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Reporting progress (or the lack of it) as promised.
Firstly, thanks guys for the various references to websites that describe astro formulae. However, so far I haven't been able to find a solution to my problem there.
The following values were measured for the center line of an imaging frame oriented along lines of equal Right Ascension and Declination and positioned at various latitudes in declination :
Latitude in Declination : Span of imaging frame in Right Ascension
0º : 30 seconds (= 0.008333... hours)
30º : 34 seconds (= 0.009444... hours)
60º : I minute (= 0.01666... hours)
80º : 2 minutes 50 seconds (= 0.047222... hours)
85º : 5 minutes 40 seconds (= 0.09444... hours)
89º : 26 minutes (= 0.4333... hours)
90º : 12 hours
These measurements are estimated by reference to my sky atlas but they should be sufficiently accurate for use in proving the validity of a formula.
The pattern of the change curve is clear. From 0º through the lower and middle latitudes the curve's rise accelerates but only very slowly . Only when latitudes above 85º are reached does the curve start to skyrocket dramatically until it tops out at 90º.
Dave - Using your formula “NewSpan := 2 * atan(tan(EquatorialSpan/2)/cos(Declination))” in a speadsheet I get the following results for an entered EquatorialSpan of 30 seconds (i.e. 0.008333 hours) :
Latitude in Declination : Formula result (rounded to 3 decimal places)
0º : 0.008
30º : 0.054
60º : - 0.009
80º : - 0.076
85º : - 0.009
89º : 0.016
90º : - 0.019
There seem to be both positive and negative results. I realise that atan, tan and cos work with radians but I don't quite see how I can relate the formula's results to the required output values.
Trent – assuming that the phrase “15cos(Dec)“ is to be used as NewSpan = EquatorialSpan x 15 x cos(Dec) I get the following results :
Latitude in Declination : Formula result (rounded to 3 decimal places)
0º : 0.125
30º : 0.019
60º : - 0.119
80º : - 0.014
85º : - 0.123
89º : 0.064
90º : - 0.056
Again there are both positive and negative results. And I don't see how I can relate them to the required output values.
I'm not too sure where to go from here.
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