A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2015 Nov 23, 22:36 -0800
Sam L., A couple of days ago, you wrote:
"One of the problems is I don't understand is this equation: cos(t) = -tan(Dec)·tan(Lat). In using the first example below my calculator gives the result of 73d 55'."
Well... apparently something went wrong! It may have been as simple as an ordinary typo, like entering 300 instead of 30. To remind us, that first example was for dec = 30° N, and lat = 40° N. Let's go through it key-by-key... Make sure your calculator is in "degrees" mode. And hit the "all clear" key to make sure there are no pending operations.
Now enter 30. Then press the 'tan' key.
At this point your calculator should be displaying 0.57735... Is that what you see? If not, stop. Figure out why, or tell us what you do see at this point.
Now press the multiply key: 'X'. Next enter 40. Then press the "tan" key again. At this point your calculator should display 0.839099... Now press equals: '=' to complete the multiplication. You should see 0.484454... Is that what you see? If not, stop and try again.
Next press the '+/-' key to change the size. The display shows -0.484454... You have worked out at this point the quantity on the
right-hand side of the equation: -tan(Dec)·tan(Lat).
The last step is to get the inverse-cosine of this value. On most calculators, you will press the 'shift' key and then 'cos'. You should now see 118.97... This is the angle 't' in degrees, and you can convert that to hours by dividing by 15. That's it -- the number of hours from transit to rise time or set time.