I thought I would play around with what is available online now to get ephemeris data. Jerry Wahl's Cadastral site is still up and there are some old ephemerides still available (link below), so I could use it to check against the settings for various sites currently available that would be needed to get the right data for azimuth determination. I looked at the US Naval Observatory site (links below) and the Jet Propulsions Laboratory Horizons site (link below). I was very pleased with what I was able to do ultimately, but it does require some effort to make sure the settings are correct and a bit of conversion to get the Greenwich Hour Angle that we are accustomed to using. I picked a date of January 1, 2014 for the three sites and compared results (comparison results are at the end).
I looked at Jerry Wahl's site and was able to find tables from 2014 at:
Sun and Polaris Ephemeris for Surveyors - January 2014 (cadastral.com)
Cadastral Ephemeris
On Jerry's site (Cadastral) he had this for January 1, 2014:
Sun
Declination: -23°01'17.2" GHA0: 179°10'23.0" Eq of Time: -3m18.46s Semi Diameter 16'15.9"
I then went the US Naval Observatory Astronomical Applications Department site:
USNO Ephemeris
On the USNO site I went to Geocentric Positions of Major Solar System Objects and Bright Stars.
Geocentric Positions of Major Solar System Objects and Bright Stars (navy.mil)
For Position Type, I selected Apparent Geocentric Right Ascension and Declination
For Celestial Object of Interest, I selected Sun
For Date, I selected 01/01/2014
For Time, I selected 12:00:00.000 AM
The results were:
Declination: -23°01'17.21" Right Ascension: 18h45m35.521sec Eq of Time: -3m18.5s
To get Greenwich Hour Angle (GHA) from Right Ascension (RA), you must also have the Sidereal Time at Greenwich (GST). The formula is
GHA=GST - RA
The Sidereal Time is available on the USNO site:
For Date, I selected 01/01/2014
For Time, I selected 12:00:00.000 AM
Tabular Interval, 1.00 Days
Iterations 1
Location 0 Latitude and 0 Longitude
The results:
Greenwich Sidereal Time Mean: 6h42m16.4224s
Greenwich Sidereal Time Apparent: 6h42m17.0580s
I used the Greenwich Sidereal Time Apparent in the formula and got:
GHA = GST - RA
GHA = 6h42m17.0580s - 18h45m35.521s
GHA = -12h03'18.463s
This converts from HMS to DMS by converting the HMS to H.hhh, then dividing by 24 (hours per day) then multiplying by 360 (degrees per full revolution) then from D.ddd to DMS which gives:
-180°49'36.945".
To make this positive add 360° which gives: 179°10'23.055"
GHA = 179°10'23.055"
The Diameter of the Sun is available from the USNO site under Topocentric Configuration of Major Solar System Bodies:
Topocentric Configuration of Major Solar System Bodies (navy.mil)
This tool also has the Right Ascension and the Declination, but the values are rounded off.
The Diameter of the Sun given from the USNO site on 1/01/2014 is 32'31.7" which divided by 2 to get the semi-diameter gives:
Semi-Diameter: 0°16'15.85
So the GHA (derived from Right Ascension and Sidereal Time), Declination, and Semi-Diameter (derived from the diameter) from the USNO match very well (within rounding errors) of the Cadastral data when all of the settings are put right (mostly using 12:00 AM for time and using 0 lat, 0 long for position, and Geocentric for position).
JPL HORIZONS Ephemeris
JPL Horizons is another option:
For this you set up what you want and can get all of the data at one time. Like the USNO site you cannot get GHA, but you can get Sidereal Time and Right Ascension which can get you to the Greenwich Hour Angle.
I used these settings:
Ephemeris Type: Observer Table
Target Body: Sun [Sol]
Observer Location: 0°E, 0°N, 0km
Time Specification: Start=2014-01-01 UT, Stop=2014-01-02, Step=1 (days)
Table Settings: custom
The Table Setting items I selected are:
2. Apparent RA & DEC
7. Local apparent sidereal time
13. Target angular diameter
Reference Time: ICRF
Date/time format: calendar format
Calendar type: mixed
Time digits: HH:MM:SS.fff
Angle format: sexagesimal format (hours/degrees minutes seconds)
Refraction Model: no refraction (airless)
The results from Horizons are:
RA: 18h45m35.48s
DEC: -23°01'13.7"
Sidereal Time: 6h42'16.957s
Angular Diameter 1951.695"
The RA and Sidereal Time give a GHA of
GHA: 179°10'22.155"
The Semi-diameter converts to
Semi-Diameter: 0°16'15.85"
Comparisons
Cadastral
GHA: 179°10'23.0" Decl: -23°01'17.2" SD: 0°16'15.9"
USNO
GHA: 179°10'23.055" Decl: -23°01'17.21" SD: 0°16'15.85"
JPL
GHA: 179°10'22.155" Decl: -23°01'13.7" SD: 0°16'15.85"
I tried a different example, from the online content that accompanies Ghilani's "Elementary Surveying: An Introduction to Geomantics"; here's the data
--------------------------------------Sun
Solar reduction using data from Example 18.17, June 29, 1988
Observer's Astronomic Position:
Latitude = 42°45'10.0"
Longitude = 73°56'30.0"
StopWatch Start Time, UTC: 0:00:00.0
DUT correction: 0.0sec
GHA of Star at 0h UT : 179°09'25.50"
GHA of Star at 24h UT : 179°06'27.40"
Declination of Star at 0h UT : 23°13'55.30"
Declination of Star at 24h UT : 23°10'30.00"
Time: 20:53:010 UTC
Azimuth to star 267°16'21"
(Only relevant parts of example included.)
Using the same navy.mil website as above, but choosing "Topocentric Positions of Major Solar System Objects and Bright Stars", I entered the above info and obtained the azimuth to the Sun as 267°16'22.1". I'm no expert on this stuff, but am I right in saying that the azimuth to the star could easily be adjusted by merely adding or subtracting the semi-diameter correction = Sun's semi-diameter/cos h where h is the angle above the horizon, depending on which edge of the Sun had been sighted? Wouldn't this skip many steps?
Keep up the good work Shawn. Naval Observatory has lots of good information. EOP etc . I have been there several times and was lucky enough to get to spend some time in the library and found that I realize just how un-educated I really am. Also how brilliant some of those people were to figure out so much and give us the mathematic foundation that we still have today in order to do all of what you just did. I mean they didn’t have computers or cesium or rubidium atomic frequency standards AKA atomic clocks. Pretty amazing how those who were stationed there and all over the world and had snail mail to get messages from one observatory to another by carriers from walking to horse boat so that they could do computations and probe and disprove theories. Now we can push a button and achieve results in mere seconds that if it were not for those before us that had the discipline and character and devotion. When you think about it a man lived through all weather conditions no grocery store AC unit or heat pump. And kept records that has set a foundation for our current Datums both locally and globally. You keep inspiring as this is the stuff that those up and comers need to see. Might be one day we will have to resort back is some huge issue happens and all the satellites get zapped by some huge solar or space activity.
I notice Jerry Wahl's data is necessarily geocentric, since there is no opportunity to put in the observer's latitude and longitude. The USNO and Horizons data is topocentric, that is, from the observer's point of view. When giving the observer's latitude, longitude, and elevation, the elevation is measured from the ellipsoid, not from the center of the Earth. So giving an elevation of 0 is not the same as a geocentric R.A. and declination.
Great find, Ashton. I was so focused on getting GHA and the right settings to get the same ephemeris data that I know works for the surveying programs I've used in the past for Azimuth determination that I didn't even notice that.
From a production standpoint, that would definitely be the way to go. I'm wanting to dig into geodetic surveying and field astronomy for my own personal interests, so I'm more interested in the components than just the final answer, but again, thanks for pointing that out.
Yes. This was one of the main points of my post was trying to find what combination of settings are appropriate for getting the ephemeris data that would work in surveying software programs I've used in the past. Topocentric vs. Geocentric was a big one.
I notice that the equations in Gilani's text make no distinction between a star, the Sun, or the Moon, except for semi-diameter. But the Astronomical Almanac for the year 2011 (pp. B84-B86) indicates a simple correction for parallax and aberration needs to be made to the R.A. and declination of the Sun because the observer is not at the geocenter; simple formulas are given. It says more elaborate corrections need to be made for the Moon because it is closer, and no formulas are provided. It appears the maximum parallax is about 8 arcseconds.
I found that also in the text I'm working from "Plane and geodetic surveying for engineers" by David Clark Vol. 2 Higher Surveying.
It gives the formula for geocentric parallax as GC= 9"*cos(h') where h' is the observed zenith angle to the Sun. "This is to be added to the observed altitude".
I played with the stated value of 9" and noticed that it corresponds to the Earth Radius (~4,000 miles) and the Distance to the Sun (93,000,000 miles). Arcsin 4,000/93,000,000 = 9"
So for the moon, I would guess the same formula would apply but use the Earth Radius (~4,000 miles) and the Distance to the Moon (226,000 miles). Arcsin 4,000/226,000 = 1°00'51" = 3,651"
The part about the moon is all conjecture on my part and could be entirely wrong.
As you play around. Polaris and the sun are not the only stars you can utilize. The sky is full of many stars that one can use. I am heading out of town in the morning for a week. But maybe i will remember upon my return and find my old notes and star charts. I imagine NGS still has a lot of information tucked away somewhere. The late Dave L did a class at Corbin I remember 1 around 2009 he conducted. I was living on the grounds at the time. He had the class randomly pick different stars and had some goggle looking things that identified them and then it was all fun time.
Now one thing that you must have is the correct amount of observation fluid. If that is not utilized the azimuth is just a guess lol. Just kidding but good old Dave D would probably say i was correct.
One possible reason surveyors might be looking through this site for astronomical azimuth information is to prepare for the NCEES surveying exam. I won't be taking that, but I looked through the free booklets (FS & PS) that can be downloaded from their site; I understand a copy of the booklet will be made available while taking the test. I didn't see anything about astronomical azimuths.
Also, I looked for the Astronomical Almanac for the year 2024 at the Government Publications Office and Amazon; it wasn't available yet. Apparently you can get it from some obscure maritime suppliers; maybe they're getting it from His Majesty's Nautical Almanac Office (HMNAO). But the fact that the book isn't readily available this late in the year indicates to me it is no longer used for day-to-day work and is only a reference book. Looks like the HMNAO's Almanac for Land Surveyors is the only remaining published almanac that can be obtained on a timely basis.
My take on this is astronomical azimuths have disappeared from the repertoire of most surveyors and has become a niche skill. But let me know if I've got this wrong.
I have done a lot of astro obs (mostly 30 to 40 years ago) using a T3 and a T2, and have used Jupiter, solar, polaris, the moon, and other stars.
When I was a student at Purdue, I suggested to my geodesy professor that we should be able to use the trailing edge of the moon, just like we do for solars. He didn't think it was possible, said that the orbit was not accurate enough. I felt it should be accurate enough using the right data, as they have had retroreflectors on the moon since the Apollo missions. I proved it was possible, using the polynomial coefficients available from the astronomical almanac. However, these polynomials are no longer provided by the USNO. It is imperative to use topocentric coordinates rather than geocentric due to the "closeness" of the moon as compared to the radius of the earth.
I did find a web page by a fellow named George Gladfelter where he has calculated these polynomials up until 2101 (item 10). Lots of other interesting stuff on this page...
I have downloaded the NOVAS software package https://aa.usno.navy.mil/software/novas_info (I downloaded the C version). It took some doing to figure out on a windows computer with the command prompt and Visual Studio, but I worked it out. It would be used by writing a short C program, and reading in a simple file of your own design that gives delta T, the difference between UT1 and UTC, the time of the observation, and the celestial body you want. The body could be the Sun, any planet, the Moon, or a wide selection of stars. In a few lines you can get the RA and declination of the body, and its azimuth and altitude. I've attached the output file for the example that comes with the software.
A few advantages are (1) it is self-contained, no need for an internet connection and (2) it runs fast; I wouldn't be able to time it with a stopwatch, I'd have to build timers into the program.
You are correct in that almost no one is doing astro obs for azimuth nowadays (other than for fun 😁), but if the GNSS systems ever go down...it will become a valuable skill
While not at all likely to happen, it could happen due to a massive coronal ejection or a war which escalates...
A mundane reason GNSS could become unusable for some people would be GPS jamming by truck drivers who don't want their bosses to know where they are, which only affects the vicinity of the truck. Or, a government shutdown could make OPUS unavailable, so those accustomed to that work flow would have trouble.
I have ephemeris files through 2015-2027 in a text file format - now posted here Document->Public folders>ehpemerisKBW. (sorry if you already saw this - I previously didn't reply in the thread)
It's been about a decade since I've done any celestial observations, and at that time I was using a manual total station with a solar filter. Very simple.
A couple of years ago, I bought a Wild T-2 and that really got me interested in doing celestial observations again. I observed the Sun on Sunday. One thing I found out is that I need to develop better skills at reading the circle. I had several observations that were off by 10' because I didn't read the scale correctly. Since it was my first field use of the T-2, I wasn't too upset by this. I'm sure that as I practice, I'll be able to read the scale quickly and accurately and be able to reflexively use the adjustment knobs without having to hunt for them.
I did two sets of 8 observations (four observations in face 1 and four observations in face 2)
I used the USNO application, and as Ashton commented, I simply had the application determine the azimuth of the Sun at the UTC for each of my observations. Eventually I'll develop a program to perform the calculations, but for the first few times, I wanted to be able to quickly reduce the observations to see if my field procedures and equipment were proper. As discussed above, the semi-diameter of the Sun must be applied (since I was using trailing edge by projection onto a white sheet of paper, watching for the vertical crosshair to disappear). This required a few steps, but ultimately appears to have given good results.
My first set of eight observations gave an azimuth to target of 7°08'23.7" with an extreme spread of 24.7" and a standard deviation of 9". One of my observations was off by 20' and another by 10', almost certainly from misreading the circle.
My second set of eight observations gave an azimuth to target of 7°07'57.5" with an extreme spread of 25.5" and a standard deviation of 8". I had four observations that were off by 10', almost certainly from misreading the circle.
So the difference between the average of the two sets is 26.2".
As I said before, the instrument is a Wild T-2 (direct reading to 1 arc-second) with an erect image. I was sighting the strobe on a radio tower that is about 7,000' away. I used my cell phone with an GPS app that gives UTC for time and used a stopwatch to clock each pointing. I'm hoping to incorporate a shortwave radio for time in the near future. Position was determined by the same cell phone GPS app. As mentioned, pointing was accomplished by projecting the image on a white sheet of paper on a clipboard, a method that works well for theodolites but not for total stations. I know my sighting of the Sun needs improvement. Catching the crosshair on the trailing edge felt a little loose.
Even though I had some decent consistency in the two observations, I still wasn't sure if they were accurate or if I had some large bias in my results, so early this morning I took my robot (GeoMax Zoom 95, with 2 arc-second accuracy) out and did observations on Polaris. One problem that I encountered is that I don't think my robot has an illuminated crosshair. I worked around it by indirectly shining a flashlight into the objective lens. This worked well, except that it required the use of my hand, which was also busy holding the stopwatch while the other hand manipulated the horizontal and vertical motion knobs.
I was pleased with my results. I turned one set of eight observations (four in face 1 and four in face 2). The average azimuth was 7°07'10.3" with an extreme spread of 25.8" and a standard deviation of 9". I was turned to the same strobe that I used in the day-time Solar observations. I say it was the same strobe, the day-time strobe is white and the night-time strobe is red, but I'm pretty sure it's the same housing and reflectors.
So my azimuths thus far are 7°08'23.7", 7°07'57.5, and 7°07'10.3". This is a pretty ugly spread, but there don't appear to be any large-scale errors. I'm sure the consistency will improve as I continue to practice.
I'm looking forward to attempting a celestial resection to determine Latitude and Longitude. I'd never heard of this process before, but it's based on the vertical angles observed to a pair of stars. The vertical angle needs to be extremely precise and atmospheric refraction must be accounted for. To test, I observed the vertical angles of Polaris while I was pointing so I could compare to the computed position of Polaris given by the USNO app to see how they compared.
To see how the vertical angle from both face 1 and face 2 would average, I noted the difference of the observed altitude to the face 1 observations to the computed altitude from USNO, and the difference in the face 2 observations to the computed altitude from USNO. Face 1 was -8.4" on average from the computed altitude. Face 2 was +7" on average from the computed altitude. This would suggest that the average of the eight altitude observations were different from the computed altitude by -1.5". From what I've read, using a 1-second instrument should yield a latitude and longitude within 2 or 3 arc-seconds with the resection method. It looks like I might be able to do just that.
I taught a course in Geodetic Astronomy at the University of New Orleans in the early 1980s. I found the course and Lab pretty easy to conduct and students were able to follow with success when I introduced the simple programmable calculator functions based on Jean Meeus. We used the old Smithsonian Astrophysical Observatory (SAO) Star Catalog and compared it to the (at the time) FK-4 Apparent Places of Fundamental Stars. Observations and calculations were easy, almost trivial. We were using one-second theodolites and one zero-point one-second theodolite (BC-4). All that old gear is now taken out once every other year for a single Lab at LSU ... whenever I get enough students for the course to "make" sufficient enrollment. I don't bother with the old HP-41CV software anymore, but that sure made it an easy task, way back then. Guess it could be resurrected nowadays with the HP41 software for iPhones ... If you restrict yourself to stars, all you need is Meeus and a Star Catalog and you'll be good to better than one arc second. The current "Explanatory Supplement to the Almanac" will work also, if you're not of the faint of heart. Meeus just cuts to the chase.
One important item that is often overlooked when using an older instrument is mislevelment, or more properly the inclination of the standing axis. Newer instruments that have dual axis compensation greatly minimize this effect. This is NOT corrected by D-R. It is amplified on steeper sights (i.e. polaris
The T2 that I have has a compensator which makes it easy to either level up very accurately or be able to apply a correction. I explain this in a paper I wrote many years ago (1997). Here is a link... https://staging.rpls.com/?attachment=1614808&document_type=document&download_document_file=1&document_file=107
From the manual...
The Stellarium app (Windows, Mac, Linux, phone, web) will provide ephemeris for most of the celestial objects (over 600,000).