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Updated information on the partial derivatives "∂" mentioned in my first contribution

(1) - IZMIR data : Direct computation results vs. differential computation from CAIRO data

(1.1) - IZMIR data direct computation results (N38°23'/E027°16'/UT=02h35m30s) (repeat)

Sun at -9.2° below the Horizon and : S 7.083/99.3  , M 7.934/98.6 ,  V 10.676/97.4

yielding :  SV 332.1° , SM 320.6° , and V-M +11.6°

(1.2) - IZMIR data obtained from CAIRO (N34°/E30°/UT=02h15m). (updated)

Partial derivatives at CAIRO now obtained through mid-point intervals (interval widths are 10° for Lat/Long and 20 min for UT), vs. right hand derivatives as earlier. Check enclosure for further details

∂SV/∂Lat= 9.8°/10°  and ∂SM/∂Lat= 15.1°/10°      hence: ∂Lat° =∂SV° and ∂Lat°= 0.7*∂SM° (see updated error budget)

∂SV/∂Lon=-2.5°/10° and  ∂SM/∂Lon= -6.5°/10°    hence: ∂Lon°= -4.0*∂SV° and ∂Lon°= 1.5*∂SM° (see error budget)

∂SV/∂UT=+1.6°/20 min and ∂SM/∂UT=-5.6°/20 min hence: ∂UT/∂SV=+12.5 min/° and ∂UTmin/∂SM°=-3.6 min/°

From CAIRO to IZMIR δLat=+4.3833°, δLon=+2.7333° (Longitudes negative to the East) and δUT= +20,5 min

Then from CAIRO to IZMIR : ΔSV= +5.9° and ΔSM= -0.30° . Hence the following results:

(2) - IZMIR data derived from CAIRO :

SV= 332.1° + 5.9° = 333.1° (vs. direct computation 332.1° ) and:

SM= 321.2 - 0.3°  = 320.9° (vs. direct computation 320.6°)

Once again, we verify in this example that the mid-point interval method has brough a quite significant improvement over previous [unpublished] results.

Reason for that : a careful review of the enclosure shows that at CAIRO there are significant differences between left and right derivatives on all 3 variables. First results and discussions were based on the use of the "right derivatives" only (lazy me having then gone for just one extra computation instead of the 2 extra computations now required for the mid-point method currently in use).

Having at hand much more reliable partial derivatives now enables the following updated discussion:

(3) - Updated error and uncertainties budget (related to "error bars") :

As per the last part of (1.2) herebaove, we are to use the SM trends which - as expected - enable significantly smaller uncertainties than the SV ones. As a final discussion:

Given the non-symetrical partial derivatives at CAIRO:

An error of 1° on SM approximately translates into an [almost unchanged] 1° uncertainty in Latitude,

An error of 1° on SM approximately translates into a [significantly improved] 1.5° uncertainty in Longitude,

An error of 1° on SM approximately translates into an uncertainty of 3.6 minutes in UT.

Kermit

antoine.m.couette@club-internet.fr