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Old 07-16-2017, 07:09 AM   #46
Rockin Robbins
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About the first point in Aries, which isn't in Aires any more. It is definitely not an arbitrary point (of course! It has to be measured and confirmed.) The first point in Aries is that point where the Sun's path crosses the celestial equator in its path from south to north. This happens on the first day of spring for us northern hemisphere denizens.

All this mess with the first point in Aries not being in Aries any more comes from the roots of astronomy in astrology, 3000 years ago. Because the Earth wobbles on its axis, the north pole makes a circle in the sky with a period of 26,000 (roughly) years. This MOVES the first point in Aries, the place where the Sun crossed the celestial equator 3000 years ago to the point where the "first point in Aries" is two constellations away now in Pisces!

For a little fun, go see the total solar eclipse, find an astrology obsessed friend and travel to the eclipse. Before the eclipse, ask them which constellation the Sun is in. Then during the eclipse, have them identify clearly that the Sun is not in its astrological constellation at all! It is two constellations over. But wait! It gets worse. Astrology says that during the year the Sun passes through 12 constellations. That is dead wrong. The Sun passes through 15 different constellations, spending the most time in the largest of them, Ophiuchus, which doesn't rate a seat at the Zodiac table!

So astrology, which as its basis says that the positions of the stars, sun, moon and planets guide our lives, doesn't even bother to track the stars, sun, moon and planets. So much for any credibility. The shock on an astrology enthusiast's face when they see that for themselves, with the Sun two constellations away from where their beloved charts say it is, is priceless.

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Old 07-16-2017, 07:35 AM   #47
Nathaniel B.
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It's actually a common belief in astrology that, like the first point of Aries, the "houses" were named for the constellations they were in when they were discovered. Don't get me wrong, I don't buy into astrology.
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Old 07-16-2017, 08:03 AM   #48
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I just noticed the text you added to your previous post. In it, you stated that...

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Originally Posted by Rockin Robbins View Post
And that's why you mentioned shooting noon positions. That's much more accurate. Straight up, you don't have to worry about atmospheric refraction. Since you are looking through the minimum thickness of atmosphere, seeing conditions affect you the least they possibly can for that particular weather condition. BUT the time of culmination, when the Sun is highest, depends on your longitude and YOU DON'T KNOW THAT. So you don't know exactly when to look to find the time of local noon. Of course navigators have sneaky and effective ways to deal with that uncertainty;
That's not exactly right. While it is true that if a body is directly overhead, at the observer's zenith, you don't have to worry about refraction...this is a rare occurrence. It only happens when the declination of the body exactly matches one's latitude. Any other time, the altitude of a body on the local meridian will be equal to 90° minus the declination plus or minus the observer's latitude (depending on whether they are in the same or different hemispheres.)

You also wrote:

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Originally Posted by Rockin Robbins View Post
How about explaining how to do a noon sight and how to use that information to develop your longitude? Latitude is a piece of cake. Just measure the altitude of Polaris. If you're being fussy you can use a polar alignment scope to correct for the offset of Polaris from the actual pole, but that's less than a degree. If you're south of the equator then the bet is off!
I'd be happy to. But it'll have to wait. I need to get some rest before work.

Also, while I was able to see the screenshot from before when you linked to it, I still cannot see any of the images you are posting in-line. I'm not sure if it's a problem on my end or what.
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Old 07-17-2017, 03:06 PM   #49
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Alright...back home from work and I've gotten some more rest. Now, for the noon sight:

The noon sight is rarely, if ever used to find longitude. The reason is that, in order to accurately find longitude at noon using a sextant (and chronometer), one needs to determine the exact time at which the Sun transits the local meridian. When the Sun is on the local meridian, it is at its highest altitude for the observer's location. A sextant measures the altitude of heavenly bodies...so that should be easy, right? Not so much. Right around noon, the Sun seems to "hang" at the same altitude for up to several minutes.

Take a look at this graph. (You should be able to zoom it if it is not clear.) The blue line shows the altitude of the Sun every fifteen minutes on July 17th, 2017 at 45°N, 0°E. The red line (which uses the right-hand vertical axis) shows the rate of change in altitude in arc minutes per minute. Notice what happens at local noon: the rate of change drops to nearly zero. That makes it very difficult to determine exactly when the Sun has reached culmination.

There is a "trick" which can be used to try and find the time of local noon: double altitudes. The navigator measures the altitude of the Sun some number of minutes before noon and notes the time. The sextant is left at whatever reading was taken at that time. Then, the navigator waits until after noon, when the Sun drops to the exact same altitude again, and notes the time. splitting the difference between these times should give the time of local noon...if you're stationary...and not on a pitching and rolling ship...and make perfect observations. But, even then, it's tough to get an accurate time.

For the sake of explanation, let's say you did get an accurate time. How does that tell you your longitude? Well, your chronometer would be set to GMT (Greenwich Mean Time or UT [Universal Time], essentially the same thing). Let's say you found that local noon occurred at 14:32:17 GMT on July 17th, 2017. Now, you know that noon in Greenwich occurred at 12:00:00 GMT...or did it? Not necessarily. You have to consider something called the "equation of time". Because the Earth speeds up and slows down in its yearly orbit around the Sun, the Sun appears to race ahead or lag behind "mean" time (the time that a regular clock keeps). On this date, the equation of time is about -6m13s. IOW, the Sun is six minutes and thirteen seconds behind where the mean Sun would be, and noon would occur later. (This information can be found in the Nautical Almanac [see the bottom of page 2 in this example].)

So, Greenwich noon occurred at 12:06:13 GMT. If we subtract that from the time of our local noon, we get 14:32:17-12:06:13 = 2:26:04. Local noon occurred two hours, twenty-six minutes and four seconds after Greenwich noon. Since we know that the Earth rotates 360° every 24 hours, we know that the Sun appears to move 15° through the sky each hour. So, if we multiply 2:26:04 by 15, we get: 2:26:04∙15 = 36°31'00"...this is our longitude. And since local noon occurred after Greenwich noon, we know our longitude is west: 36°31'00"W.

However, as we have learned, the noon sight is not typically used to find longitude. What it is used for is to find latitude. So, how is this done? Well, in this case, it's kind of handy that the sun "hangs" at the same altitude for several minutes. Because that's what we're after - the maximum altitude. Let's say that, after correcting for index error, height of eye, refraction and semi-diameter, we get a maximum altitude of 66°05.5' on July 17th, 2017 at 14:32:17 UT. We subtract the altitude from 90° to get the "zenith distance" - the distance the Sun is from being directly overhead. (This is equal to the distance we are from the Sun's GP.) 90°-66°05.5' = 23°54.5'. Now, we look in our almanac and find, after interpolation, that the Sun has a declination of N21°05.5'. Since the Sun's declination is in the same hemisphere as our DR, we add the declination to the zenith distance to find our latitude: 23°54.5'+21°05.5' = N45°00.0'.

Finding longitude was usually done by "time sight". But that is another subject altogether.
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Old 07-17-2017, 05:02 PM   #50
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That raises the question of how accurately can you measure the altitude of the Sun, an extended object, on the pitching deck of a submarine? I bet you couldn't duplicate two sightings within 10' of arc. I wouldn't be a bit surprised at an error envelope of a half degree. That would make finding longitude with a noon sight impossible.

It still seems to me the altitude of the north pole is the best way to establish latitude. If you're on land that can be done with incredible precision using a polar alignment scope. Alternately, you could use Polaris itself when the position angle of the pole is parallel with the hofizon. That happens twice a day.

The altitude of the Sun is always going to be a problem. The Sun isn't a point, its a disk. You have to find and align on the exact center of the disk.
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Old 07-17-2017, 07:17 PM   #51
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Typically, a series of sights are taken around noon. The navigator can choose to use the highest measured altitude directly, or can plot all of the observations onto a graph and rough a curve through them. The top of the curve can then be used as the culmination altitude.

Included in the Nautical Almanac (and also in some sight reduction tables) is a table for correcting the offset of Polaris from the elevated pole. The navigator simply calculates LHA Aries and enters the table to find the needed correction for the time at which the sight was taken. An accurate latitude can be determined fairly easily this way. A corrected azimuth can also be obtained for checking a compass.

It's practically impossible to accurately shoot the center of the Sun or Moon with a sextant. That's why a correction for semi-diameter is included in the calculations. The navigator shoots the lower limb (typically, but sometimes the upper limb for the Moon) and corrects the altitude for half of the diameter to find the altitude of the center. The SD of the Sun is listed at the bottom of each daily page, but the correction is included in the altitude correction tables for both Sun and Moon.
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