Re: Online calculators for position angle

In article <436BDEAE.6010203@xxxxxxxxxxxx>,
Bill Owen <wmo@xxxxxxxxxxxx> wrote:
>canopus56 wrote:
>> Mark Gingrich wrote:
>>
>>>William Kahan['s] original solution to this very problem [of small angle
>>>angular distances, not position angle] -- a solution he claims is both
>>>accurate for *any* angular separation and efficient:
>>> http://www.cs.berkeley.edu/~wkahan/Math128/angle.pdf
>>
>>
>> That's an interesting implementation - convert the two positions to the
>> X,Y,Z coordinates on a unity sphere and then use the 3-D Pythagorean
>> formula. Meeus's small angluar distance formula is basically the
>> same, except he uses the 2-D Pythagorean formula.
>
>Cartesian coordinates are definitely the way to go, especially when you
>then use rotation matrices to transform between coordinate systems.
>Just figure out the sequence of rotations you need in order to put the z
>axis along your pole of interest (it's the primary star for the position
>angle and separation problem we've been discussing), and then you can
>use asin(z) [or, better, atan2(z, sqrt(x^2+y^2)] to get the latitude
>kind of angle and atan2(y,x) to get the longitude kind of angle. Or,
>acos(z) to get the polar angle.
>
>Incidentally, the "standard American" way of measuring azimuth CCW from
>north implies a *left-handed* coordinate system, with x north, y EAST,
>and z up.

I don't thin that standard is US specific -- don't most countries use
that standard?

Anyway, if you instead put x east, y north, and z up, you'll get a normally
oriented right-handed coordinate system. And that's an argument to
favour east positive longitudes rather than the older astronomical
standard of west positive longitudes.


>-- Bill


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