Astronomical Visual Limiting Magnitude calculation

• Four bugs have been removed from Bogan's JavaScript program.
  Some of these bugs had major influence on the circumstances around heliacal events.
  Bogan reverted one error back in his web page (accessed on Sep. 11th, 2012 and Jan 28th, 2021):
  KA=KA*Math.pow((1-.32/Math.log(RH/100.0)),1.33)*(1+SL*Math.sin(RA)) should be KA=KA*Math.pow((1-.32/Math.log(RH/100.0)),1.33)*(1+0.33*SL*Math.sin(RA))
  This error can cause KA to become 0 (around December), and having such a low KA is not correct.
  I have informed him (Oct. 15th, 2016) about this erroneous reversion, no reaction yet (Jan. 2021).
  
• Instead of elongation one gives the azimuth compared to the Object
• Auto calculation of Topocentric altitude
  One can give a Goal Magnitude and in that case the object's topocentric altitude will be calculate in such a way that the Object becomes just visible.
  If this Goal Magnitude=NA, no change to object's topocentric altitude will be made.
• Extinction angle
  By inputting the Object(/star)'s magnitude in Goal Magnitude, and putting both Moon and Sun well below the horizon (say their topocentric altitudes at -45 degrees); the script calculates the Object's  topocentric altitude as its topocentric extinction angle.
  

If Goal Magnitude = 99:
The Visual Extinction Magnitude just visible with the unaided eye is calculated from conditions specified in the form below. This number depends on the location and phase of the Moon, the location of Sun, the humidity, your location and height as well as the Object's topocentric altitude.
If Goal Magnitude <> 99:
The Object's topocentric altitude when just visible with the unaided eye is calculated from conditions specified in the form below. This number depends on the location and phase of the Moon, the location of Sun, the humidity, your location and height as well as the Goal Magnitude (Magnitude of the Object). 

Try various input parameters to observe the effects of each variable. For more details see the reference sited above.

Intermediate results of astronomical extinction, sky brightness and air mass are presented in the tables at the bottom.