BalloonTrack the balloon tracking software I plan to use during our
flights includes the ability to generate Alt/Az to the balloon from
up to four locations. The telescope at the Centennial Observatory
requires positions in the form of hour angle and declination. In
order to use these positions to aim the telescope, they must be
converted.
I've found a pair of equations to convert Alt/Az to HA/Dec and written
a program for my HP15C calculator. First the equations...
- sin(Az) * cos(Alt)
HA = atan( ------------------------------------------------------ )
cos(Lat) * sin(Alt) - sin(Lat) * cos(Az) * cos(Alt)
Dec = asin( sin(Lat) * sin(Alt) + cos(Lat) * cos(Alt) * cos(Az))
Now the program...
001 - 42,21,11 - Lbl A # Label A jumps to entry routine
002 - 44 1 - Sto 1 # Store existing Alt in R1
003 - 31 - R/S # Wait for Az
004 - 44 2 - Sto 2 # Store Az in R2
005 - 42,21,12 - Lbl B # Label B jumps to Calc HA
006 - 45 1 - Rcl 1 # Compute HA
007 - 24 - Cos
008 - 45 2 - Rcl 2
009 - 23 - Sin
010 - 20 - X # Multiply
011 - 16 - CHS
012 - 36 - Enter
013 - 45 0 - Rcl 0
014 - 24 - Cos
015 - 45 1 - Rcl 1
016 - 23 - Sin
017 - 20 - X
018 - 36 - Enter
019 - 45 0 - Rcl 0
020 - 23 - Sin
021 - 45 1 - Rcl 1
022 - 24 - Cos
023 - 20 - X
024 - 45 2 - Rcl 2
025 - 24 - Cos
026 - 20 - X
027 - 30 - - # Minus
028 - 10 - / # Divide
029 - 43 25 - Atan
030 - 31 - R/S
031 - 42,21,13 - Lbl C # Label C jumps to Calc Dec
032 - 45 0 - Rcl 0
033 - 23 - Sin
034 - 45 1 - Rcl 1
035 - 23 - Sin
036 - 20 - X
037 - 36 - Enter
038 - 45 0 - Rcl 0
039 - 24 - Cos
040 - 45 1 - Rcl 1
041 - 24 - Cos
042 - 20 - X
043 - 45 2 - Rcl 2
044 - 24 - Cos
045 - 20 - X
046 - 40 - +
047 - 43 23 - Asin
048 - 31 - R/S
To execute the program:
Enter the latitude into R0. This only needs to be done once, unless
the value changes.
Enter the Altitude, Press f-A
Enter the Azmuth, Press R/S
Calculator runs, then displays HA in degrees.
Press R/S, calculator runs then displays Dec.
Pressing f - B runs the HA calculation on the values stored in memory.
Pressing f - C runs the Dec calculation.
You can enter DDD.mmss then press g - ->H (2) to convert from DDD.mmss
to DDD.hhhhh, if that is the format you have data available in.
Test data:
Lat - 43.07833
Alt - 59 05 10
Az - 113 18 29
Results:
HA - 336.683
Dec - 19.1824
NOTE: HA initally comes out negative, Add 360 to normalize.
Equations and test case from:
http://idlastro.gsfc.nasa.gov/ftp/pro/astro/altaz2hadec.pro
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