday, October 14, 2010 6:06 AM
To: [email protected]
Subject: Re: [Vo]:Anyone recognizes this astronomy integral?
On 10/11/2010 01:50 PM, OrionWorks - Steven Vincent Johnson wrote:
Hi again,
Today is a state-wide furlough day for most state of Wisconsin employees,
like me. ... How nice to have an extra "holiday" to explore some of Mile's
concepts. I'll rake the lawn later...
Regarding the distinction between using particles or waves to explain how
the universe works, including the nature of gravity, I place far more faith
in the proclivity of wave theory than I do in individual particles. Putting
my faith in "particles", to me, would seem to be nothing more than
worshipping a static snap shot in time of what is actually happening in the
universe on an infinitely dynamic scale. It might seem contradictory for me
to say this, particularly since my own computer simulations could easily be
perceived primarily as examples of the nature of particle theory. Not true!
What I find far more interesting is the gradual build up of millions and
trillions of individual "point/particles" as they gradually construct
computer generated graphic patterns. These graphic patterns end up looking
more like the influences of dynamic wave theory in action. It just takes
time, and a lot of "particle" build up! ;-)
As of Sunday evening I've managed to plow through Mile's "Explaining the
Ellipse" paper - twice. Rather mind-bending at times. I also ordered his
book through Amazon.
It is obvious to me that my own CM computer simulations are completely
mechanistic & heuristic in nature. They don't necessarily explain how
gravity truly works.
While I'm willing to explore Miles' premise that "tangential velocity"
shouldn't be confused with "orbital velocity", the distinction Miles
attempts to paint between the two concepts still eludes me to a large
extent. Fortunately, Miles is aware of the fact that the distinction tends
to baffle most of his readers. He attempts to compensate by giving
additional examples. If I understand Mile's commentary, it seems obvious to
me that my own CM computer simulations, which are obviously heuristic in
nature, involve the feeding back of "orbital velocities" (not "tangential")
into the algorithm in order to get the next x,y coordinate position of the
orbiting satellite. It's a simple algorithm to compute, and I've done this
for years. Nevertheless, in my heuristic oriented computer programs there is
no need to incorporate a third factor - a repulsive E/M (1/r^4) function.
Granted I could easily incorporate the additional function of (1/r&4) - and
I HAVE incorporated similar exploratory repulsive functions in the past just
to see what would happen, such as 1/r^3 in repulsive mode. As far as I can
tell, however, there does not appear to be any practical/heuristic need to
do so. Also the 1/r^4 force will QUICLY become negligible in most cases -
which I gather is precisely what Mathis is saying as well. It would only
begin to possibly influence the position of an orbiting satellite as it
approaches main attractor gravitational body. In fact, it would have to be
VERY close indeed to the main attractor body for the repulsive forces to
begin visibly manifesting.
Well... maybe I need to rethink that! (I'm thinking out loud here.) I must
confess that my own CM computer simulations based strictly on using 1/r^2
(with no additional algorithmic enhancements) have indicated to me a strong
suspicion that all computed "orbital ellipses" are inherently unstable -
given enough time to let the simulation run its course. Err... Well... this
gets even messier! I think it would be more accurate to state the fact that
my orbits become unstable when the feed-back values become too large (or too
coarse) between iterative feed-back steps, particularly as one approaches
the central orbiting body and the individual vector values increase
geometrically. This is where I've noticed that chaos will be entered into my
computer simulations. The introduction of what is presumed to be "unwanted"
chaos is also precisely what has fascinated me for years, even if the
introduction of such "chaotic" behavior has absolutely nothing to do with
accurately predicting "true" CM orbital behavior. Incorporating a repulsive
1/r^4 function into the original equation might help ameliorate the chaotic
blow a bit, but I don't tend to think of it as the real solution,
particularly since my algorithms are strictly heuristic in nature anyway and
probably don't really explain the actual effects of "gravity".
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.
Any thoughts on the matter? I seem to recall that you previously stated that
you have explored computer simulations of multiple planet solar systems and
the orbital perturbations that were generated. I gather you're an old hand
at performing these kinds of computer simulations. No?
Yes, I've extensively used the excellent Gravity Simulator, by Tony Dunn.
I've never developed my own, till now.
Regards,
Mauro
