Roger Bailey wrote:
How wonderful it is to see proficiency itself at work!
Thank you Roger. And... I wish I had that 7-dollar calculator :-)
- fernando
> At 10:53 AM 12/27/99 -0200, Fernando Cabral wrote:
> >
> >
> >Given the longitude, latitude and altitude of two points, plus
> >the day of the year, is there an easy and straightforward
> >way to find which one will see the sun first?
> >
> >Let's say we have place "X" at 8 S 34 W altitude 200m and
> >place Y at 22S 42 W, altitude 1000m.
> >
> >It is winter Solstice in the North Hemisphere.
> >
> >Supposing there is a sundial at each place, which one
> >will mark the hour first?
> >
> >- fernando
> >
> >Hi Fernando,
>
> Welcome back from your desert trek to ask my favourite question, the time
> of sunrise. The mathematical solution involves solving the Sunrise Equation
> "Cos t = - Tan D x Tan L. This formula is mathematically exact for the time
> (t) when the zenith distance of the center of the sun is 90 degrees. To get
> to the time of sunrise, there are corrections for refraction, dip and
> semidiameter. More on this later.
>
> For your examples, the solution for the time angle t from local noon is
> straight forward. This gives me a chance to use the new scientific
> calculator I got for Christmas that does trig and decimal degree to DMS
> conversions.
>
> 1. L=8, D=-23.5, Cos t =-Tan 8 x Tan -23.5 so t = 86.496 degrees or 5:45:59
> 2. L=22, D=-23.5, Cos t=-Tan22 x Tan -23.5 so t = 79.882 degrees or 5:19:32
>
> These times are local solar times. To put them on a consistent basis,
> convert to UT by adding the longitude correction (LC). Longitude as an
> angle in degrees /15 = longitude as time is hours.
>
> 1. Long = 34 W so LC = 2:16 and sunrise UT is 5:45:59 + 2:16 = 8:01:59.
> 2. Long = 42 W so LC = 2:48 and sunrise UT is 5:19:32 + 2:48 = 8:07:32.
>
> This calculation does not consider the corrections required for real
> sunrise, the instant of the first ray of sunlight above the horizon. For
> this you have to consider =semidiameter ~16', refraction ~32' and dip due
> to the height of the eye above the horizon (5 ft ~ 2'). Altitude can come
> into the correction a couple of ways depending on the horizon you are
> using. Generally it is the height of eye over a common horizon like sea
> level. In this case the correction is .97 x square root of height in feet.
> Altitude also affects the refraction correction as does barometric pressure
> and temperature. Most published calculations are based on a total
> correction of the altitude of -50' or a zenith distance of 90:50. The
> longer solution of the navigation triangle must now be used.
>
> Sin Altitude = Sin L x D + Cos L x D x Cos t.
>
> Rearranged this gives Cos t = (Sin (-50')- Sin L x Sin D)/ Cos L X Cos D
>
> Solving this using my new $7 calculator, the times are:
> for 8 S, 34 W, 5:42:18 local solar (7:58:18 UT) and
> for 22 S, 42 W, 5:15:32 local solar (8:03:32).
> As expected, these times are a few minutes earlier.
>
> For an explanation of the spherical trigonometry, see my previous posting
> at <http://dialist.webjump.com> one of the sites David Bell set up for
> storing attachments.
>
> Happy Solstice,
> Roger Bailey
> N 51 W 115
>
--
Fernando Cabral Padrao iX Sistemas Abertos
mailto:[EMAIL PROTECTED] http://www.pix.com.br
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