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    Re: Correction to measuring Octant instrument error
    From: JC Sutherland
    Date: 2000 Sep 20, 2:42 AM

    In my last message I made an error in the mathematics, a fundamental one I am
    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
    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.
    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

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