Establishing North with Polaris

I always had to interpolate

Any celestial object can be determined to within 15" position using manual readings of a 0.1" clock.

However Polaris is much easier, it stays within 1° of true North over a 24 hour period. Over a 12 hour elongation E-W it covers 120 minutes of arc, 10 minutes of arc per hour. To get 15" precision one merely has to observe the time to within +/- 1 minute.

Calculations and interpolations are very easy.

It can be observed during the daylight hours with proper equipment, such as a darkened toilet paper roll tube to shade the lens.

Paul in PA

Not sure what you mean by "real time ephemeris".

I use MICA, which is the digital replacement for the Astronomical Almanac. The current version is 2.2.2,

MICA 2.2.2

the accuracy is way more than could ever be needed for surveying (except for maybe the moon, for which I use the lunar polynomials available online from USNO). The limiting factor is time, you need to accurately record the time of observation, and convert to UT1 from UTC (using DUT1). You can get a prediction of DUT1 or you can get a value for past dates (similar to broadcast versus precise ephemerides for GPS).

Using Polaris time is not so critical, especially at elongation.

John Hamilton really answered your question with his suggestion to observe Polaris at elongation.

The star appears to move vertical for about 10 minutes at elongation.

I have used a sun and Polaris calculator called SPADE, which I found as a free download somewhere. I don't know if the ephemeris in it is still good enough.

Near Polaris elongation, you can do well with time to the nearest several seconds or even minute. I use my handheld GPS for location and time.

I saw little improvement in visibility using the black tube over the objective. It will depend on your sky conditions (altitude and humidity). Even without it I can track Polaris for much of an hour after sunrise, or before sunset. It helps greatly to have a starting azimuth sufficient to put the star in the field of view of the scope. Be sure to allow about a minute for vertical refraction.

If your instrument doesn't have a built-in reticule light, be careful how you illuminate the crosshairs. When I put a light in front of the objective, blocking a small part of its field, I have seen a shift in the star image of several arc seconds. I can't explain it for sure. Perhaps it is parallax due to imperfect focus?

Be sure to apply the Laplace correction, which is the difference between astronomic and geodetic North due to your local deflection of the vertical as you bring the star azimuth down to the horizon. It may amount to several arc seconds depending on your location. The NGS Toolkit will give you the value.

Thanks for that tip. I hadn't been aware of MICA. I've been using an app on my iPhone (Go Sky Watch). I can probably interpolate using that, and may compare the two to see exactly when the app (or whatever database it's using...it may well be MICA), clicks off the .01 degree increments (or decrements). It's certainly convenient. And yes, I use the correction factor(which around here is 03'.

The LARGEST potential error source is mis-levelment of the instrument. Since Polaris is at the same elevation angle as your latitude (±1° or so), the affect on the azimuth varies as tan H (where H is the elevation angle, or 90-Z, the zenith angle).

I have used a newer model T-2 a lot for star observations, it has a compensator, similar to an automatic level. It is fairly easy to get it level, just read the vertical angle (any angle, not necessarily to the star) at 90° left and 90° right of the direction to the star. By using the footscrews one can use that procedure to get the trunnion axis level. Alternatively one can read these values after each star pointing, and correct the direction to the star by the formula:

((V_r-V_l)/2)*tan H

Modern dual compensator instruments like a Trimble S6 (which is what I now use) automatically compensate for this. Note: taking D+R observations DO NOT correct this.

I also have a T-3 which has a sensitive bubble. I always "read" the bubble (numbered) after each pointing, and, knowing how much each graduation is, apply a correction that way.

In my experience this potential error is far greater than the laplace correction, but the laplace correction can get large where there is a steep slope of the geoid.

I have posted this link before, but here is a paper I wrote years ago (probably needs to be updated):

Azimuths (pdf file)

I hope to give a class on astro azimuth determination at the Trimble Dimensions conference in November but I have not yet heard back if they accepted my proposed topic.

In 24 hours the questions on Polaris observations were answered on what took me (self learned) 2 months to study and figure out for a daytime Polaris shot. This is one awesome board...Some great surveyors are only a button push away. 🙂

Pablo B-)

By coincidence I was just running thru the calculations for hour angle azimuth - sun, Polaris. I highly recommend doing so with pencil paper and an HP41 as an excercize. The calculations aren't hard, but we all get rusty. Observations are a skill that should be dusted off, kept sharp,and passed on to new crew members. Measure a simple base line with post processed gps and then take an astro azimuth. There is a lot to gain from getting the same azimuth the old fashioned way and with gps. You should easily get 5-15 seconds. And the student may learn a thing of two.

If you don't get the same azimuth, figure why. Did you miss a sign on convergence? Apply semi diameter the wrong way?

I would love to learn how to do that stuff. No one ever showed me how to shoot stellar objects and reckon your way back home. They made me a button-pusher and I was good at that but knew there was way behind it.

Do you have access to T2? Do you know where an NGS disc is that you can occupy? Maybe a radio tower with published coordinate in view?

a few months ago I did just that. Occupied a 1st order station and measured an azimuth to a tower. Just for drill. Even shooting the sun, applied LaPlace, checked against inverse and agreed to 4 seconds. Timing is the only tricky part. I use my HP41 clock function. There is a phone app that will grab time true UTC to sub-second. Then the knack is to catch the edge of the sun. That takes a little practice. Online I see a lot of software but most of them are crude because they are mostly for solar panels. so a long hand calculation is rewarding.

Maybe it's time to make a video.

> Do you have access to T2? Do you know where an NGS disc is that you can occupy? Maybe a radio tower with published coordinate in view?
>
> a few months ago I did just that. Occupied a 1st order station and measured an azimuth to a tower. Just for drill. Even shooting the sun, applied LaPlace, checked against inverse and agreed to 4 seconds. Timing is the only tricky part. I use my HP41 clock function. There is a phone app that will grab time true UTC to sub-second. Then the knack is to catch the edge of the sun. That takes a little practice. Online I see a lot of software but most of them are crude because they are mostly for solar panels. so a long hand calculation is rewarding.
>
> Maybe it's time to make a video.

I have no instrument. I might could borrow an S6. I have plenty of compasses and my HP33 and plenty of paper and pencils. I do know the night sky quite well. AS to NGS marks I don't of any specifically nearby but I do where a couple of local monuments are. They may have been published. The local county has them established and I think the corps of engineers has them occupied as well. One is easy walking distance from here at the house. Now that I say I know for a fact the corps has them occupied since they use them for damn monitoring and benchmarks. I have ran into a few surveyors occupying the one nearby. We usually end up knowing some of the same people. One even knew about me - maybe too much.

A video would be good. Need some help? I got nothing else better to do as I am oft to say these days.
E.

Don't try solar with the S6. Everything I've read says you'll burn out the EDM. Stick to Polaris.

My second year in surveying (early 80's) I was an instrument man. I had gone out and bought the book Davis, Foote et al, and was trying to learn as much as I could. It wasn't easy, because I was usually on a traveling crew, and the party chief was a drinker, he liked to go to the bar at happy hour and stay until late. So of course I had to do that too.

So one day we are doing sedimentation surveys on a lake. This entailed recovering a pair of monuments at each end of a range line (4 total), and then running a profile from the mons to the waters edge, then doing a hydro survey on that line using a K & E transit observing stadia to a large board on the boat, painted with stadia lines, then from the other water's edge up to the monuments on the other side. The mons had SPC on them, and we had 1:2400 maps showing the location and the topography.

One range we really struggled to find anything, it was swampy, flat, and featureless. Finally we found one, but it was thick and difficult to see where to go from there. I told the party chief that I could do a solar and calculate it on my HP41 (I had a pocket ephemeris). He laughed at me and wandered off searching for the line. I did one, and I think to humor me he had the rodman start cutting line. After a few hundred feet, we found the next mon, pretty well hidden.. The line hit the mon right on.

Made a believer out of me (and the party chief). After that, I was the only person on the four crews who could do an astro (and calc it), so I was in demand.

I definitely agree, calc one by hand (using a calculator of course for the trig functions) to get an idea of what is involved.

It's a lot easier on land than at sea

When I started this thread, I did so out of curiosity if some of the same principles applied that have been used at sea for ages. My own background, to wit: I spent 15 yrs+ sailing about the earth, driving sailboats for others (both contract and fully employed). I've got many, many, logbooks filled with the hand calcs required to "know where you are". (I did cheat some with my HP 25).

This was in the days way before GPS. Heck, some of it was before Loran C! I'd say it was before Omega, but that'd be giving away my age, big time, so I won't go there.

I was preparing my Plath Sextant for sale on Ebay when I started looking for an optical Theodolite. I heartily endorse the posters who have stated that learning to do the calcs manually (if only once or twice), can be of huge benefit to learning the principles of this art (of both Cadastral and Geodetic surveying).

Having done thousands of Sun, Moon, Star and Planet sights at sea, and a few Polaris shots here on land, I can attest that doing them on land is a piece of cake by comparison! They hardly move around on ya',

To those thinking of adding the skill into their toolbox, I would offer this: Don't forget about planets. They're often much much brighter than Polaris, and therefore easier to see earlier in the evening or later in the morning; they don't require the filters the Sun does. They do move faster than Polaris, but not as fast as the Sun, so interpolation works fine with them, so long as you have an accurate time piece (or an iPhone).

It's a lot easier on land than at sea

How do you reconcile when a planet goes retrograde?
I imagine Ptolemey, Newton and Gallileo would love to jump in on this conversation. I know I'd love to be in that sort of company.

>It's a lot easier on land than at sea

That's for sure, but then the requirements get tightened on land. I expect you were pretty happy with 1 arc minute at sea, but on land people are going to expect 5 or 10 arc seconds.

Intersection stations, like church steeples and radio towers, are frequently altered. In the many years since NGS positioned them, many have changed. Be sure to carefully read the description of the point observed. Many water tanks were observed using tangents (observing the apparent left and right edges) and not a light or vent atop. Some lights were used and some vents. Lights on radio towers are frequently altered.

Boring anecdote. Years ago I was working in the vicinity of Walla Walla, WA. I included observations to a water tank in the penitentiary in my network. It did not work. Naively, I called the prison to see if there had been any changes to the tank. They were more than a little curious about what I was doing. Thankfully, this was the days before caller ID.

I do not know whether it is still available on line but her Leitz ephemeris had some clear explanations of the computations and some code for computing astronomical observations using the HP41. The last edition I saw was probably 2007 or earlier. Authors were Senne and Knowles I believe.

I wrote a Matlab script from the equations. They appear here: http://geodesyattamucc.pbworks.com/w/file/21237505/astroAZexample.m

HTH,

DMM

It's a lot easier on land than at sea

> How do you reconcile when a planet goes retrograde?
That's not a problem. You don't care whether it's in retrograde or not...all you care about is its precise azimuth at any given time, and the rate of change of azimuth.

Those old timers could not have imagined the power of the tools we carry in our pockets today.