NavList:

   

Reply

My Dear Friend,




Thank you for your in depth study of the example of our upcoming Lunar covered 
in [NavList 11087]. Than you in particular also for mentioning the JPL 
"HORIZON" Server which I was just vaguely aware of before your post.

*******

First of all, I am very sorry for having given you trouble - which you sorted 
out quite well indeeed ! congratulations !!! - when using a TT-UT value 
different from the one you had access to. This 66.7 second value was simply 
the one predicted by the Nasa document referenced in [NavList 11087]. I was 
just a bit lazy ...


Nonetheless, since it is extremely easy for me to recompute this example with 
a more correct value of 66.06 seconds - any TT-UT value in fact- here are the 
results accordingly updated.


23 Dec 2009   Height of Eye = 17 ' T = 59d F , P = 29.92" HG Estimated UT / 
Position :  16h58m53.0s / N3707.1W01253.7 - All observations assumed to occur 
at the same time - Distance SUN-MOON = 77d53'7 , SUNL = 5d50'1 , MOONL = 
50d05'0 . All sextant measures are corrected for Instrument error (and only 
instrument error), i.e. all other corrections (dip, refraction, SD, Parallax 
... ) need to be performed from the "raw data" hereabove.


UPDATED VALUES :

o   With delta-T = 66.06 seconds (current best value for Dec 23, 2009) :

    � Lunar Distance UT = 17h00m01.38s - i.e. TT = 17h01m07.44s (unchanged 
value as expected) - hence UT error = -1m08.38s, cleared distance = 
78d34.00', and
    � We also get the following position at time of Lunar Distance :
N3659.9W01300.5 (result of 2 body fix), and
    � Crosscheck with Frank's on-line computer (you need to enter both 
heights) : Error in Lunar : -0.1', approximate Error in Longitude 03.9',      
 cleared distance = 78d33.9'

*******

NOW, back to the results first published with TT-UT=66.7 seconds.


You also took great care in checking the results I published. So on my side, I 
did some further research on my own to try explaining the minor discrepancy 
between the published results and the ones you reworked through "HORIZONS" as 
well as your own software.

First of all, I verified that the planetary coordinates I am using are not 
"too far off". Comparison was made here with INPOP06 from 
http://www.imcce.fr/page.php?nav=fr/ephemerides/formulaire/form_ephepos.php. 
I used TT=17h01m07.4s which is the value I was initially referring to.

I am using the following values :

SUN RA = 18h08m44.2064s, Dec=-23d25'24.5165", Dist=.9836273 UA, yielding SD=0.271005d and HP=8.9405"

Comparison with INPOP06 (extremely close from DE406) shows the following errors in absolute values :

For the SUN :

Coordinates error < 0.08", SD error < 0.005" and HP error < 0.0001"

For the MOON :

Coordinates error < 1.7", SD error < 0.1" and HP error < 0.35"

As a result, the Approximate Ephemeris I am computing are well under the NAL tolerances.

I am also noticing that, compared to HORIZON, I am using exactly the same 
unrefracted augmented SD's as the ones which you quoted : MOON .25177d 
(HORIZON : .2517d ) and for the SUN .2710 ( HORIZON : .2710)


The difference in corrected altitudes for the MOON is negligible (1.2") and 
the difference in corrected altitudes for the SUN, although more important 
(3.6") is not significant since the SUN altitude is only 5.5d and - according 
to various sources - refractions are not reliably known to such accuracies 
below 8d or 10d.

Given the geometry - namely the arrival/departure orientations - of the 
shortest great circle line joining up both apparent limbs, the combined 
effects of both the difference in the SUN and Moon altitudes (3.6" and 1.2") 
and the Moon overall inaccuracy (1.9") seem to almost fully explain the 4.8" 
remaining difference with your own "refined" results taking in account 
"refracted" semi-diameters.

Just one question here : I am not quite familiar with the definition of 
"refracted" semi-diameters. They imply some kind of "Center". From which such 
"center" are they reckoned ? Obviously, given the irregular apparent shape of 
both bodies - and especially the Sun who is quite low with such a distorted 
limb - refracted semi-diameters will vary according to the directions in 
which they are measured. This is a bit intricate to compute, but this can be 
accurately done with to-day computing power.

However, and from the information you give, I am under the impression that 
your definition of the "refracted center" might be the apparent point which 
is the image of the non-refracted center. I would then guess that you compute 
the great circle distance between both refracted centers and then substract 
both refracted semidiameters measured alongside the relevant "departure and 
arrival" directions reckoned alongside this great circle. So far so good, 
BUT, there seems to be no reason why the great circle joining up both 
"refracted centers" - as defined hereabove - would be exactly the shortest 
distance between both apparent limbs. When both bodies are high in the sky 
and therefore almost undistorted, no problem at all - the line joining the 
refracted centers is extremely close from the shortest line joining up both 
limbs - , but when either body or both are quite low on the horizon, are both 
such lines still "fully merged" / "exactly the same ones" ? Is it a safe and 
"mathematically correct" assumption to keep considering that they are still 
"fully merged", and if so, to which accuracy level ?


That you for your Kind Attention, and


Best Regards


Antoine


Antoine M. Cou�tte

-- 
NavList message boards: www.navlist.net
Or post by email to: NavList@navlist.net
To , email NavList+@navlist.net

   

Reply