It looks like you're using an Ad Blocker.
Please white-list or disable AboveTopSecret.com in your ad-blocking tool.
Thank you.
Some features of ATS will be disabled while you continue to use an ad-blocker.
Originally posted by wirehead
Using Newtonian physics, our most exacting mathematical methods were able to determine the position of mercury so precisely that [color=salmon]when we noticed a small discrepancy on the order of 3 arcseconds, it was only later explained by Einstein's theory of general relativity and is now seen as one of the slam-dunk confirmations of his theory.
The Actual Motion of The Moon
In the late 19th century, Hill developed methods with which results of given accuracy could be achieved with much reduced labor. These methods have been effective in the discussion of the general prblem of three bodies (wikipedia: Three Body Problem) as well as in the practical solution of the lunar problem. The two principal features were (1) the introduction of the value of the ratio of the mean motions of the Earth and Moon from the outset to avoid convergence difficulties and (2) the use of a rotating rectangular coordinate system. Hill developed a rather elegant method of determining the motion of perigee that was also applied by John Couch Adams to the motion of the node. Hill's methods were used by Brown to develop the lunar theory that has been generally used to compute the coordinates of the Moon since 1923, although the theoretical motions of node and perigee were still unsatisfactory and were replaced by the observed values.
Brown's series contain about 1,500 terms, five times as many as in Hansen's Theory. The evaluation of these series is very laborious, and Brown, like some of his predecessors, prepared tables for the simplification of this work. They filled 650 quarto pages, and [color=gold]one man working alone could extract the coordinates just fast enough to keep up with the real Moon. The advent of the digital electronic computer has relieved this burden and also made feasible the direct evaluation of the series.
Encyclopedia Britanica, Inc
Volume 12
Page 417
( c ) 1980
Originally posted by davidgrouchy
Yes, I heard that one too.
But has anyone actually ever looked into it.
To see if there is something to the method,
to use it as an aid to doing one's own research?
I did.
It's propaganda.
But don't take my word for it.
Take Encyclopedia Britanica's word on the reality of the situation.
The Actual Motion of The Moon
In the late 19th century, Hill developed methods with which results of given accuracy could be achieved with much reduced labor. These methods have been effective in the discussion of the general prblem of three bodies (wikipedia: Three Body Problem) as well as in the practical solution of the lunar problem. The two principal features were (1) the introduction of the value of the ratio of the mean motions of the Earth and Moon from the outset to avoid convergence difficulties and (2) the use of a rotating rectangular coordinate system. Hill developed a rather elegant method of determining the motion of perigee that was also applied by John Couch Adams to the motion of the node. Hill's methods were used by Brown to develop the lunar theory that has been generally used to compute the coordinates of the Moon since 1923, although the theoretical motions of node and perigee were still unsatisfactory and were replaced by the observed values.
Brown's series contain about 1,500 terms, five times as many as in Hansen's Theory. The evaluation of these series is very laborious, and Brown, like some of his predecessors, prepared tables for the simplification of this work. They filled 650 quarto pages, and [color=gold]one man working alone could extract the coordinates just fast enough to keep up with the real Moon. The advent of the digital electronic computer has relieved this burden and also made feasible the direct evaluation of the series.
Encyclopedia Britanica, Inc
Volume 12
Page 417
( c ) 1980
Originally posted by davidgrouchy
I have no arbitrary number of my choosing, magic or otherwise.
I have a systematic method of analysis.
One that I can input any data for orbital periods into
and get simplified formulas out as our result.
For instance, notice that in your posts there is a different period given for the orbital period of the Earth than the one I listed in my previous posts. I just used the current periods as listed on Wikipedia for each body. As you may know these change. Both from year to year, and as more accurate observations are made.
But either way,
I could also run the analysis using any numbers anyone wishes.
It's "The Method" as described by Archimedes that I'm using,
and that I find so spectacular.
Originally posted by wirehead
Any decimal representation can be rewritten as an infinite sum of fractions, this is not news at all.
3.1416 = 3 + 1/10 + 4/100 + 1/1000 + 6/10000
1/4 geometric series method that followed Eudoxus that used the same tradition.
that proved the accuracy of a [color=gold] finite
Originally posted by AwakeinNM
The trouble with these math threads is that people like me can never tell if these guys are arguing or not.
Originally posted by wirehead
Edit: If you can "run this analysis" on any pair of numbers, perhaps it would be simpler if you could run the analysis on the two numbers 2, 5 as a demonstration?
Originally posted by wirehead
Please, elaborate on this system. What are you trying to show in your equations? I caution that I've not read any of your other threads. Just break it down for me simply.
What is the relationship between orbits that you are attempting to show? Are you trying to predict orbital periods? Draw connections between orbital periods of different bodies?
The solar system has no comon denominator
Originally posted by davidgrouchy
That would be "uninteresting" as neither of those are irrational numbers.
The ecliptical orbits of the bodies of the solar system, are well modled using Newtonian physics, some special cases more accurately with Einstein (Newtonian being considered a subset of Relativity now), but the fundamental question still remains.
How did the orbits orgininate in the first place.
For that we get answers that contain a lot of hand waving
like acretion, capture, cooling, big bank, etcetera, etcetera...
Isn't it interesting, though, that there are no orbital periods that are
comensurate with any other. That they are all irrational when compared
to each other. One would think that by pure chance, at least one orbital body
would have a whole number relationship with at least one other orbital body.
But they don't.
The solar system has no comon denominator.
What we have is the theory of gravity.
And this works great.
But so far it only works to define the predicted orbit (apparently born like athena
fully formed from the brow of Zeus) and detect new bodies by the perturbations of
that predicted orbit.
Using Archimedes method B with Egyptian recursive fractions it becomes possible
to analyse the relationships between the irrational numbers themselves.
And with such tools unexamined trends in the solar system become evident.
For instance:
Preliminary math
===========================
Orbital period / Rotation Period =
Take Luna
Orbital period = 27.32166 earth days
Rotation Period = 27.32166
27.32166 / 27.32166 = 1
===========================
How many bodies in our solar system have a 1:1 ratio of Orbital Period to Rotation Period?
This should be impossible, even once, considering that all orbits are eliptical.
The current theory is called Tidal Locking.
But people tend to only be aware of
our own Moon's tidal locking,
and the math looks good
in that one case.
But how many cases are there?
Well here is the list
...
There are 46 "moons" that always show the same face to the body they orbit.
. [color=gold] This is a major trend and fundamental property of our solar system.
Is so-called "tidal locking" sufficient to explain how this happens with eliptical orbits. Eliptical orbits should make the ratio of orbit to side facing the orbited body impossible. Are all of the moons at the same distance to mass ratio as all the others exhibiting so-called tidal locking?