page: Roxy's Ruler timestamp:20190310194416 year: 2019 month: March day: 10 substed: yes
The morphological parameters of spiral galaxies can be directly measured from photographic plates and both line width and rotation curve can be measured in many different frequencies using radio astronomy. This method has the advantages of being independent of red shift and luminosity. If vmax is the maximum orbital speed of material in a galaxy in kilometers per second (kps) and αs is the measured distance between spiral arms along the major axis of the galaxy, then the distance to the galaxy, D, in parsecs, is given by the formula:
D = 3.12 X 109 / (vmax X αs)
A demonstration of how to use this method can be found in WikiHow.
A Brief History of Galactic Distance Measurements
An acknowledgement that various nebulae lay far beyond the bounds of our own galaxy did not occur until 1920, as a result of the great debate. Since then research into galactic structure and distances to galaxies exploded into a plethora of both amateur and academic papers and study.
Shortly after the realisation that the universe is much larger than previously thought, an already discovered method of measuring the distances to Cepheid variable class stars was utilised to find the distances to relatively nearby galaxies by Edwin Hubble. Hubble compared the distances to these galaxies to their red shifts and concluded that the universe was expanding with led to the theory of the Big Bang. This method of measuring the distances to galaxies extends to about 22 MegaParsecs(MPc).
Later it was discovered by astronomers R. Brent Tully and J. Richard Fisher and published in 1977, that there existed an empirical relationship relationship between absolute luminosity and the maximum rotation velocity of a galaxy, vrot. The parameter, vrot, is determined through line width. Line width is also known as the asymptotic rotation velocity of a galaxy. The Tulley-Fisher relationship states that the luminosity is relative to vrot squared. This discovery increased the ability to determine the distances to galaxies independently of red shift and advanced understandings of the large scale structure of the universe.
Cosmic Distance Ladder
Various other means of measuring the distances to galaxies have been found and are grouped together in various rungs on a ladder measuring farther and farther into space. This is known as the cosmic distance ladder.
Discovering Roxy's Ruler
The flat velocity rotation curve of NGC3198, as measured by K.G. Begeman, indicated there may exist some form of non-luminous material, i.e. dark matter, causing this effect. A three-line algebraic calculation  showed that a flat velocity rotation curve of NGC 3198 could only be explained if the galaxy was a linear orientation of material having a constant linear density according to Newtonian orbital dynamics. As bizarre as this result seems, it also complied with measurements of luminosity distribution made by Harlow Shapely. A successful determination of the algebraic formula for a spiral galaxy was found to be:
ř = θ / ῶ0.
Here ř is distance in light years (ly) and ῶ0 is in radians per year and is found from the formulae:
ῶ0 = ṽmax / (2π)
ṽmax = vmax /c, where c is the speed of light.
This is the formula for an Archemede's spiral.
By overlaying the spiral produced by the above equation onto a photograph of a corresponding spiral galaxy, the intrinsic size of the galaxy is known and its distance determined. Roxy's Ruler has been used to explain the structure of spiral galaxies, galactic rotation curves and to argue for a static universe.
There are significant consequences to the formula known as "Roxy's Ruler" and its derivation. No only can the distance to the galaxy be determined, but so can its mass, linear density and linear momentum. Furthermore, the Tulley-Fisher relationship is found to have a mathematical foundation. A derivation of the shape of a galaxy's rotation curve can be found through the formula:
vtan= vmax (ῶ0 r) / √(1+ ῶ02 r2).
which is the result of the metric in a curved space, namely:
ds2 = c2 dt2 / (γω2) - dr2 - γω2 dθ2.
γω = √(1+ ῶ02 r2).
Another consequence of this discovery is that both the flat rotation curve and spiral shape of NGC3198 is explained without having to resort to using dark matter or MOND.
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