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From: Craig Markwardt on 11 May 2010 04:00
On May 10, 5:09 pm, Archimedes Plutonium
<plutonium.archime...(a)gmail.com> wrote:
> Craig Markwardt wrote:
> > On May 10, 4:37 am, Archimedes Plutonium
> > <plutonium.archime...(a)gmail.com> wrote:
> > > Enrico wrote:
>
> > > > A couple of formulas here:
> > > >http://en.wikipedia.org/wiki/Beam_divergence
>
> > > Yes it gives a Divergence formula of 2arctan Df-Di/2L
>
> > > I suspected it was linear rather than the intensity of normal light
> > > being inverse square
>
> > Huh? The formula above describes a constant beam opening angle. A
> > emitting source with constant opening angle still falls off in
> > intensity with the square of distance. I.e. *inverse square* still
> > applies. Since your conclusions are based on a faulty premise, the
> > conclusions are not relevant.
>
> Do you know what "linear" means in mathematics as opposed to
> inverse square? Probably not.

You are being cavalier about the phrase "linear." The equation
referenced by "Enrico" describes the *diameter* of a beam spot, as a
function of distance - not intensity [*]. If the diameter would grow
linearly with distance, then the *area* A of the beam spot must grow
quadratically. If a laser power P is distributed over the beam spot
area A, then the intensity (= P/A = Watts per square meter) would fall
quadratically with distance, which is basically inverse square law.
Thus you are in error.

[*] in any case, the equation is not linear since it contains a
arctangent function.

> The reason a laser beam is used
> to reflect off a mirror on the Moon planted by the astronauts decades
> ago
> is because the laser beam is not a inverse square with distance.
> Otherwise,
> just use a white light flashlight for the roundtrip to the Moon.

You are incorrect. Beam divergence can be described as a cone with a
given opening angle. The area of a cone increases as the square of
distance. The divergence for laser ranging is small - a few arcseconds
[1], but it's enough to cause significant inverse-square losses during
the trip to the moon (and back).

[1] - example laser divergence of McDonald observatory is up to 20
arcseconds.
http://ilrs.gsfc.nasa.gov/stations/sitelist/MDOL_sitelog.html#5.%20%20%20Laser%20System%20Information

.... remainder deleted for brevity ...

CM
From: Craig Markwardt on 11 May 2010 04:26
On May 10, 4:37 pm, Archimedes Plutonium
<plutonium.archime...(a)gmail.com> wrote:
> Craig Markwardt wrote:
>
> > It's fruity to think that telescope designers and observers do not
> > consider the limiting capabilities of the telescope.  Of course they
> > do!
>
> Fruityer yet is that Craig thinks the redshift is unique to speedy
> galaxies
> and a speedy Space:

I note your lack of response. *You* made the claim that astronomers
didn't understand the limitations of their telescopes. I showed a
counter-example.


> > There are no known physical processes - other than Doppler shift or
> > cosmological expansion - which could shift the center wavelength of
> > all spectral lines emitted by an astrophysical source.  Dust
> > absorption or scattering certainly does not.  Note that your
> > "scattering" experiment is irrelevant because it involves a continuum
> > ("white") emitter.

....
> > Even a cursory search of Google for "hst limiting magnitude" finds
> > pages like this:
> >  http://www.stsci.edu/hst/acs/documents/handbooks/cycle18/c05_imaging3...
> > which shows an observational limiting magnitude of ~28 or better for
> > most modern HST instruments over a wide optical/IR wavelength range.
>
> > Considering M87 as an example, the *absolute* magnitude is about -22 -
> > this is the total magnitude of a galaxy as seen at 10 parsec
> > distance.  Using the definition of astronomical distance modulus -
> > which uses the inverse-square law of intensity - the limiting distance
> > for an M87-like galaxy would be about 100 billion parsecs, or 300
> > billion light years.
>
> > Intrinsically larger and brighter galaxies than M87 could be seen to
> > further distances, and smaller/fainter galaxies to shorter distances.
>
> > CM
>
> Okay, Craig, do you ever stop to think that what you are concluding
> makes
> commonsense? That the astronomy community concensus is a Universe
> with age of less than 14 billion years old, but you seem to think the
> reporting using the HST of a quasar at 28 billion light years or
> something
> at 300 billion light years is justifiable. How you reconcile the
> unreconcilable?

The estimate that I showed is straightforward to construct using the
absolute magnitude of M87 and its distance modulus of ~31.4. You
could have tried it yourself, but you did not.

The distance I quoted assumes a flat spacetime in an unchanging
cosmology - in other words classical Newtonian physics. If you
subscribe to such a cosmology, there is no "age" of the universe, so
there is no problem with a 300 Gly distance.

Your reference to an "age" of the universe must be interpreted in the
context of a cosmological model which describes the age. In the
standard cosmological model, the "luminosity distance" and the light
travel time behave differently. Luminosity distance Dl is what makes
the inverse-squre equation L / (4*pi*Dl^2) work out, by definition.
This is different than light travel time, because clocks ticked
differently in the cosmological past.

A luminosity distance corresponds to a redshift of about 10 in the
standard cosmology. This can be verified with Ned Wright's cosmology
calculator:
http://www.astro.ucla.edu/~wright/CosmoCalc.html
(redshift 10, luminosity distance ~300 Gly, light travel time 13.2
Gly)

CM
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