NavList:

Dear Robin,

Yes I remember quite well our former exchanges quoted in your last post.

There are various ways of computing the Parallax in Azimuth on an Ellipsoid.

As I had earlier mentioned it, I am computing it using 3D Vectors.

With the definition given here : Z topo =  Z geoc + Parallax in Azimuth

- (1) Compute 3D Vectors Moon Geocentric Azimuth Z geoc

- (2) Compute 3D Vectors Moon Topocentric Azimuth Z topo

- (3) Compute Parallax in Azimuth Par(Z) through the formula : Par(Z) = Z topo - Z geoc 

To the best of my knowledge only 3D Vectors computations (or equivalent 3D computations) can easily and accurately solve all cases of Par(Z), including all the extreme cases such as the one mentioned here.

While I am aware that the following example has no practical consequence (and is rather a "mathematical curiosity") - since in particular who is going to shoot the Moon overhead with a Sextant with all the well-known difficulties to put it onto the horizon from such a height - as an exercise, compute the Moon Par(AZ) from the following data:

Moon HP = 1°00'000

Moon GHA = 0°.00'000

Moon DEC = 24°59'900

Observer at N25°00'000 W000°'00.0000

You should get Moon Z topo = 360°00000

and 

Moon Z geoc = 180°00000

Hence Par(Z) = 180°00000

I have not found yet any one single algebric formula adequately solving all cases including such "extreme case" while on the other hand subtracting Azimuths obtained from 3D Vectors is immediate.

Thanks you for your Kind Attention, and

Best Regards

⚓  Kermit - antoine.m.couette[at]club-internet.fr ✈