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The effect of refraction on semidiameter has been mentioned. William
Chauvenet ("Manual of Spherical and Practical Astronomy", 5th edition,
page 409) derives "corrections for the elliptical figure of the discs of
the moon and sun produced by refraction."

https://archive.org/details/manualofspherica01chauiala/page/408/mode/2up?view=theater

He says a sufficiently accurate correction is the vertical SD
contraction, multiplied by the squared cosine of position angle. (That
angle is zero toward the zenith.)

At the 90 and 270 position angles this gives zero contraction. For
lunars that's good enough. But Meeus ("Astronomical Algorithms") says,

"the horizontal diameter of the solar disc is slightly contracted by
reason of the refraction... Danjon writes that the apparent contraction
of the horizontal diameter of the Sun is practically independent of the
altitude and approximately 0.6″."

The following method can calculate refracted semidiameter at any
position angle. Begin with the azimuth and altitude of the Sun. For
simplicity, azimuth can always be 0. For altitude, I'll use 10°.

Now calculate az/alt of a second point which is 1) on the limb, and 2)
at the desired position angle (90° in this example). Two sides and their
included angle are known, so celestial sight formulas (such as the
Bygrave formulas) can solve the problem: exchange the pole and observer,
so "declination" is the complement of unrefracted SD (I'll use 89.733°),
"latitude" is altitude (10°), and "hour angle" is the 90° position angle.

The solution is az = 359.74614, alt = 9.99990. Az/alt of both points,
including refraction per the Bennett formula:

000.00000 10.08911 center
359.74614 10.08901 limb

Compute separation angle. Again, a sight reduction method can be
employed since separation angle is the complement of altitude. I get
separation 0.24993. Refraction has reduced horizontal SD 0.00007°
(0.25″), which is close to the 0.3″ from Danjon.

The page for my Lunar program describes a vector version of that
algorithm ("Tests: Sun Lunar with JPL Horizons").

http://sofajpl.com/lunar4_4

--
Paul Hirose
sofajpl.com

   

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