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In addition and conclusion to numerous recent contributions among which :

(1) - Geoff Hitchcox indicated :

Refracted 1st contact UT(rfc) = 15:36:08.0 and unrefracted 1st contact UT(ufc) = 15:36:11.5, difference of 3.5s

Refracted last contact UT(rlc) = 18:51:10.5 and unrefracted last contact UT(ulc) = 18:51:08.5, difference of -2.0s

(2) - Paul Hirose first replied :

(2.1) - I don't think [refraction] makes a difference to the contact times.

(2.2) - Paul went further here, giving a formula to accurately compute the contraction effect on "slant distances", i.e. non-horizontal ones.

(3) - After questioning Geoff's results in (1), Kermit fully agreed with Paul's conclusion given in 2.2 hereabove :

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.

(4) - Then Geoff published the details of his initial "last contact" JPL Horizon example summarized in (1) here-above.

(5) - To which both Kermit and Chuck Varney immediately noticed that the JPL Horizon Sun and Moon diameters remain unchanged, whether refracted or not.

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(4) - Explanation and quantification of the JPL Horizon Software error

There is definitely something wrong with the JPL Horizon software results because we know that refraction significantly affects not only horizontal and vertical Sun and Moon Diameters but also affects them alongside any slant/oblique line.

Starting from this observation, I am hereafter explaining in detail the errors of the JPL Horizon results published in (1) here-above.

First of all, we need to accurately compute the contraction of the Sun-Moon Centers alongside their respective oblique/slant lines at first and last contacts. Many ways are available here, and I resorted to the easiest one for me in this case : simulation.

(4.1) - First contact

At UT(rfc) the refracted Centers distance is 31.23303' , while the unrefracted one is 31.25199', which makes a difference of 1.14".

In its computation of UT(ufc) JPL Horizon [erroneously] keeps using the refracted SD's values instead of their unrefracted ones. This systematic error - extremely close from of 1.14" - is covered here at a closure rate of 0.34"/sec. It therefore needs 3.4 seconds of time to be covered. Since the Center distances are decreasing, we must conclude that the actual first unrefracted contact occurred 3.4 seconds earlier than the JPL Horizon unrefracted first contact result. Hence we must subtract 3.4 seconds to the JPL Horizon UT(ufc) result : 15:36:11.5 - 3.4 = 15:36:08.1 , i.e. we are recovering exactly the JPL Horizon result for UT(rfc).

(4.2) - Last contact

At UT(rlc) the refracted Centers distance is 31.28216' , while the unrefracted one is 31.29273', which makes a difference of 0.63".

In its computation of UT(ulc) JPL Horizon [erroneously] keeps using the refracted SD's values instead of their unrefracted ones. This systematic error - extremely close from 0.63" - is covered here at a closure rate of 0.31"/sec. It therefore needs 2.0 seconds of time to be covered. Since Center distances are increasing, we must conclude that the actual last unrefracted contact happened 2.0 seconds later than the JPL Horizon unrefracted last contact result. Hence we must add 2.0 seconds to the JPL Horizon UT(ulc) result : 18:51:08.5 + 2.0 = 18:51:08.5, i.e. we are again recovering exactly the JPL Horizon result for UT(rlc).

(5) - LESSONS LEARNT, CONCLUSION

This conclusively indicates that there is a significant bug - i.e. significant to their number of digits published for Sun and Moon Diameters - in the JPL Horizon Software. Refracted Sun and Moon Diameters values are not equal to their unrefracted counterparts as incorrectly showing from the current JPL Horizon Software results.

And finally, with the exception of the differential refraction effect described in part (2) of this post and assuming Lady Moon to be a perfect sphere, Refraction does NOT modify the times of 1st and last contact in a Sun eclipse.

Kermit