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Bill,

thanks very much for your thorough response. I'm really encouraged by all
this attention devoted to my sunrise/sunset calculation.

"I recall .... using..... binoculars to spot the moment of sunrise/sunset"

Readers be warned never to do this if you value your eyesight.

I like your idea of finding the GHA of the sun from its LHA and then using
the published values for the GHA of the sun at different times to avoid the
EoT.

If you want to work it out right down to the second of arc of where you are
and second of time then you must consult refraction tables and work your dip
out carefully. For this there is a formula making using of the square root,
but the one I'm thinking of is a rough approximation.

"Back on track, if you have a longitude, elevation (given as -0d 49!6 to -0d
49!8 for the center of the Sun) "

May I ask do you mean zenith distance by elevation?

"0d 49!6 to -0d
49!8"

What units are these in? I'm thinking you are referring to to semi-diameter,
but not sure.

CS




----- Original Message -----
From: "Bill" 
To: 
Sent: Thursday, June 18, 2009 11:32 AM
Subject: [NavList 8686] Re: Basics of computing sunrise/sunset


>
>>> I'm trying to solve the following sunrise/sunset astronomical triangle
>>> and
>>> am encountering unexpected pitfalls.
>
> When I am playing that game with myself just for the fun of it, I recall
> the
> counsel of the list when I first joined and wanted to establish an LOP
> using
> HO229 tables, and binoculars to spot the moment of sunrise/sunset.  The
> fly
> in the ointment ("problem" for non US of A readers) as counseled by the
> list
> gurus is that the actual refraction from the tables in the front of the
> Nautical Almanac (NA) can be *quite* different from the published values
> of
> -0d 49!6 to -0d 49!8 for the center of the Sun (even if corrected for
> temperature and barometric pressure) due to the amount of atmosphere the
> light passes through and other gremlins.
>
> To your quest, if longitude and latitude are known, the variables are
> declination and refraction.  Not too much we mortal layman can do about
> refraction unless living on a celestial body without atmosphere (in which
> case there are other problems to deal with, but the exact moment of
> sunrise
> may be quite important if Hollywood movies are to be believed). Therefore
> declination becomes the variable you can nail down.
>
> When I play (jump starting my brain in the AM by calculating sunset--and
> the
> moment the sun is due west--I hate mornings) I look in the NA for sunset
> on
> the daily page for my latitude, then correct for any difference in
> latitude
> using the "Table for Interpolating Sunrise, Moonrise, Etc." on page xxxii
> in
> the back of my NA.  That adjusted time is corrected for longitude before
> or
> after the 15d increments defining my time zone with the usual method (arc
> to
> time). Then I have a time within a couple of minutes (refraction ignored)
> for my known position. For calculated time I can interpolate a declination
> that is more than good enough for practical purposes.
>
> Now the fun begins. When doing sight reductions I use the sine formula for
> elevation of the body and the cosine formula for azimuth. As a sidebar, if
> I
> recall George H. has tangent formulas for azimuth--one if memory serves,
> that can derive azimuth without first establishing elevation of the body.
> Please see the archives for these.
>
> Back on track, if you have a longitude, elevation (given as -0d 49!6
> to -0d
> 49!8 for the center of the Sun) and declination you can flip the cosine
> formula normally used for determining azimuth when elevation has already
> been solved. This gives you the Local Hour Angle (LHA) of the body, and as
> I
> use it is a derivation of the classic time sight (as used by Sumner et al)
> and explained by Frank in the archives.
>
> Specifically:
>
> cosine LHA = (sin elevation - (sin lat * sin dec)) / (cos lat * cos dec)
> Hope I have that right--I have not posted in a long while.
>
> Combine the computed LHA with the longitude in the usual manner, and you
> have your Greenwich Hour Angle (GHA).
>
> Take the computed GHA and find the value just below it on the daily page
> for
> your date.  Subtract that tabular hour's  GHA value from your computed GHA
> and convert the difference from arc to time.  That time conversion plus
> the
> UT/GMT for the hour used is the UT of your sunset or sunrise.
>
> The above allows you to escape messy Equation of Time adjustments and
> interpolations for your local time.
>
> It may sound complicated. A few passes with a TI-30Xa (three memory banks)
> and I can knock it out in few minutes even with the NA interpolations.
> With
> the hourly rate of change of declination now (mid June) interpolating
> declination is pretty easy ;-)
>
> Bill B.
>
>
>
>
> >


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