A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2013 Apr 14, 12:13 -0700
Tonight will be a good night for a practice lunar sight if the skies are clear. For observers in eastern North America, the Moon will be about three degrees to the left of Jupiter tonight during evening twilight. A lunar like this, with a very short angular distance, and with the Moon's motion nearly 90 degrees from the direction to the other body were not used historically for getting GMT, but they are fine for modern practice, and they work well for position-fixing by lunars (as was used as a backup on the Apollo moon missions over forty years ago). It's an excellent "training" lunar.
To try this lunar, make sure your sextant is properly adjusted, and then get the best value for your instrument's index correction that you can manage. Jupiter itself can be used for this if you're careful, and if there's minimal "side error" in your sextant. Just place Jupiter's reflected image on top of its direct image. Use the highest magnification you have available. You can even try my trick of placing a spotting scope in the line of sight where the telescope would normally be. Take four to ten index correction measurements and then average.
For lunars, pre-setting to the correct angle is standard practice. Set your sextant for three degrees (four on the US west coast) and then aim at the Moon. You will need to hold the sextant horizontally. In the direct view you'll see the Moon. Keeping the Moon visible in the direct (horizon glass) view, a little rocking should bring Jupiter into view in the index mirror. Turn the micrometer to line them up more nearly letting Jupiter just kiss the limb of the Moon nearest to it. You don't need to get it perfect right away. The angular distance changes very slowly for any lunar and especially under this particular geometry. I recommend using both hands to hold the sextant frame to get a stable view. Rock the sextant a bit to get Jupiter to swing back and forth across the Moon's limb. If it cuts too deep or doesn't quite cross the Moon's limb, don't try to adjust the micrometer "live". It's not necessary with lunars. Instead, give your arms a rest and tweek the micrometer by a couple of tenths directly --not looking through the instrument as you make the adjustment. Then look again and see if the alignment is better. Repeat as necessary. I have long found that this indirect micrometer adjustment, using both hands to stabilize the instrument when performing the actual observation, yields considerably more accurate results. Note that Jupiter is big. It has a visible disk which you will be able to see as a small dot (rather than a point) with any magnification above about 3x. For lunars, you should place this "dot" symmetrically on the Moon's limb, cutting it in half, rather than treating it like a small body with its own limb and semi-diameter. Shoot three or more lunar distances this way, recording the GMT as nearly as possible for each, though given tonight's geometry a five second error in time will make little or no difference.
Of course, clearing lunars used to be a nuisance, and would have been especially difficult for a short angle observation like this. But not so in the 21st century. You can use my lunars clearing tool at http://ReedNavigation.com/lunars and find out how well you're doing in just a few seconds. The site is designed for small screeens, so you can even call this up on any Internet-capable phone or tablet and check your observations just as you take them. The output from this clearing tool shows the error in your observation and also an equivalent error in longitude. Please remember that this is a typical error in longitude for a "normal" lunar, not this specific lunar which could not be used for getting GMT (because the Moon's distance from Jupiter is changing so slowly as it moves in a direction nearly perpendicular to the measured lunar arc).
Why do this? The most obvious reason for a modern observer is to test for arc error. After you've eliminated all other sources of error, residual error in lunars, if it's consistent and repeatable, is arc error --which is the same quantity you find on traditional sextant calibration certificates. So tonight's observations, if you're successful, will anchor your calibration certificate at the low end. Arc error at such a small angle (not due to incorrectly measured index error) is relatively unlikely, so you will most likely find that your observations are accurate to a few tenths of a minute of arc with no significant residual error.
PS: This hasn't come up in a long time. If you're shooting any celestial sights, lunars or otherwise, from an inland site, up on a mountain, don't forget that the air is thinner up there. Refraction is reduced in direct proportion to the decrease in air density. Barometric pressure is normally reported as a value that has been extrapolated to sea level so that meteorologists can make meaningful comparisons of weather observations from points that are close together on the map but far apart in altitude. For refraction, you have to remove that altitude extrapolation. You can do this approximately by taking the reported barometric pressure and multiplying by exp(-h/h0) where h is the height of your observing station above sea level and h0 is the "scale height", which for a quick approximation can be taken to be 11 kilometers or about 36,000 feet. For an even easier approximation, multiply the barometric pressure by (1-h/40,000ft) which is reasonably good for altitudes up to 10,000 feet. A generic name for the "scale height" here is the "e-folding height". It's the change in altitude that reduces the density by a factor of e, the base of the natural logarithms (the density is reduced by "e-fold" in analogy with "three-fold", e.g., when the altitude increases by that distance h0). You can also think it through in terms of the "2-folding" or "halving altitude" --the increase in altitude that decreases the density of air by a factor of two. A little simple math will show that the halving altitude is equal to the e-folding height or "scale height" multiplied by 0.6931. If the e-folding height is 36,000 feet, then the halving altitude is nearly 25,000 feet. Incidentally, if your do a little integration, you'll find that the e-folding altitude or scale height is also equivalent to the depth that the atmosphere would have if the whole mass of the atmosphere were compressed into a layer that has constant density from sea level up to the top and then drops right to total vacuum. That's all the air there is: about 36,000 feet at sea level density.
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