Can AU mean something other than Astronomical Units? Given this formula:

(m1 + m2)T^2 = a^3

T=years
m=solar masses
a is in units of AU

Can anyone guess what this equation means?  Is there another meaning of AU 
related to acceleration?

Thanks.

"Robert"  wrote in message 
news:4814c5f7$0$11638$607ed4bc@cv.net...
> Can AU mean something other than Astronomical Units? Given this formula:
>
> (m1 + m2)T^2 = a^3
>
> T=years
> m=solar masses
> a is in units of AU
>
> Can anyone guess what this equation means?  Is there another meaning of AU 
> related to acceleration?
>
> Thanks.
>
>


Very often arbitrary units.

In uk.sci.astronomy message <4814c5f7$0$11638$607ed4bc@cv.net>, Sun, 27
Apr 2008 14:28:21, Robert  posted:
>Can AU mean something other than Astronomical Units?

Angstrom Units.  Australia.  Aberdeen University.  ...

> Given this formula:

>(m1 + m2)T^2 = a^3
>
>T=years
>m=solar masses
>a is in units of AU
>
>Can anyone guess what this equation means?

Ask Kepler.  There, m should be M.  Start with the obvious GMm/r^2 =
mrw^2 ; extract m ; put T = 2pi/w ; and eliminate G by knowing that a
circular orbit about the Sun at 1 AU takes a year.  Now re-do it for M
not >> m, and orbits around the barycentre.

>  Is there another meaning of AU
>related to acceleration?

If followed by DI, there's said to be plenty available.

-- 
 (c) John Stockton, nr London, UK. ?@merlyn.demon.co.uk  Turnpike v6.05  MIME.
 Web  <URL:http://www.merlyn.demon.co.uk/> - FAQqish topics, acronyms & links;
  Astro stuff via astron-1.htm, gravity0.htm ; quotings.htm, pascal.htm, etc.
 No Encoding. Quotes before replies. Snip well. Write clearly. Don't Mail News.

On Apr 27, 11:30 pm, Dr J R Stockton  wrote:
> In uk.sci.astronomy message <4814c5f7$0$11638$607ed...@cv.net>, Sun, 27
> Apr 2008 14:28:21, Robert  posted:
>
> >Can AU mean something other than Astronomical Units?
>
> Angstrom Units.  Australia.  Aberdeen University.  ...
>
> > Given this formula:
> >(m1  m2)T^2 = a^3
>
> >T=years
> >m=solar masses
> >a is in units of AU
>
> >Can anyone guess what this equation means?
>
> Ask Kepler.  There, m should be M.  Start with the obvious GMm/r^2 => mrw^2 ; extract m ; put T = 2pi/w ; and eliminate G by knowing that a
> circular orbit about the Sun at 1 AU takes a year.  Now re-do it for M
> not >> m, and orbits around the barycentre.
>
> >  Is there another meaning of AU
> >related to acceleration?
>
> If followed by DI, there's said to be plenty available.
>
> --
>  (c) John Stockton, nr London, UK. ?...@merlyn.demon.co.uk  Turnpike v6.05  MIME.
>  Web  <URL:http://www.merlyn.demon.co.uk/> - FAQqish topics, acronyms & links;
>   Astro stuff via astron-1.htm, gravity0.htm ; quotings.htm, pascal.htm, etc.
>  No Encoding. Quotes before replies. Snip well. Write clearly. Don't Mail News.

When you are a naturally talented astronomer,you get to enjoy how
Newton unethically tranfered  mean motion along planetary orbits to
mean Sun/Earth distances -

"PHÆNOMENON IV.
"That the fixed stars being at rest, the periodic times of the five
primary planets, and (whether of the sun about the earth, or) of the
earth about the sun, are in the sesquiplicate proportion of their mean
distances from the sun. " Newton

What Kepler actually wrote,based on orbital comparisons -

"The proportion existing between the periodic times of any two planets
is exactly the sesquiplicate proportion of the mean distances of the
orbits, or as generally given,the squares of the periodic times are
proportional to the cubes of the mean distances." Kepler

The sidereal framework  or rather the solar/sidereal fiction is based
on mean Sun/Earth distances insofar as there is no indication of
Kepler's orbital geometry nor variations in orbital speed  in that
framework and that is where it dovetails with Newton's ridiculous
invokation of celestial sphere geometry into heliocentric reasoning
as shown above -

http://upload.wikimedia.org/wikipedia/commons/1/1d/Tiempo_sid%C3%A9reo.en.png

You are wasting each other's time and all the sloppy  non geometric
equations in the world cannot disguise that that it all amounts to
formalised astrology.

I will make it easy for you,a programming mind generally cannot
comprehend the language of astronomy,it is actually painful for you
and your mates to consider that the genuine framework,insights and
methods of astronomers exists outside the calendrically driven
clockwork solar system created in the late 17th century.While I do
sympathise that you do not have a feel for the intutive correction
system which keeps insights on track,the damage which the 'scientific
method' approach to astronomy is just too unstable and ridiculous at
the moment to do anything other than condemn it.

In message <Je-dnXXpMbkkQonVnZ2dnUVZ8h-dnZ2d@plusnet>, Neil 
 writes
>"Robert"  wrote in message 
>news:4814c5f7$0$11638$607ed4bc@cv.net...
>> Can AU mean something other than Astronomical Units? Given this formula:
>>
>> (m1 + m2)T^2 = a^3
>>
>> T=years
>> m=solar masses
>> a is in units of AU
>>
>> Can anyone guess what this equation means?  Is there another meaning 
>>of AU  related to acceleration?
>>
>> Thanks.
>>
>>
>
>
>Very often arbitrary units.

In the above AU means astronomical unit. The equation above represents a 
generalisation of Kepler's 3rd law, and 'a' denotes the semi-major axis 
of the orbit.

The selection of units makes the constant of proportionality equal to 1; 
for a different set of units the equation becomes (m1+m2).T^2 = k.a^3

Consider the Earth. Then m1+m2 is negligibly differ from the mass of the 
Sun, so m1+m2 = 1 solar mass. The orbital period is 1 year, to T^2 = 1. 
The semi-major axis is 1 A.U., so a^3 = 1.
-- 
Stewart Robert Hinsley

On 28 Apr, 13:31, Stewart Robert Hinsley <{$new...@meden.demon.co.uk>
wrote:
> In message <Je-dnXXpMbkkQonVnZ2dnUVZ8h-dnZ2d@plusnet>, Neil
>  writes
>
>
>
>
>
> >"Robert"  wrote in message
> >news:4814c5f7$0$11638$607ed4bc@cv.net...
> >> Can AU mean something other than Astronomical Units? Given this formula> >> (m1  m2)T^2 = a^3
>
> >> T=years
> >> m=solar masses
> >> a is in units of AU
>
> >> Can anyone guess what this equation means?  Is there another meaning
> >>of AU  related to acceleration?
>
> >> Thanks.
>
> >Very often arbitrary units.
>
> In the above AU means astronomical unit. The equation above represents a
> generalisation of Kepler's 3rd law, and 'a' denotes the semi-major axis
> of the orbit.
>

All this insisting on a law when Kepler just drew a correlation
between orbital period and distance from the Sun,-


"But it is absolutely certain and exact that the ratio which exists
between the periodic times of any two planets is precisely the ratio
of the 3/2th power of the mean distances, i.e., of the spheres
themselves; provided, however, that the arithmetic mean between both
diameters of the elliptic orbit be slightly less than the longer
diameter. And so if any one take the period, say, of the Earth, which
is one year, and the period of Saturn, which is thirty years, and
extract the cube roots of this ratio and then square the ensuing ratio
by squaring the cube roots, he will have as his numerical products the
most just ratio of the distances of the Earth and Saturn from the sun.
1 For the cube root of 1 is 1, and the square of it is 1; and the cube
root of 30 is greater than 3, and therefore the square of it is
greater than 9. And Saturn, at its mean distance from the sun, is
slightly higher  than nine times the mean distance of the Earth from
the sun." Kepler


> The selection of units makes the constant of proportionality equal to 1;
> for a different set of units the equation becomes (m1).T^2 = k.a^3
>

Now for the junk dumped on Kepler's correlation -

"PHÆNOMENON IV.
"That the fixed stars being at rest, the periodic times of the five
primary planets, and (whether of the sun about the earth, or) of the
earth about the sun, are in the sesquiplicate proportion of their mean
distances from the sun. " Newton

So sunshine,where in all heliocentric astronomy was the Sun about the
Earth and the Earth about the Sun ever proposed as a working principle
let alone in dealing with Kepler's correlation between the periodic
orbital times of a planet and its distance from the Sun ?.

The utter stupidity of neglecting how Copernicus and Kepler used the
periodic times argument for planetary  to determine the arrangement of
planets around the Sun does not and never included any geocentric/
heliocentric Sun/Earth orbital equivalency.




> Consider the Earth. Then m1 is negligibly differ from the mass of the
> Sun, so m1 = 1 solar mass. The orbital period is 1 year, to T^2 = 1> The semi-major axis is 1 A.U., so a^3 = 1.
> --
> Stewart Robert Hinsley- Hide quoted text -
>
> - Show quoted text -

I wish somebody woulod some day actually read and interpret the text
of Copernicus,the determination of the heliocentric arrangement was
based  on orbital periods where the points of contention were the
location of Mercury and Venus -

"Of all things visible, the highest is the heaven of the fixed stars.
This, I see, is doubted by nobody. But the ancient philosophers wanted
to arrange the planets in accordance with the duration of the
revolutions. Their principle assumes that of objects moving equally
fast, those farther away seem to travel more slowly, as is proved in
Euclid's Optics. The moon revolves in the shortest period of time
because, in their opinion, it runs on the smallest circle as the
nearest to the earth. The highest planet, on the other hand, is
Saturn, which completes the biggest circuit in the longest time. Below
it is Jupiter, followed by Mars.

With regard to Venus and Mercury, however, differences of opinion are
found. For, these planets do not pass through every elongation from
the sun, as the other planets do. Hence Venus and Mercury are located
above the sun by some authorities, like Plato's Timaeus [38 D], but
below the sun by others, like Ptolemy [Syntaxis, IX, 1] and many of
the modems. Al-Bitruji places Venus above the sun, and Mercury below
it. "

De Revolutionibus 1453

http://webexhibits.org/calendars/year-text-Copernicus.html

Where you get the Earth about the Sun or the Sun about the Earth in
referencing planetary motion against the 'fixed stars' is
unadulterated junk of Newton,it is both unethical and damaging to the
original correlation Kepler drew between orbital periods and their
distances.

Are you lot quite finished now dumping junk into the celestial arena
and making wonderful and easy to understand astronomical correlations
into contrived  empirical junk

In article <M9b0HzCOOcFIFwwe@meden.invalid>,
Stewart Robert Hinsley  <{$news$}@meden.demon.co.uk> wrote:

>>> Can AU mean something other than Astronomical Units? Given this formula:
>>>
>>> (m1 + m2)T^2 = a^3
>>>
>>> T=years
>>> m=solar masses
>>> a is in units of AU

>In the above AU means astronomical unit. The equation above represents a 
>generalisation of Kepler's 3rd law, and 'a' denotes the semi-major axis 
>of the orbit.
>
>The selection of units makes the constant of proportionality equal to 1; 
>for a different set of units the equation becomes (m1+m2).T^2 = k.a^3

If you neglect the earth's mass compared to the sun's, and equate the
gravitational force between the two bodies (GMm/r^2) with the force
to maintain a circular orbit (mw^2r), you will find that k is 4 pi^2 / G.

So in the above units, G is 4 pi^2.

-- Richard

-- 
:wq

On 28 Apr, 15:50, rich...@cogsci.ed.ac.uk (Richard Tobin) wrote:
> In article <M9b0HzCOOcFIF...@meden.invalid>,
> Stewart Robert Hinsley  <{$new...@meden.demon.co.uk> wrote:
>
> >>> Can AU mean something other than Astronomical Units? Given this formula:
>
> >>> (m1  m2)T^2 = a^3
>
> >>> T=years
> >>> m=solar masses
> >>> a is in units of AU
> >In the above AU means astronomical unit. The equation above represents a
> >generalisation of Kepler's 3rd law, and 'a' denotes the semi-major axis
> >of the orbit.
>
> >The selection of units makes the constant of proportionality equal to 1;
> >for a different set of units the equation becomes (m1).T^2 = k.a^3
>
> If you neglect the earth's mass compared to the sun's, and equate the
> gravitational force between the two bodies (GMm/r^2) with the force
> to maintain a circular orbit (mw^2r), you will find that k is 4 pi^2 / G.
>
> So in the above units, G is 4 pi^2.
>
> -- Richard
>
> --
> :wq

You have to affirm that Newton's idiosyncratic geometric framework is
correct first -

"PHÆNOMENON IV.
"That the fixed stars being at rest, the periodic times of the five
primary planets, and (whether of the sun about the earth, or) of the
earth about the sun, are in the sesquiplicate proportion of their mean
distances from the sun. " Newton

He means the astrological framework at rest,the calendrically driven
clockwork solar system imposed against zodiacal geometry and it would
be funny if it were not the dominant framework for structural
astronomy and cosmological evolution  .It is no wonder Kepler called
you lot the 'inferior tribunal of geometers', it is  worse now since
you lot even managed to jettison geometry entirely for an inaccurate
non geometric equational treatment.

I enjoy Newton's idiosyncratic take on retrogrades and his idiotic
take on Kepler's Panis Quadragesimalis based also on retrogrades,pity
you do not have the astronomical talent to enjoy either the correct
Copernican/Keplerian treatment and the childish maneuvering of Newton.

On 27 Apr, 19:28, "Robert"  wrote:
> Can AU mean something other than Astronomical Units? Given this formula:
>
> (m1  m2)T^2 = a^3
>
> T=years
> m=solar masses
> a is in units of AU
>
> Can anyone guess what this equation means?  Is there another meaning of AU
> related to acceleration?
>
> Thanks.

You are a kid and hardly know of the battles fought to restore
stability to astronomy,some treat the symptoms within the system while
there are rare people who know the root of  the disease.You probably
learned Newton's famous equation that he never wrote and much of it is
involved with the ins and outs of his treatment of Kepler's geometry
and where he got his astronomical unit from.

Take the following statement to heart as just a tiny fraction of a
festering condition introduced by the careless mathmatician into
astronomy.even those who were quite good,like Petr Beckmann,never
managed to move the topic beyond the mediocre state where it now rests
-

" I challenge anyone to quote a single, solitary place where Newton in
the Principia or elsewhere said F=ma. He was much too careful a man to
assume the constancy of mass and never, but never, went beyond F =
d(mv)/dt and never took the m out of the parenthesis as constant. That
was done by the guesswork-loving intuitive physicists who lived after
him. Of course, the Principia are not written in the language of
algebra, but of geometry."  Petr Beckmann


This is uk.sci.astrology and you hardly know it.

In article ,
oriel36   wrote:
>Petr Beckmann

Ah, Petr Beckmann, who decided that Einsteinian relativity must be
wrong, apparently because it didn't fit with his "objectivist" views.
He proposed what amounted to an entrained ether, but it turned out not
to match reality.

-- Richard
-- 
:wq

On Apr 28, 5:31 pm, rich...@cogsci.ed.ac.uk (Richard Tobin) wrote:
> In article ,
>
> oriel36   wrote:
> >Petr Beckmann
>
> Ah, Petr Beckmann, who decided that Einsteinian relativity must be
> wrong, apparently because it didn't fit with his "objectivist" views.
> He proposed what amounted to an entrained ether, but it turned out not
> to match reality.
>
> -- Richard
> --
> :wq

It takes a rare individual to know what Newton was up to with those
definitions of absolute/relative space and time and unfortunately even
genuine mathematical minds never figured out the ins and outs of what
he was talking about.Mach was partly right but Newton's phrasing of
absolute/relative time as the Equation of Time while working of the
solar/sidereal framework of Flamsteed makes it virtually impossible
for an outsider to rresolve -

"This absolute time can be measured by comparison with no motion; it
has therefore neither a practical nor a scientific value; and no one
is justified in saying that he knows aught about it. It is an idle
metaphysical conception."
Mach, Analyse der Empfindungen, 6th ed.

So, this is what got  Mach so upset -

"Absolute time, in astronomy, is distinguished from relative, by the
equation or correlation of the vulgar time. For the natural days are
truly unequal, though they are commonly considered as equal and used
for a measure of time; astronomers correct this inequality for their
more accurate deducing of the celestial motions. It may be, that there
is no such thing as an equable motion, whereby time may be accurately
measured." Principia

The Equation of Time distinguishes the natural noon cycle from the
human devised 24 hour cycle and from there into terrestrial geometry
therefore there is a geometrical resolution to all this,a proper one
instead of the junk of the last century.

The geometrical framework which Newton worked off is nothing other
than the invention of Flamsteed -

http://upload.wikimedia.org/wikipedia/commons/1/1d/Tiempo_sid%C3%A9reo.en.png

No wonder Mach was upset but like most mathematicians he had  little
understanding of geometrical principles where the 24 hour day is
transfered to the axial cycle as a constant,basically,the 24 hour day
corresponds to no observed cyclical reference.This surfaces when
physicists talk of the Earth speeding up and slowing down by using a
zodiacal framework and using the value of 23 hours 56 minutes 04
seconds for constant axial rotation.

In retrospect,all these guys running around and proclaiming 'time is
not absolute'  looks unintentionally funny for even a brief look at
Newton's definition shows it to be the commonplace but exquiste
difference between the variations in the natural day and the 24 hour
day.Which one would you care to reject !.

As for absolute/relative space,well,that is a different story that
dovetails with absolute/relative time,it is basically a mutation of
Copernican reasoning in the matter of retrogrades and how they are
resolved.I have little interest in the 20th century nonsense and even
if I do pity the loss of so many great minds in attempting to turn
things around,people like Essen and Beckmann,there were not enough of
them and they simply do not have that astronomical talent to reach the
level of Newton and his maneuvering.

The worst thing you can do to a person is feign honesty when promoting
astronomical methods and insights,people expect that even if there are
enormous mistakes that nobody will intentionally deceive another
through feats of intentional confusion unfortunately the Scholium IV
of the Principia corresponds to that unsatisfactory status -

http://upload.wikimedia.org/wikipedia/commons/1/1d/Tiempo_sid%C3%A9reo.en.png

The point is not to make a scene out of Newton's 17th century
maneuvering and its early 20th century outriggers which followed from
the astrological framework  but rather to point out what 21st century
imaging can do.It may be that Kepler's orbital framework indicates a
galactic orbital component where the movement of the central Sun in
its gactic orbital motion may be partly responsible for less than
circular orbits,it is just the briefest glimpse that when Ptolemy
proposed the Equant,Copernicus the epicycle and finally resolved by
irregular orbits and motions of Kepler that they were glimpsing the
barest details of our solar system's galactuic orbital motion.The
problem of a localised solution which Newton provedes speaks for
itself -

"Cor. 2. And since these stars are liable to no sensible parallax from
the annual motion of the earth, they can have no force, because of
their immense distance, to produce any sensible effect in our system.
Not to mention that the fixed stars, every where promiscuously
dispersed in the heavens, by their contrary actions destroy their
mutual actions, by Prop. LXX, Book I." Newton

Relativity is a nuisance and it is not really fit for human
consumption other than it highlights the actual flaws in Newton's
agenda by promoting them rather than obliterating them,even Newton's
maneuverings amount to wasteful junk when compared to what was
correct.In this respect I would have nothing to gain by being sucked
into a relativity perspective that contains the same astrological core
as Newton's work did.

"Richard Tobin"  wrote in message 
news:fv4u4c$1kfh$2@pc-news.cogsci.ed.ac.uk...
> In article 
> ,
> oriel36   wrote:
>>Petr Beckmann
>
> Ah, Petr Beckmann, who decided that Einsteinian relativity must be
> wrong, apparently because it didn't fit with his "objectivist" views.
> He proposed what amounted to an entrained ether, but it turned out not
> to match reality.
>
> -- Richard
> -- 
> :wq
>
All that was a bit too difficult for me; but Beckmann's "Health Hazards of 
Not Going Nuclear" is wonderfully clear.