how to program a TI 89 (calculator) for navigation

Something practical to avoid spending too much time with calculations for navigation, especially when the sea is rough and when we have a heavy meal inside our stomach, ready to leave it, probably on the map to draw a new iland, or in the companion way : if we program a calculator before, we get more time instead of waste it inside the boat, it's less boring and the most of time we avoid some seasick problems.

on internet "l'almanach du marin breton" has published programs ready to be included in a TI83 calculator for the height line, the sun's height range, and capable arcs. For a TI89 those programs work very well, there are just one or two small things to do:

On the file, "E" symbol is not the exponential fonction. it's a kind of scientific abreviation : E^2=100, E^3=1000…And when we use it we don't write the "^"on the calculator's screen. In a program we always have to indicate every time the program's end “IF” by a “ENDIF” otherwise the calculator will score “syntax error” something like that. that's why on the line 2 of paragraph “celestial mechanics in the Julian calendar” the sentence does not end with “End” but “Endif”. in the program useful to get the sun's height range we have to add up “Endif” Missing for the program validity.

when we are looking about those programs, we are able to guess others like a meridian program, the orthodromic distance, orthodromic's angle, or a program able to give our distance from a seamark with a known height:

For the calculation of the solar declination, marin breton's program take care of the elliptic nature of earth motion around the sun (part: “celestial mechanics in the Julian calendar”) which gets involved in declination's evolution all the year, and begins from an accurate sun's point in the time. Nevertheless there is a simplified formula to get sun's declination which doesn't care about the elliptic shape of earth's motion but coniders it like a circle (in our reality it's almost a circle, its elliptic shape is very weak with an elliptic excentricity roughly equal to 0.017. a circle's excentricity is 0 to have a little idea). This formula, less accurate than the first one displayed at the beginning, is still efficient even useful and in the same time very simple!

Déclinaison=(23+26/60)*sin((360/365.256363)*(284+J))

This formula is a precious tool to make a little sun's declination program depending on the day, the month, the hour (for 2015 when we compare it with marin breton's program difference is not overtaking 1 degree around mid-October, for the rest it's pretty accurate) without having ephemeridis on board. A second program allows us to have a better result (because we consider the elliptic shape in that way) :

For those declination's formulas we use a sinus fonction because if we write year days and declination's values ina same coordonate system, we get a sinus shape. with a cosinus fonction instead it would be possible. for sinus fonction parameters, in fact how to cope with it to change its period, its range and its departure point it's quite simple : we will use this exemple : A*sin(B(x-H)). "A" parameter adjusts the range's fonction (maxi and mini value it can reach), "B" adjusts period because sinus fonction's period is equal to 360/B ( absolute value). "H" parameter adjusts the phase, For exemple the fonction y=sin x is an impair fonction with a symetry center which is o origin, so if x=0 then y=0. if now we have y=sin (x-3), then y=0 if x=3 so we will have shifted sinus fonction about 3 on the right on absciss line, we have phased it about 3 finally.