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Author
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Topic: Index Correction and High School Science
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SMadden
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posted February 10, 2006 12:25 PM
I have recieved my materials for the home-study celestial navigation
course and am through chapter 4. I love the presentation. I do,
however, have a few questions:
In Section 11.6 of the text there is a discussion of how to measure
index correction. I'd like to confirm with you that the measurement
described in steps 4 and 5 amount to measuring the angular size of the
Sun. Equivalently, if one made this correction using the Moon the result
would amount to the angular size of the Moon. As an astronomy teacher
I'd like to be able to use such measurements with my high school
students.
That's all for now, thanks for your time,
Sean P. Madden
From: Greeley
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David Burch
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posted February 10, 2006 12:57 PM
Yes, the technique we call Solar Index method does in fact end up with a measurement of the semi-diameter of the sun, since we are measuring effectively the height of the top edge (upper limb) relative to that of the bottom edge (lower limb.)
We have a form for carrying out these measurements, as you may have found, and the process is discussed in the course materials. This is an old technique, used extensively long in the past, but rarely mentioned in modern texts on cel nav.
This might indeed make an interesting science project, which should start out by noting that we must be careful in concluding what we are measuring here. It is the vertical angular extent of the sun, not exactly the "size" of the sun, because in principle the refraction correction is different at the top edge of the sun compared to the bottom of the sun, especially at very low elevations—check out the refraction corrections in an almanac for Ha less than 10°. At elevations above some 20° or so, i would guess this does not matter much, but for the giant suns we see near the horizon, this could be an interesting effect to investigate. Note that in some pictures of the sun low on the horizon it appears as an eclipse due to this effect. Which is why we use the term "semi diameter" rather than "radius".
Let me know if you want to pursue this thought.
As for applying this to the moon, you could get some rough data, but this is a bit trickier to both measure and to evaluate. First you need to know the phase, and the moon is usually tilted to some extent relative to the axis of illumination. Also in the case of the moon, we would have to think on how the horizontal parallax might enter into the analysis.
So, it depends on the level of the classroom science project. To first order, yes you are indeed measuring the size of the sun or moon—in the most basic sense that you are using an angle measuring device and measuring the angle subtended by the body, just as you might do the same thing for the angular height of a building down the street somewhere. If you know the height of the building, you can then use basic trigonometry to compute how far away the building is.... a nice science-math class project.
In principle, then, since we can look up the actual diameter of the sun or moon in miles from reference books, we could use our sextant measurements of the sun or moon widths to compute how far a way they are. But this is where the analysis gets a bit tricker if we want to do the best job... all doable from what you know already in cel nav, but still we must be careful, and this is in particular where the difference in the sun and moon are the greatest. Because the moon is so close, we have extra corrections to make, not only in routine cel nav, but in this science project as well.
From: Starpath, Seattle, WA
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