Techniques > Variations of Existing Techniques

Sunrise, Sunset and Solar Azimuth

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adi:
LOL I often hear old timer sailors talking like you do about nav. They do all come together eventually if you spend the time to be observant ;)
 

captain paranoia:
> Spherical Trigonometry,  was around before the Internet, by about two millennia {Ptolemy}

Yes, I know, but I like to work things out for myself; it's how I learn best, and I don't like to take things as gospel unless I understand how they've been derived.  This can cause difficulties if I can't figure it out...

And yes, I'm certainly thinking about rotating, inclined spheres orbiting, not in 2D.  The 2D picture is an attempt to capture this 3D thinking.

One difference is that I've been working in the solar ecliptic reference plane, looking at the changing angle (I've called it 'inclination') of the earth's axis of rotation relative to the sun, whereas, looking up the astronomical terms, they're based on an earth reference plane, so the celestial sphere is an earth equatorial coordinate system.

Having looked back at my earlier maths, I've understood why I'd decided this inclination is equal to atan(tan(obliquity).sin(orbit_angle)), and I think I was correct.  An additional approximation error is assuming a circular earth orbit, which it isn't.  That brings me to within 4 minutes of the daylight time given by the NOAA page.  Whilst that page doesn't give the mathematics used, it must have a mathematical model behind it that allows the computation of sun rise/set etc for any location and time.  And, hopefully, that model accommodates for all the approximations I've made in mine.

captain paranoia:
Lyle, your little tool looks interesting.  I can see some PostScript being written, if I can figure out the mathematics of the scale; my gut feel is that it shouldn't be linear.  Certainly, the length of the solar day doesn't vary linearly between the solstices; the rate of change is small at the solstices (there's a point of inflection as the sign changes), and maximum at the equinoxes, which is why winter seems to be drawing in very quickly at the moment.

What do you do for the months at the side?
Surely, these months must fall into the maximum end of the amplitude scale, because the sunrise position doesn't come to an abrupt stop in mid November...?

adi:
I am a simple grunt, I know what you guys are trying to say but I cant make head or tail of what your actually saying! Is it really that complicated? People were doing this stuff before modern mathematics. I am not knocking anyone's enthusiasm or knowledge but can we possibly have it in simple English? The reason I ask is because people come here to learn simple to understand  navigation skills. I for one am completely lost. Although everyone's hard work on this thread is very much appreciated and I am sure some people are reading this and understand what is being said but I am sure for many people are being switched off.


     

adi:
Are you trying to work out the time of sunrise/set or location of sunrise/set?

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