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    Re: Star-Star observation equipment
    From: Frank Reed
    Date: 2010 Mar 10, 18:54 -0800

    Skimming the patent quickly, it looks like it's a device that was intended to be both a two star sextant (capable of shooting two stars at the same time) and also a non-electronic sight reduction calculator. It's an interesting idea, but, as you say, presuambly a "dead end". There were a number of similar sorts of instruments developed in the past couple of hundred years with varying degrees of complexity. Here's an example of one invented by the prolific navigation instructor, Janet Taylor, back in the 1830s:
    None of these ever caught on to any significant degree. These devices, though, are not actually related to the "star-star" sights that we've been discussing.

    Since there hasn't been a general description of what's going on here with "star-star" observations in a while, I should just say that it's not a navigational method. It's a method for testing a sextant. When a sextant is set to, let's say, 30 degrees exactly, we just assume that it is accurately measuring an angle of thirty degrees after applying the usual index correction. But this is not generally true. Sextants have centering errors and arc graduation errors, and other issues. These small errors combine to give something that we often call "arc error." A century ago, someone suggested calling it "Kew error" since the certificate from Kew Observatory (and nowhere else at that time in the UK) listed the errors at various angles (and "Kew error" was apparently a common expression for the barometers and thermometers that they tested). The majority of modern sextants come with similar certificates. It's not uncommon to see listed errors of 20 or 30 seconds of arc at various angles. Many sextant certificates state simply that the instrument is "free from error" for practical use, if we believe that. This arc error is like index error, but normally it cannot be tested without special equipment or procedures. Navigators have usually just trusted the certificate (even though it may date from decades earlier) or ignored the matter entirely as negligible for practical navigation. Star-star sights provide one possible means of testing sextant arc error at home or at sea. And by the way, it's something that you can do from an inland observing site --like Iowa.

    The idea behind "star-star" sights is that we can calculate the exact angle between any pair of stars at any time and then compare against that angle measured with a sextant. To do this, you need two things: calculated distances between prominent, easily-identified stars accurate to a fraction of a minute of arc, and also a method for clearing the sights for the effect of refraction. Neither of these is difficult in principle. We can take the positions of the stars from an almanac or any star catalog of sufficient accuracy and then the distance between them is a great circle distance calculation, just like calculating the great circle distance across an ocean between two ports on the surface of the Earth. Some of the stars are moving fast enough across the celestial sphere (proper motion) that they either have to be avoided or the distances need to be recalculated every few years. Also, star positions are shifted by up to 40 seconds of arc by annual aberration so really we need to get the positions for the current date, within a week or two, if we expect any serious accuracy from these calculations. As for clearing for the effects of refraction, this is just a matter of taking the normal altitude corrections for stars and applying them to an arc that may be at some funny angle across the sky. It's a straight-forward geometry problem. No big deal. As it turns out, as long as both of the stars are above 45 degrees, the refraction can be "cleared" from the measured star-star angle by a simple rule: add a tenth of a minute of arc for every five degrees of measured distance (the more general case can be solved easily with a little spherical trigonometry). Example: two stars are observed to be 26 degrees and 23.4 minutes apart, and they are high in the sky, falling under the scope of the rule that they both be above 45 degrees... 26 divided by 5 is 5 so the correction is about 0.5'. We add that to the observed distance giving 26d 23.9'. Then we compare that to the pre-calculated distance. If they don't match, any difference is a combination of arc error mixed up with any residual random error in the observation. If we do it four or five times and always get the same bias, perhaps the observed distance is on average 1.0 minutes greater than the pre-calculated, then it's a fair bet that we have made a good estimate of the arc error for an angle of 26 degrees. We write that down and move on to another pair of stars. With enough star pairs, we can build up a complete sextant certificate, without paying five shillings to Kew (that was the going rate, and a very good deal, back in 1900).

    As for making the observation itself, sometimes it's a little inconvenient and if you've never used a sextant for anything but altitudes (vertical angles), it can be a little weird at first. Generally the sextant has to be held so that the frame of the sextant is in the plane containing the two stars and your eye. It's easy to make the observation if you know the stars fairly well, and if you pre-compute the distance. You pre-set the sextant for the unrefracted distance, aim right at the more convenient of the two stars so that you see it in the horizon glass. Then rotate the instrument slowly about that line of sight (keeping the first star always centered in the horizon glass) until the second star pops into view. It should line up almost exactly with the first, and unless we're really unlucky, a false match is very unlikely. Then we adjust until the images overlap as exactly as possible and read off the numbers.

    Some of us have found that dark adaptation is a "bad idea" when taking these star-star sights. When the eye is fully dark adapted, stars can look like spikey "blobs" rather than small sharp points. As I've noted in another post, I usually get results with star-star sights that are "good but not great". I can detect arc errors larger than 0.5 minutes using these sights and frequently somewaht better than that, but not as fine as a tenth of a minute of arc. For any such observations, you should use the highest power telescope included with your instrument. The basic resolution of the human eye, properly focused, is 1.0 minutes of arc or slightly better. If you use a 10x telescope, you can resolve a tenth of a minute of arc.

    By the way, it's important to eliminate all other sources of error before trying this sort of test. The index mirror has to be as exactly perpendicular as possible. The horizon mirror should be nearly perpendicular (but this is not critical). The telescope should be collimated (its axis parallel to the instrument frame). And the index correction must be found as exactly as possible. This last check is critically important.


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