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The "Astronomical Almanac" has formulas for computing topocentric
position, including the effect of dinural parallax and dinural
aberration. The latter is caused by Earth's rotation giving the observer
a velocity with respect to the geocenter, and is only about .3" at most.

I have a free Windows positional astronomy DLL online which does these
things. There's also a C++ example which uses the DLL to compute
geocentric and topocentric positions of a star and the Moon.
http://home.earthlink.net/~s543t-24dst/sofajpl/lunardist.html

There's very little math in the main program. Basically, it just sets up
function calls to the DLL, where the real work is done. Almost all the
function calls in the sample program are documented here:
http://home.earthlink.net/~s543t-24dst/sofajpl/sofajpl_sup1.h.html

Because the algorithms are in the DLL, you have to study its source code
to understand how it works. All the source code is at the site, but it
may be easier to use formulas from a book, especially if you prefer to
use spherical trig. The DLL and sample program use spherical coordinates
only for input and output. Internally, the computatation uses vectors.

The basic process is to get the geocentric rectangular coordinates of
the body with respect to the true equator of date, i.e., RA and
declination converted to xyz. Get the observer coords in the same
system. Then do (body - observer) to get the relative position of the
body with respect to the observer.

For the observer coordinates, the key routine is called psh_cobsvec().
Inputs are latitude, longitude, height, and the properties of the
ellipsoid: equatorial radius and flattening. Outputs are the observer's
xyz coordinates. These are constant for a given observing position. But
to put those coords into the same system as the body, you must rotate
about the z axis by UT1 expressed as an angle. This is performed by
psh_cobspv(), which outputs the position and velocity of the observer in
vector form. These vectors are one of the inputs to psh_jplanet(), which
outputs the apparent position of the desired body. The interfaces of
these functions are explained on a web page at the site (the second link
above), but to see the implementations you have to go to the Downloads
section on the main page and get the second zip file. As I said, it may
be easier to just look in the Astronomical Almanac! (Sections B and K)

By the way, I'm rewriting the DLL for the Microsoft .NET Framework. The
present form is inconvenient because the documentation and function call
convention favors C or C++ programmers. In addition, the DLL isn't
object-oriented. E.g., there's no "vector" object so you can add two
vectors with the + operator.

With the new DLL, any .NET Framework language (such as Visual Basic,
C++, or C#) will have full access to a variety of positional astronomy
classes such as vectors, rotation matrices, Julian dates, and the like.
The user won't even be able to tell what languages were used to write
the DLL.

So far I've ported and tested the IAU SOFA library and JPL planetary
ephemerides, and created all the supporting classes. There's a lot more
to do, though.

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