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Re: Sine curve to approximate declination
From: Trevor Kenchington
Date: 2004 May 19, 21:13 +0000
From: Trevor Kenchington
Date: 2004 May 19, 21:13 +0000
Frank Reed wrote: > A big part of this error results from the fact that the ecliptic only > looks like a sine curve. It's not a bad approximation, but the real > curve has "broader shoulders" than a sine curve. It's easy to see this > by imagining what the ecliptic would look like if the Earth's axis were > tilted, say, 80 degrees instead of 23.45. Frank, It may be easy for you to visualize that but I'm afraid I can't see it. I can visualize how things would be if the Earth's axis lay in the plane of the ecliptic (i.e. a 90 degree tilt), since that reduces to 2D geometry. But in that most extreme case, and assuming a perfectly circular orbit, I think declination would change linearly from solstice to equinox and vice versa -- meaning that the curve would have "narrower shoulders" than a sine curve. Can you explain how you see the "broader shoulders"? Or does the explanation lie in the departure from circularity of Earth's orbit? Trevor Kenchington -- Trevor J. Kenchington PhD Gadus@iStar.ca Gadus Associates, Office(902) 889-9250 R.R.#1, Musquodoboit Harbour, Fax (902) 889-9251 Nova Scotia B0J 2L0, CANADA Home (902) 889-3555 Science Serving the Fisheries http://home.istar.ca/~gadus