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    Re: Correction to measuring Octant instrument error
    From: JC Sutherland
    Date: 2000 Sep 21, 6:43 PM

     I have just read George Huxtables reply to my first letter on this subject and I accept
    most of what he says. However I am still confident that the method can work.
    Taking calibration sights at the seaside is I think more prone to error, as well as the
    risk of getting sand in the works.
    The maximum angle available using the sun is (90+23.5)-LAT. It would be better to
    calibrate the octant over the whole range of its arc.
    The existence of Irradiation is an open question and my copy of Bowditch suggests  a
    value of about 1.2 min exists but says the magnitude depends on the individual observer.
    The avoidance of glare remains a problem.
    Refraction is a problem that is more difficult than first I assumed. It is not
    sufficient to find stars of the same altitude as George has reminded me. The problem is
    that the refraction works vertically from the horizon but the correction for it must be
    made in the direction between the two stars and this is across the sky. It is the same
    problem that besets Lunar distances measurements and clearing the observations was the
    thing that made them so difficult to our forbears.
    However I am reluctant to give up the method. With all those stars in the sky, their
    position known to the many decimal places it must be possible to use them. These two
    addition mathematical procedures now necessary are after all only button pushes on a
    calculator or a few lines of programing on a computer. It will not be necessary to
    measure the altitude of the two stars as a program can calculate these and the
    observations can still be done anywhere even without a horizon.
    With my suggested method, dealing with Refraction is probably the biggest problem
    remaining especially if the sight lines are over the land with its unpredictable
    temperature profile. however its effect can be reduced if the choice of stars is limited
    to those of high(ish)altitude.
    Measuring the horizontal angle between two stars can be quite easy if the octant can be
    clamped a photographic tripod say. The movement of the stars is quite slow and should be
    visible and alignable together in the field of view for long enough to make an accurate
    The calibration of precise optical instruments is always difficult for us amateurs and
    deserves attention in its own right. Bill should have no concerns about this discussion
    and I wish him success in what ever method he chooses. I am eager to hear how he gets
    Clive Sutherland wrote:
    > In my last message I made an error in the mathematics, a fundamental one I am
    > afraid.
    > Of course the Octant will measure the Great Circle distance between the two stars
    > and this is not the same as the dif SHA even when stars of the same DEC are chosen.
    > It is necessary to calculate the Great Circle Angle between the stars (a) and (b) on
    > the
    > list using
    > Gt Cir Angle =
    >             arccos[(sin(DEC a).sin(DEC b))+(cos(DEC a).cs(DECb).cos(difSHA)]
    > and this is the angle that is compared with the instrument measurement.
    > It does not change the need to find stars that have the same altitude as this is
    > necessary to avoid refraction problems, but it does mean that Stars with much larger
    > difference in their Declinations can be used. This angle is not now the same as the
    > 'book' value of course. The method is not changed in practice but I bit more work on
    > the maths is needed, sorry about that.
    > Regards
    > CLIVE
    > Clive Sutherland wrote:
    > > Perhaps could add a little fuel to this discussion on octant calibration.
    > > Of course the final proof of the instrument calibration will be the accuracy of
    > > sights taken of the Sun etc as George Huxtable suggests. However this is the end
    > > point not the starting point of the exercise. All the corrections that we know
    > > and love,  necessary for a Sun sight e.g. Height of eye, Dip, Refraction
    > > Semi-diam, Irradiation,  all dilute the confidence in the calibration so
    > > obtained, A Sun sight also requires the use of Filters to reduce the glare and
    > > any refraction in them would be inseparable from the calibration.
    > > In my humble opinion it would be better to use the octant to measure the
    > > horizontal separation between selected pairs of stars in the night sky rather
    > > than the altitude of the Sun in daytime. This measurement can be compared
    > > directly with the 'book' value.
    > > By referring to a Star catalogue, pairs of bright stars having similar
    > > Declinations (within a degree or so) should be chosen in advance and a list made
    > > of (a) Their 'difference in SHA' and (b) their 'mean SHA'.
    > > To verify the whole scale of the instrument, collect values of 'Dif SHA' over as
    > > wide a range of angles as the octant can measure.(see below)
    > > To use suitable stars from the list,  calculate the time of the Meridian Passage
    > > of their 'mean SHA ' for the day you are going to observe. That is to say
    > > calculate the time of GHA Aries when the
    > >                        'mean SHA' of the pair + 'GHA Aries' = 360 deg
    > > (About half of the list will have values of Mer.pass, that would put them in the
    > > daylight part of the sky at a that time, but these pairs can be put aside for use
    > > later on in the year).( Compare my Oct/May values)
    > > Select several pairs for increasingly later times during the night hours.
    > > The octant would be set up with the expected Angular separation of the chosen
    > > pair and the two stars observed  with the octant held horizontally. Any
    > > difference from the calculated value would be the error in the octant calibration
    > >
    > > Several angles on each pair would be measured and averaged,(just before to just
    > > after the calculated Meridian Pass) to ensure that the two stars of the pair will
    > > have the same Altitude.
    > > No correction will then be needed for Refraction.
    > > Using Stars of the same Declination  will ensure that their angular separation is
    > > the same as the difference in their SHA .
    > > No Horizon is necessary so the observations can be made anywhere and at any time
    > > there is a visible dark sky.
    > > No filters are needed on the octant and aligning two pinpoints of light is much
    > > easier than observing the edge of the Sun or Moon.
    > > Rocking the octant slightly will aid precise conjunction.
    > > The stars are not changing their separation so there is no hurry in taking the
    > > measurement
    > > There are very many pairs of stars to chose from and with practice it would be
    > > possible to use 'not so bright' stars, provided that one of the stars is easily
    > > found. The octant can be previously set with the expected angle, pointed at the
    > > brighter star and when it is properly horizontal the other should pop into view.
    > > I am not sure just how much tolerance in the declination of the pairs of  stars
    > > can be accepted but I guess a spherical trig calculation might be needed to
    > > determine their true separation if they differ in Declination by more than say
    > > about 5 degrees. However the familiar Sight Reduction formula or tabular methods
    > > could  be adapted for this purpose should it be necessary,
    > > I have roughly calculated with the aid of a spread sheet a few pairs of stars
    > > just to illustrate what I am talking about, I have used the short list of stars
    > > in the 1997 Nautical Almanac so to be any use the numbers would need to be
    > > recalculated using a current edition.
    > >
    > > NAME names of  stars in pairs, limited to those greater than -40 deg DEC
    > > DEC  approx  to show how similar they are. Decimal degrees.
    > > SHA   approx  sometimes =/- 360 deg needs to be applied to get Dif SHA.
    > > dif SHA Approx. Difference in SHA between the two stars. NOTE This value needs
    > > accurate recalculation as it is to be compared directly with the Octant
    > > measurement
    > > Mer Pas(OCT) ) Local Time when the two stars are horizontal and equally
    > > Mer Pas(MAY) ) spaced either side of the Southerly Meridian.
    > >    It is the time when the GHA Aries = 360 - (mean SHA of the two    stars)
    > > tabled for two representative months of the year.
    > >
    > > NAME  DEC  SHA  dif SHA Mer Pas(OCT)Mer Pas(MAY
    > >
    > > Gienah S 17.5 176.2    13:00  23:00
    > > Zubenel' S 16.0 137.3  38.9
    > >
    > > Regulus N 12  207.9    13:00  23:00
    > > Rasalhague N 12.6 96.3  111.6
    > >
    > > Fomalhaut S 29.6 15.6    14:00  00
    > > Adhara S 29.0 255.4  120.2
    > >
    > > Gienah S 17.5 176.2    14:00  00
    > > Sabic  S 15.7 102.4  73.8
    > >
    > > Shaula S 37.1 96.6    15:00  01:00
    > > Menkent S 36.4 148.4  51.8
    > >
    > > Antares S 26.4 112.7    17:00  03:00
    > > Nunki  S 26.3 76.2  36.5
    > >
    > > Elnath N 28.6 278.5    02:00  12:00
    > > Alpheratz N 29.1 357.9  79.4
    > >
    > > Alpheratz N 29.1 357.9    03:00  13:00
    > > Pollux N 28  243.7  114.2
    > >
    > > Diphda S 18.0 349.1    05:00  16:00
    > > Sirius S 16.7 258.7  90.4
    > >
    > > Pollux N 28  243.7    06:00  16:00
    > > Elnath N 28.6 278.5  34.8
    > >
    > > Alphard S 8.7  218.1    07:00  17:00
    > > Rigel  S 8.2  281.4  63.3
    > >
    > > Sirius S 16.7 258.7    09:00  19:00
    > > Gienah S 17.5 176.2  82.5
    > >
    > > I dont know where Bill  lives or I would have set up the data to suit his
    > > location. These numbers are calculated for the Greenwich Meridian but they should
    > > not be very far wrong for any longitude if this is applied to adjust the times to
    > > GMT. The times only change slowly with date (about 4 mins a day) The times to the
    > > nearest hour on the first of the month
    > >
    > > Regards
    > > CLIVE
    > >
    > >   ------------------------------------------------------------------------
    > >
    > >   Clive Sutherland 
    > >
    > >   Clive Sutherland
    > >     
    > >     Netscape Conference Address
    > >     Netscape Conference DLS Server
    > >   Additional Information:
    > >   Last Name
    > >   First NameClive Sutherland
    > >   Version   2.1
    >   ------------------------------------------------------------------------
    >   Clive Sutherland 
    >   Clive Sutherland
    >     Netscape Conference Address
    >     Netscape Conference DLS Server
    >   Additional Information:
    >   Last Name
    >   First NameClive Sutherland
    >   Version   2.1

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