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AU other than Astronomical Units?
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. |
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AU other than Astronomical Units?
"Robert" wrote in message
... 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. |
#3
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AU other than Astronomical Units?
In uk.sci.astronomy message , 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. 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. |
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AU other than Astronomical Units?
On Apr 27, 11:30*pm, Dr J R Stockton wrote:
In uk.sci.astronomy message , 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. *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/wikipedi...3%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. |
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AU other than Astronomical Units?
In message Je-dnXXpMbkkQonVnZ2dnUVZ8h-dnZ2d@plusnet, Neil
writes "Robert" wrote in message ... 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 |
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AU other than Astronomical Units?
On 28 Apr, 13:31, Stewart Robert Hinsley
wrote: In message Je-dnXXpMbkkQonVnZ2dnUVZ8h-dnZ2d@plusnet, Neil writes "Robert" wrote in message ... 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+m2).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+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- 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/yea...opernicus.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 |
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AU other than Astronomical Units?
In article ,
Stewart Robert Hinsley 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 |
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AU other than Astronomical Units?
On 28 Apr, 15:50, (Richard Tobin) wrote:
In article , Stewart Robert Hinsley 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 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. |
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AU other than Astronomical Units?
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. |
#10
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AU other than Astronomical Units?
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 |
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