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Referring to the vectors to the Sun center and the limb, after
transformation to a horizontal coordinate system, I wrote

> In spherical (lambda,
> phi) form, these are (0°, 20°) and (.283780°, 19.999774°).

> Apply refraction to the altitudes. At 1013.25 mb and 15 C, refraction is
> .044138 at center of Sun. Refracted center altitude is 20.044138°. Limb
> refraction is .044139° and refracted altitude 20.043913°.

A shortcut is possible because the vector to the body center will always
have lambda exactly zero and phi equal to its refracted altitude. So
it's simple to create that vector directly, instead of starting with a
vector to the nadir.

However, the algorithm is easier to understand if the center and limb
vectors are created and transformed in parallel as I did in my first
message. That's how my implementation is written. Unless speed or size
of the executable is an issue, the simple, obvious algorithm is better
than the tricky, "efficient" one - especially if you're the one who has
to maintain the code.

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