NavList:

Any taker(s) here ?

Since a sleeping pilot is a working pilot - of course you need recharging your batteries now and then, including in the cockpit - further to last night frustration, and after some adequate sleep I decided to improve my research method.

Working from this previous enclosure I subsequently indicated that :

"for 17:45:00.0 ut, i.e. T=0:45:00.0 actual values for heights difference is 4.955' and "distance" between Azimuths is 3.684' while averaged values between 17:00:00.0 UT and 18:30:00.0 UT - i.e. between T = 0:00:00.0 and T = 1:30:00.0 show up as 8.170' and 6.354'.".

In orther words simply 1st order interpolating between end values at UT#1 = 17:00:00.0 UT (T#1 = 00:00:00.0) and UT#2 = 18:30:00.0 (T#2 = 01:30:00.0) is insufficient since at mid-interval (T = 0:45:00.0) we need a correction of -3.21' for Heights differences, -2.67' for Azimuth distance and 0.04' for Moon SD.

We can fully correct for that, at least for mid interval.

With T' = (2T/1.5 -1) if we correct :

- Height Differences by a variable quantity equal to -3.21' * (1 - T'**2) , 

- Azimuth distances by a variable quantity equal to -2.67' * (1 - T'**2), and

- Moon SD values by a variable quantity equal to + 0.04' * (1 - T'**2)

then we should get better results.

My previously published wrong results indicated " The Sun LL is covered by Lady Moon between 17:10:13.5 UT and 18:17:32.0 UT ".

And in fact, using corrected values as per the precepts hereabove, and from this updated quadratic approximation (vs. the initial linear interpolation) I am now deriving that the Sun LL is covered by the Moon between 17h07m09s and 18h21m26s.

This new determination is a definite improvement significantly closer from, let's say this time, the last results published by Geoff showing as :

QUOTE :

My numbers are now within 8 seconds (of time) of Lars. And within 4 seconds (of time) for Frank's Stellarium technique.

Using Moon Alt to squish Azimuth delta

2023-Oct-14 17:07:48 Sun LL is covered by the Moon
2023-Oct-14 18:20:40 Sun LL is covered by the Moon

Using SunLL Alt to squish Azimuth delta

2023-Oct-14 17:07:49 Sun LL is covered by the Moon
2023-Oct-14 18:20:40 Sun LL is covered by the Moon

UNQUOTE

Lessons learnt :

(1) - Quite instructive drill. Thanks again Frank, David, Lars, Paul and Geoff.

(2) - To the accuracy aimed at, assuming that relative heights differences and azimuth "distances" are linear functions of time between UT#1 = 17:00:00.0 UT (T#1 = 00:00:00.0) and UT#2 = 18:30:00.0 (T#2 = 01:30:00.0) is an incorrect assumption.

(3) - To the accuracy aimed at (+/- 4" actually) a quadratic approximation fares better but is still insufficient.

(4) - Lars, I am interested at you "research" method here ...

Best Regards to all,

Kermit

antoine.m.couette[at]club-internet.fr