NavList:

A few more details about 2 of my recent posts

(1) - CONTRACTION OF SUN's and MOON SD's DUE TO REFRACTION

Lars, you earlier brought the subject of the Contraction of the SD's, to which I gave only a partial reply here,

with in particular the general formula :

dSD/SD = dcosh/cosh = -dh sinh/cosh = -dh tgh , or shorter :

(1.1) -  dSD/SD = -dh tgh ,

with dh being the refraction value in radians for a given height h.

Numerical application : for SD = 16.0000', h = 50° , dh = 0.8' = 23 E-5 radian , get dSD = -0.0044'  = - 0.264"

On the other hand, for h > about 10°, dh (again, "dh" is the refraction) in arcminutes almost equal to 1/tg h , or in other words :

for h > 10° , dh in radian almost equal to 0.00029 rad / tg h.

Substituting in (1.1) , we find that for h > 10°,  dSD/SD is almost equal to 0.00029 which has now become a [quasi-] constant relative value.

(1.1.1) - Check : ASTRONOMIE GÉNÉRALE, ASTRONOMIE SPHÉRIQUE ET ÉLÉMENTS DE MÉCANIQUE CÉLESTE par André DANJON, LIBRAIRIE SCIENTIFIQUE ET TECHNIQUE ALBERT BLANCHARD   2^ème Édition 1980 .

In Chapter paragraph 78 on page 156 André Danjon indicates that the Diameter contraction is almost constant and close to 3/10.000 : same value as above. Here he gives a Diameter contraction absolute value very close to 0.6" : same value again.

(1.1.2) - For conventional CelNav, [Semi-]Diameter contraction is totally irrelevant and most often skipped in Navigation Treaties. For ultra-precise work on Sun Eclipses, it may have to be considered.

(2) - SUN ECLIPSES : EFFECT OF REFRACTION ONTO THE TIMES OF FIRST AND LAST CONTACTS

Based upon his own JPL Horizon results, Geoff lately indicated that the times of refracted limbs first and last contacts can be [significantly] different from the times of their unrefracted counterparts.

Paul Hirose - thank you again Paul - you just worked on this exact Geoff's example (1st contact) and concluded that in your view [refraction does not make] a difference to the contact times.

Meanwhile I had had been questioning this quite strange numerical result published by Geoff : " If we keep assuming that the MOON is a PERFECT SPHERE ... Anybody with a solid explanation here ? "

Regarding refraction "behaving" differently on Sun and Moon, the only way I can think of is the differential refraction due to parallax.

Check the attachment, most probably already published on NavList earlier, but I could not retrieve it. Here it is again.

Back to our specific example on Oct 14th, 2023 at 15:36 , with the Moon Center height at 42.6° and the Moon Parallax 55.2' , and if both MOON and SUN were in the very same Azimuth, this specific differential refraction due to the parallax is 0.001" for the Moon and 3" E-6 for the Sun.

Hence a totally negligible effect so much smaller than the 1.2" difference earlier quoted.

So, unless an authoritative voice tells us the contrary, we probably should keep in mind that - with the exception of the differential refraction effect described above and assuming Lady Moon to be a perfect sphere - Refraction does NOT modify the times of 1st and last contact in a Sun eclipse.

Again, André Danjon - see (1.1.1) here-above same Chapter, same page and Paragraph 79 - gives a very detailed study of such differential refraction due to parallax. 

For the Moon, assuming HP = 1° this effect is only 1.2" at the horizon where it goes absolutely undetected - and undetectable - due to refraction uncertainties.

But for much closer bodies, e.g. the ISS at 400 km AGL, with HP = 70° , for h = 15° differential refraction due to parallax is 4.4" , or a for a very low altitude satellite at 200 km AGL with HP = 76°, for h = 15° differential refraction due to parallax is 8.2", a quite significant angle.

Well, to-day happens to be Oct 13th 2023. I think we are now all full ready to observe to-morrow's Eclipse.

I am going to navigate my flying carpet all the way to N28°00.0' - W090°00.0' and will stay hovering there at 17' ASL for all the duration of the eclipse.

See you there :-) !

Kermit