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    Capella - Betelgeuse - Canopus
    From: Antoine Couëtte
    Date: 2016 Aug 4, 03:15 -0700

    CAPELLA BETELGEUSE - CANOPUS vs. CANOPUS - ACHERNAR - FOMALHAUT and also VEGA and ACRUX.

    Aug 04th, 2016

    Hello to all,

    In my recent Skywatcher Quizz post ( http://fer3.com/arc/m2.aspx/Skywatcher-Quizz-Couëtte-jul-2016-g35938) I wrote : " (10) To-morrow morning, I will admire the magnificent unique and only 1st Magnitude star line-up : CANOPUS - ACHERNAR - FOMALHAUT  from East to West about one hour before Sun rise ".

    Well ... I was not entirely right then. You will learn why hereafter …

    *******

    This morning when flying my A343 towards an easterly direction to land at Darwin (again !) in the last part of the night, and while we had to twist our necks to admire from the cockpit right windows our well known and now familiar CANOPUS - ACHERNAR - FOMALHAUT alignment (with this latter star being our neck twisting one) 

    … I was amazed to "discover" a second remarkable 1st Magnitude Star alignment just in front of us - just over the horizon and surrounding the Darwin City lights glowing against a dark night contrast - as follows:

    On AUG 04th, 2016 by 18:50 UT, from a position around 100 NM West of Darwin, N.T. Australia (we were flying towards the East), and at FL140 I could see from left to right in our front windows CAPELLA BETELGEUSE - CANOPUS *** above the horizon at respective heights not exceeding 20 degrees.

    This one is definitely a splendid alignment of bright Celestial Navigational Stars too.

    *******

    Let us then take the opportunity to crunch a few numbers in the following drill:

    For each of the "CANOPUS - ACHERNAR - FOMALHAUT" and "CAPELLA - BETELGEUSE - CANOPUS" alignments:

    1 - Compute the angular separation between its extreme stars (i.e. CANOPUS - FOMALHAUT and CAPELLA - CANOPUS), and compare it to the sum of the angular separations when proceeding through the intermediate star (e.g. the sum of the angular separations between CAPELLA - BETELGEUSE and BETELGEUSE - CANOPUS).

    The comparisons here-above already give 2 interesting results:

    1.1 - Comparing the 2 segments of each same alignment enables to check how well they equally visually “balance” each other, with the best results being visually obtained when the distances of each segment are [nearly] equal.

    I am under the visual impression that the CAPELLA - BETELGEUSE angular separation is almost the same one as the BETELGEUSE - CANOPUS angular separation. This does not seem to be so much the case for the other "CANOPUS - ACHERNAR - FOMALHAUT" alignment. True ??? Wrong ???

    1.2 - Comparing the direct angular distances between the extreme stars (e.g. CANOPUS - FOMALHAUT) with the sum of the 2 intermediate segments gives a rough approximation of the “Quality” of the alignment itself. The closer they are, the better the alignment.

    2 - Let us then use a different method to estimate how well the stars of each alignment are lined up together.

    Compute the angular minimum separation between each middle-star (ACHERNAR and BETELGEUSE in our both examples) and the great circle joining the extreme stars (respectively CANOPUS - FOMALHAUT and CAPELLA - CANOPUS here). The smaller this minimum separation, the better their overall alignment.

    Again, I am under the visual impression that CAPELLA - BETELGEUSE - CANOPUS are better aligned in this respect thanCANOPUS - ACHERNAR - FOMALHAUT, i.e. that the CAPELLA - CANOPUS great circle comes closer from BETELGEUSE than the CANOPUS - FOMALHAUTgreat circle does from ACHERNARTrue ??? Wrong ???

    We should notice that this second tool in part 2 used to rate the quality of the alignments is much better than the first tool in part 1. It is exactly like rating very small angles through sines instead of cosines. Sines perform much better under such cases.

    3 - From the above we can attempt defining a First Magnitude 3 Star alignment as being an Alignment of 3 First Magnitude Stars [almost] equally spaced and [almost] on the same great circle and visible simultaneously from one same point on the Earth Surface. I also wish to add that such stars should clearly single out of their environment. In other words: the more isolated such bright stars are, the more remarkable and prestigious their alignment. So an alignment including one of the bright stars of [/ close to] Lady Southern Cross would be less remarkable in this respect.

    4 - Given the definition here-above and in addition to the 2 previously mentioned ones, are there ANY OTHER first Magnitude 3 Star alignment in the heavenly skies as seen from our Planet Earth in the Solar System?

    5 - There is also a very long - and rather excellent - First Magnitude 5 (maybe 6?) Star alignment including VEGA and ACRUX. But to the best of my memories it is not entirely visible from any point on Earth. What is this alignment?

    6 - Just for our number crunchers addicts:

    From the ICAO en-route fix “SIDER” (not Cider alas !!!) at position S 12°48’8 E129°35’8 which we checked at FL140 on Aug 04th, 2016 at 18h58m53,2s UTC we overflew a fishing boat. At what Heights and Azimuths could her skipper then see all five stars, i.e. from left to right: CAPELLABETELGEUSECANOPUSACHERNAR and FOMALHAUT ? You may or may not include [standard] Refraction as you wish.

    Thanks in advance for publishing your replies.

    Important noteFor 1 and 2 no need here to compute the effects of refraction. The Stars coordinates can be chosen from a number of data bases (current or older contemporaryAlmanacs, or even 2000.0 coordinates) since the final results involving only angular separations are subject to essentially the stars proper motions which are not significant when using our ordinary eyes vision.

    *** Well, I might better say now: CAPELLA α ORIONIS :-) - CANOPUS !

    Kermit

    Last note: Some of you may have noticed that I am using day-to-day life experiences to relay them to your Kind Attention and Sagacity.

    Exactly like Jeremy did not so long ago …
    Where are you Jeremy? No more Lunars? No more real world CelNav problems for us to solve?

    Well ... I am assuming that - as a Big Merchantman Skipper now - you no longer have time for all these examples of yours which enchanted me then!            Ahoy, Mate!

       
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