NavList:

   

Reply

I spoke too hastily about my error in alternate renderings of
the spherical law of cosines formula.

Originally I had said that

cos(c) = sin(a)*sin(b) + cos(a)*cos(b)*cos(ab)

was an alternate form, and then Bill Arden pointed out that for
use with Hc it should have read

sin(Hc) = sin(a)*sin(b) + cos(a)*cos(b)*cos(ab)

the difference being the left hand side of the equation.

However, I went back and found support in Smart's book for the
form that I had written, i.e.,

cos(c) = sin(a)*sin(b) + cos(a)*cos(b)*cos(ab)

in determining the length of twilight and other such calculations.

In thinking about things I realized that both versions are
right, but it simply is a matter of origin.  Are the angles
measured down from the pole (co-latitudes and such) or are
they measured from the equator up (latitudes)?
They are equivalent.

The mental picture that I work from is the canonical version,

cos(c) = cos(a)*cos(b) + sin(a)*sin(b)*cos(ab)

and then I don't get into problems, because that is the one
that I learned from.

So we were both right.

Dan

   

Reply