Shoot The Sun

I haven't seen it.

I never got to within 10 arc seconds.

A minute yes.

The last one I did was in a deep canyon in the late 1990's. I had GPS so I stopped doing solars in those days, but I couldn't get any kind of a fix in that canyon, even static didn't work with the trees so I broke out the instrument and did a solar. It was suspect and weak because the sun was difficult to capture. I did it and the resulting bearings were 3degrees different than the record survey. That job lingered on as the owners fought, finally years later I was able to get my newer GNSS receivers in there and I was only 90 seconds different from my solar, the old timers were way off, probably a compass issue. By then I knew visually they were skewed so I wasn't surprised.  

At one time the great Jeff Moog programed our HP48 calculators which we used as DC and all you needed to do was sight the sun and hit the button, it spit out the AZ. 

Then got new DCs, no more canned solars. I needed to carry the pamphlet with ephemeris and formulas and do the calcs during lunch. Usually took about 15 minutes of concentration. 

Out in the open I could get within 1/2 a minute sometimes. Not much better than that. 

The sun passes through 360 degrees in 24 hours so 360/24=15. Every second of time is 15 second of arc, more or less. Time is usually the limiting factor.

When accurate time was not available, you needed to observe the vertical angle to the sun as well as the horizontal. Refraction added uncertainty, so the accuracy was around a minute of arc. 

With good time, good ephemeris, and a good instrument you should be able to get 5 to 10 seconds of accuracy. 

Accurate time, accurate location, both were difficult in those days.

We would plot our location and scale it off a quad sheet.

The time was always problematic.

Some surveyors would time the radio ping on the hour and adjust a stopwatch or their regular watch. We would also adjust the time in the HP-48 but that wasn't great. You could call a number and get an accurate time count. Can't say if that's still available, haven't used it in decades. Now I suppose with GPS time and location are easy, however, with GPS I ain't gonna do another solar. 

US Naval Observatory time 202-762-1401

Posted by: @lurker

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US Naval Observatory time 202-762-1401

It must be almost 30 years since I called that number. Maybe it was a different number then. There is this disembodied voice counting down the time, you had to try and sinc up to it the best you could.  

I suppose you could get good at it and help to make the solar closer to the 10 seconds. Even in the old days we almost aways were on State Plane bearings from NGS monuments. It was the odd little surveys that might get a solar. 

From the 1980s I had a Radio Shack time radio to take to the field. With the radio on, I set a stop watch with a lap function to zero on 'minuet' then checked a lap time to the radio. The lap time was recorded with each pointing, 3 direct, 3 inverted. At the end, the stop watch was again checked against the radio. Pointing time was 'radio set time' plus 'lap time'.

The direct pointings were paired with inverted to produce 3 azimuth solutions. Usually the spread would be under 20 seconds. 

I developed a method to use the moon rather than the sun. This can be easier since no filter is required, but the moon moves faster so it requires a bit more skill. Also, because there are more perturbations to the orbit, the computations are more complex. When I developed the method the USNO published daily polynomials in the Astronomical Almanac. A few years ago they stopped including that data. I found an online resource where somebody calculated these polynomials for many years into the future, but that link seems to be defunct.

Also, because the moon is relatively close to the earth, you need to compute the topocentric position (i.e. from the surface at the location of the observations) rather than the geocentric position of the moon. 

Here are the steps to compute the azimuth for each observation

1) compute UT1 (from UTC) and TT (Terrestrial Time, formerly called Terrestrial Dynamic Time) which is UTC+32.184+leap seconds

2) compute the astro latitude and longitude from the geodetic latitude and longitude (deflection of the vertical from deflect18) and ECEF coordinates

3) get polynomials 

4) compute GAST (Greenwich Apparent Sidereal Time)

5) compute LAST (Local Apparent Sidereal Time)

6) compute right ascension, declination, and horizontal parallax

7) compute the distance to the moon r

8) compute the topocentric position vector of the moon

9) transform the right ascension and declination from geocentric to topocentric 

10) compute the topocentric hour angle

11) compute the topocentric azimuth to the center of the moon

12) compute and apply the semi-diameter of the moon to get the azimuth to the edge

13) apply laplace correction

Example computation (a little messy, it is from a 30 year old word document): 

Station = CLIFTON

08/07/97 20:18:05.30 EDT      UTC=00:18:05.30 (8/8/97)      DUT=+0.48s

f=40°17¢54.23² N   l=80°02¢42.19²W    ellip h=267 m

angle from R to leading edge of moon: 20°09¢32²

vertical circle left=278°36¢10²      right=278°34¢54²

• compute astro coords from DEFLEC96: x= 2.54” h= -2.53” Laplace=+2.15”

   F=40°17¢56.8² N       L=80°02’44.7”W

• compute UT1 from UTC and DUT UT1=00:18:05.78
• compute LAST

GMST at 0h                    21:06:09.7685

DMST from 0h to 00:18:05:78   00:18:08.7528

GMST at 00:18:05.78                 21:24:18.5213

equation of equinoxes               -0.0886

GAST at 00:18:05.78                 21:24:18.4327

subtract west longitude       05:20:10.9800

LAST                          16:04:07.4527

• compute TDT=UTC+63.18 TDT=00:19:08.48
• using the polynomial coefficients (page D40 of the 1997 Astronomical Almanac), compute a, d, and HP (horizontal parallax) for TDT:

a=12:25:48.826          d=-1°11¢10.61²     HP=0°54¢08.950²

• convert latitude, longitude, ellipsoidal height of station to ECEF XYZ:

X=(N+h)cosf * cosl

Y=(N+h)cosf * sinl

Z=(1-e²)N+h)sinf

where N is the radius of curvature in the prime vertical:

;

a is the semimajor axis and b is the semiminor axis of the

earth ellipsoid, a=6,378,137 m, b=6,356,752.314 m

X=             842,163 m

Y=          -4,798,202 m

Z=          4,103,484 m

• compute the geocentric distance of the station,

r=6,369,502 m

and the geocentric latitude of the station:

y=40°06¢31.2²

• compute the true distance to the moon:

 = 404,943,011 m

• compute the topocentric position vector of the moon:

(q₀ is the LAST)

    = -399,931,391 m

     = - 41,242,112 m

        = - 12,487,028 m

• compute topocentric values:

        =  402,246,137 m

                 =  12:23:33.0478

            = -1°46¢44.16²

• compute the topocentric hour angle:

               = 55°08¢36.073²

• compute the azimuth to the center of the moon:

A=244°23¢24.5²

• compute and apply the semi-diameter correction

altitude=24°33’23

     =  0°14¢45.3²

semi-diameter correction      =  0°16¢13.3²

azimuth to leading edge =244°39¢37.8²

• correct the azimuth for inclination of standing axis:

C=-17.4”

corrected azimuth=244°39¢55.2²

• subtract angle from RM to obtain astro azimuth to RM:

astro azimuth to RM=224°30¢23²

• apply Laplace Correction to obtain geodetic azimuth:

geodetic azimuth to RM=224°30¢25.3²

I agree with lots of the above and has been 30 yrs since I did a solar observation.  And, I do remember calling the observatory and the tick tick tick to get the precise second.  I do remember redundant shots and noting the spread.

How did you determine the accuracy?

The solar ephemeris by Elgin, Senne and Knowles (2001 Sokkia edition) includes errors for solar observations in Table 1. It clearly shows that local noon on the summer solstice is not a good time to do a solar by the hour angle method.

Posted by: @nate-the-surveyor

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I inherited a book, called "Shoot The Sun", from a long deceased surveyor. Inside the front cover it says:

"Shoot the Sun is a simple method of computing a solar observation to determine a true bearing of a line, and is accurate to within one minute".

Requirements for this method are: A good Transit; the latitude in your area; the sun's declination (from ephemeris of the sun); a table of natural sines, and follow the method outlined in this book.

It has a total of 22 pages.

I've never seen this book before... However, I did overhear a nice argument, between Jim Scott, and some other person, at a surveyor's convention, about 30 yrs ago. Jim Scott was arguing "You cannot take a solar shot, and get closer than a minute", and the other fellow said 10 arc seconds was pretty do-able. Well, this may have explained this argument. Jim may have been using the method contained in this book, and the other surveyor was using the hour angle method.

Anyway, I could not find any of these booklets online, and I suspect it is very out of print.

Anyway, I am thinking of scanning it, and sharing it, simply for it's historic value. The copyright is G Lawrence Robinson, 1961.

Very likely out of print.

Anybody else ever seen this, or is interested?

Thanks!

Nate

please do share. Always fun looking at different methods. I had an old Lietz that had the little round cylinder compass that slid on top. If I did sun shot with it and compared the magnetic azimuth and corrected for declination as a check to my sun shot that sucker seemed to almost always fall within about a minute. I used RE Buckner’s method mostly back then.  

@john-hamilton

The resemblance is uncanny 🤓 

For those who want a free pdf of this, drop me an email.

Would you prefer it in a DIRECT scan, single pages, or I can take the staples out, and scan it sheet by sheet, (It's about 7 sheets, 2 sides) Then, you can sort of re create it, with staples.

IF anything, donate to Wendell.

Nate

@nate-the-surveyor 
a thing like that you could just attach to a posting, Nate.

[email protected]

Yup.

Way back in my youthful field days, we were taking solar observation one day. I was on the stopwatch. Party chief says to the I-man while lining up on the sun, "don't forget to get a distance". I-man replied, "you want me to double it, too?"

In the 60's in the Forest Service we took sun shots with a 1 minute transit using the horizontal and vertical angle method and the leading edge of the sun. In the 80's and 90's in Calif we used the HP48GX Survey card method and I made a sheet for jotting down the data. The phone number on the sheet for Universal Coordinated Time is still active. We did not have a sun filter so it was a 3 man effort using a T2. One guy held the white board keeping the crosshairs in focus, I-man ran the tangent screws on the T2 and called out the angles, chief ran the stopwatch and kept notes. We only made the shot to get a Basis Of Bearings on jobs that did not have any published ROS maps with pipes that we could find and use.

Back in my Artillery days we did other ‘astro’ observations but simultaneous observations of the sun from two separate stations was our go-to field expedient method to establish an azimuth. If I recall correctly, the estimated accuracy was about +/- 0.3 mils.  This would equate to about 1 minute in DMS.  It has admittedly been many, many moons since I last performed any astronomic observations. 🤔