Re: [Phys-l] Moon's speed

[Bernard Cleyet <bernardcleyet@redshift.com>]

I answer my own question:

from the FAQ in the below URL:


     Technical Definitions and Computational Details

Sunrise and sunset. For computational purposes, sunrise or sunset is 
defined to occur when the geometric zenith distance of center of the Sun 
is 90.8333 degrees. That is, the center of the Sun is geometrically 50 
arcminutes below a horizontal plane. For an observer at sea level with a 
level, unobstructed horizon, under average atmospheric conditions, the 
upper limb of the Sun will then appear to be tangent to the horizon. The 
50-arcminute geometric depression of the Sun's center used for the 
computations is obtained by adding the average apparent radius of the 
Sun (16 arcminutes) to the average amount of atmospheric refraction at 
the horizon (34 arcminutes).

Moonrise and moonset. Moonrise and moonset are defined similarly, but 
the situation is computationally more complex because of the nearness of 
the Moon and the eccentricity of its orbit. If the computations are 
carried out using coordinates of the Moon with respect to the Earth's 
center (the usual method), then moonrise or moonset is defined to occur 
when the geometric zenith distance of the center of the Moon is

   90.5666 degrees + Moon's apparent angular radius - Moon's horizontal
   parallax

Under normal atmospheric conditions at sea level, the upper limb of the 
Moon will then appear to be tangent with a level, unobstructed horizon. 
No account is taken of the Moon's phase; that is, the Moon is always 
regarded as a disk in the sky and the upper limb might be dark. Here 
again, a constant of 34 arcminutes (0.5666 degree) is used to account 
for atmospheric refraction. The Moon's apparent radius varies from 15 to 
17 arcminutes and its horizontal parallax varies from 54 to 61 
arcminutes. Adding all the terms above together, the center of the Moon 
at rise or set is geometrically 5 to 10 arcminutes above the observer's 
"geocentric horizon" - the horizontal plane that passes through the 
Earth's center, orthogonal to the observer's local vertical.

Accuracy of rise/set computations. The times of rise and set phenomena 
cannot be precisely computed, because, in practice, the actual times 
depend on unpredictable atmospheric conditions that affect the amount of 
refraction at the horizon. Thus, even under ideal conditions (e.g., a 
clear sky at sea) the times computed for rise or set may be in error by 
a minute or more. Local topography (e.g., mountains on the horizon) and 
the height of the observer can affect the times of rise or set even 
more. It is not practical to attempt to include such effects in routine 
rise/set computations.

The accuracy of rise and set computations decreases at high latitudes. 
There, small variations in atmospheric refraction can change the time of 
rise or set by many minutes, since the Sun and Moon intersect the 
horizon at a very shallow angle. For the same reason, at high latitudes, 
the effects of observer height and local topography are magnified and 
can substantially change the times of the phenomena actually observed, 
or even whether the phenomena are observed to occur at all.

Twilight. There are three kinds of twilight defined: civil twilight, 
nautical twilight, and astronomical twilight. For computational 
purposes, civil twilight begins before sunrise and ends after sunset 
when the geometric zenith distance of the center of the Sun is 96 
degrees - 6 degrees below a horizontal plane. The corresponding solar 
zenith distances for nautical and astronomical twilight are 102 and 108 
degrees, respectively. That is, at the dark limit of nautical twilight, 
the center of the Sun is geometrically 12 degrees below a horizontal 
plane; and at the dark limit of astronomical twilight, the center of the 
Sun is geometrically 18 degrees below a horizontal plane.

This information is derived from the Explanatory Supplement to the 
Astronomical Almanac 
<http://aa.usno.navy.mil/publications/docs/related.html#expsup>, ed. P. 
K. Seidelmann (1992), pp 482ff.



Bernard Cleyet wrote:

> "I also notice that tables of apparent moonrise depend steeply upon
> refraction near the horizon *, a notoriously variable quantity."
>
> Good point, I had forgotten.  However, I suspect the table, whose URL ** I forgot to include, is derived from orbital formulae and ignores refraction, etc.  I suspected the variation is due to eccentricities in the elliptical orbits, but anything else? e.g. precession; way too small an effect and periods too long?
>
>
>
> * also since the moon subtends v. ~ 1/2 deg, and "moves" ~ 14 deg/hour, 
> it takes v.~ > two minutes to rise.  What's the definition of rise?
> ** 
> http://aa.usno.navy.mil/data/docs/RS_OneYear.html
>
>
> bc, will send to requesters a plot (JPEG) of this years first 65 rises.
>
> Brian Whatcott wrote:
>
>  
>
> > At 06:23 PM 9/1/2007, you wrote:
> >
> >
> >    
> >
> > > A friend wished to program his rotary table, so he could photo' the moon
> > > over time w/ its position in the focal plane constant and supplied me w/
> > > the Navy's moon rise table.  He wondered about the variation.  I do
> > > also.  I plotted the cumulative moon rise time and the differences.  It
> > > has a 3%  variation (+/- from the mean).  The variation has two periods
> > > * one about 27 days (not surprising), and another of about ten days w/
> > > about one third the amplitude.
> > >
> > >
> > >
> > > * very obvious w/o FFT'ing the data.
> > >
> > > Explanation please.
> > >
> > >
> > > bc,  too lazy to wiki.
> > >   
> > >
> > >      
> > Without searching the available resources or even examining the basis
> > of one of the excellent moon phase visualization programs, I first want
> > to suppose that it is not necessary that particular motions (like a
> > pendulum's instantaneous amplitude, for example) follow a sinusoidal path.
> >
> > The consequence of a Fourier analysis of such a physical cycle is to
> > show odd harmonics for phase-symmetrical differences.
> > I also notice that tables of apparent moonrise depend steeply upon
> > refraction near the horizon, a notoriously variable quantity.
> >
> >
> >
> > Brian (Mr. Indolence) Whatcott    Altus OK   
> >
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