Quote:
Originally Posted by Vlaxie
I took a sun shot a few hours after the local noon and I applied the formula
(sin(Ho) - sin(Dec.) · sin(Lat.)) / (cos(Dec.) · cos(Lat.)) and I'm pretty sure I've input all the correct information, the latitude is correct, the declination taken from the almanac for the exact day and hour when I took the shot and the altitude angle as well but I'm not sure what to do with the resulting number (I did make sure to set the calculator to display the result in degrees). For reference, the number that I got at the end was 0.82, and the sun's GHA at the time of measurement is 59° 58.0'.
I know that my actual longitude is around 19° 4'E but how do I get to that number from what I calculated?
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Could you provide the latitude, declination and Ho (altitude) of the Sun? That would help me double check the calculation.
You left out the "cos(LHA)" part of the equation above, so I'm not sure if you took that into account. It means that you must find the arccosine of the result from what you did quote. Another way to write the equation (which might make more sense) is:
acos((sin(Ho) - sin(Dec.) · sin(Lat.)) / (cos(Dec.) · cos(Lat.))) = LHA
Also, one thing I forgot to mention is that, technically, the result you get is not necessarily the LHA proper. It is actually what is sometimes referred to as "t": the "meridian angle" of the Sun (or how many degrees away from the local meridian the Sun is, either east or west). If you took your sight after local noon, t = LHA. If you took your sight before local noon, 360° - t = LHA.
The difference between the LHA and GHA of the Sun is your longitude. If your actual longitude is indeed 19°04' E, then the Sun will be 19°04' farther
west at your location. If we add your longitude to the GHA of the Sun, we get: 59°58' + 19°04' = 79°02'. That is what the LHA of the Sun will be at your location. (Hint: when comparing GHA to LHA,
add longitude to GHA if east of Greenwich,
subtract if west.)
If we take the arccosine of 0.82, we get t = 34.9152... or 34°54.9'. Since you state that you took the sight
after local noon, t = LHA. This is clearly way off from the expected value of 79°02'. On the other hand, assuming you
did take the arccosine of the result, 0.82° = 0°49.2' ... also way off.
But, again, I would need all of the actual data to begin to track down exactly what went wrong. It could very well be that the sim does not have the Sun at the correct altitude for your location. Multiple people on this forum have come to the conclusion that SH does not correctly model the positions of the heavenly bodies. I do not play SH, so I cannot personally verify this.