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Sine curve to approximate declination
From: Dan Allen
Date: 2004 May 19, 13:09 -0700

```Here is my shot at it.

The sine function takes angles from 0 to 360 degrees.  In comparing this with
the sun's declination, we will take our zero point to be the spring / vernal
equinox, say March 20th.

The sine(0) is 0, which is what the sun's declination is on either equinox.

Now, as the sun's declination grows from 0 to 23.44 degrees by the summer
solstice (let's say June 20th), we have 92 days to stretch out the sine
function.  That happens to be very close to the 90 degrees we want to stretch
over this interval of zero to 90 degrees.  (If you want better accuracy, you
could have 365.2422 days in a year / 360 degrees for the full 0 to 360 range.)

So what date corresponds to the sine(10)?  Well, 10 * 92/90 days after the
starting point of March 20th, which would be about March 30th.  Take the
sine(10) which is .1736, multiply it by 23.44 (the maximum declination), and
you would get a declination approximation of 4.07 degrees.  The actual
declination is about 3.82 degrees.

I made a spreadsheet with 4 columns to get a look at this.  Do this in your

Column 1: angles every 5 degrees, from 0 to 360.
Column 2: the sin of column one (remember to convert to degrees by multiplying
column 1 cells by pi/180)
Column 3: column 2 times 23.44
Column 4: first cell set to the date 20 Mar 2004, then each succeeding cell to
be 5 * 365.2422/360 days later that the cell before it.

It is common for the declination estimates to be off by up to half of a
degree.

I too often make up a table of sun declinations and put in it my sextant box,
but I actually generate the table from the real declinations from a good sun
almanac, and I do not use this sine approxmiation, but if you were lost
without anything you could start with this and it would be better than
nothing.

Dan

-----Original Message-----
From: Navigation Mailing List
[mailto:NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM]On Behalf Of William Allen
Sent: Wednesday, May 19, 2004 9:39 AM
Subject: Re: HMS Bounty

Fred,

Could you please give a little more explanation on using the sine curve
to approximate declination?  Maybe a short example?

Thanks,
Bill Allen
Fred Hebard

```
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