Surveying by the Stars, Part II: Solar Observation (Hour-Angle Method) and Polaris Observation

Please obtain written permission from author/compiler Wayne Twigg, (copyright 2017 A.D.) before using for educational and instructional exercises. We Surveyors today record our measurements to [a supposed] accuracy of one second of arc. In fact, one second of arc subtends the width of a human hair at……..

Facts: Earth’s radius = 3,961± miles. At this place on the Earth’s surface, 1 second of Latitude = 101’±; 1 second of Longitude = 78’± “He must be blind who does not at once see, from the best and wisest structure of things, the infinite wisdom and goodness of their almighty Creator; and he must be mad who refuses to acknowledge them.”

….preface to the 2nd Edition of Sir Isaac Newton’s The Principia by Roger Cotes, Plumian Professor of Astronomy, Cambridge, England, 12 May 1713  Radio Station WWV broadcasts UTC time scale (Coordinated Universal Time).  Available over shortwave radio at 2.5, 5, 10, 15 and 20 MHz.  WWV telephone (303)499-7111. There is a time announcement delay of less than 30 ms (“land line”) and up to 150 ms (cell phone).  To convert to UT1 (Survey Time), apply DUT correction in 0.1 seconds, which is encoded in the voice announcement as the number of double-ticks during the first 16 seconds of each minute; positive sign in seconds 1 – 8; negative sign in seconds 9 – 16. The Equator is perpendicular to the Poles. The Horizon is perpendicular to the Observer’s Zenith. Complementary angles: Latitude and Co-Latitude; Altitude and Zenith; Declination and Polar Distance. Angle Z is the angle west (or east) from the N. Pole. By definition, all meridians pass through both Poles. The “t” (a.k.a. meridian) angle is formed at the Pole. If LHA is < 180° (as shown), then “t” and LHA are =. In other words, Local Hour Angle (t) = Greenwich Hour Angle – West Longitude. Here is (Only a star teasing! chart to Every- help one can locate find the the Sun Sun). in the sky.  Accuracy to 5 seconds of arc  Minimum of 3 observations (but you can easily get 5)  Needs both Latitude and Longitude  Must be timed using Precise Time, such as tuning to Station WWV with a shortwave radio. Accuracy of time is critical.  Does not need Vertical or Co-Vertical (a.k.a. Zenith) Angles  Instrument leveling must be very precise; use a striding level if you can get one.  Use Hour Angle Method when observing (1) between ½ hour after sunrise and 9:00 a.m. Local Standard Time, and (2) between 3:00 p.m. and ½ hour before sunset Local Standard Time. The closer it is to noontime, the faster the Sun moves and the steeper it is in the sky. Then you can’t see it through your scope anyway without a right angle eyepiece. ½ hour after sunrise to 9:00 a.m.; 3:00 p.m. to ½ hour before sunset Here is a DIRECT He puts Sun’s recommended image on the D&R sequence proper side of for sighting the the vertical Sun. cross-hair (as The Surveyor shown). The acquires the REVERSE instant the Sun Sun’s image on a “leads” onto the white card. He vertical hair’s focuses both point-of- image and tangency, he hits cross-hairs. “lap” button. Let’s practice with the stopwatch. ✓ Contact Station WWV by shortwave radio or cell phone (303)499-7111, but remember that switching may cause delay of 150 msec. Start stopwatch at exact minute (may need more than one call). ✓ Two-man crew: Instrumentman/Observer sets up instrument and acquires backsight Direct on Zero; then he turns to the sun, gets the white card ready and notifies Notekeeper when he has acquired the sun’s image and is ready to start readings. ✓ Notekeeper writes start time as hour and exact minute. He will record “lap” time for each observation. At end, he checks stopwatch against WWV and notes DUT as well as synchronous correction, if any. ✓ During the observation session, the Observer calls “Rea-a-a-a-d-y-y-y” “TICK” when sun’s image becomes tangent to the vertical crosshair. He reads the horizontal angle aloud to the Notekeeper. ✓ Immediately at “TICK”, the Notekeeper hits “lap” button and afterward writes the minutes, seconds and tenths of seconds. Subsequently he records the horizontal angle as he heard it from the Observer. ✓ Observer re-acquires sun’s image and again calls “TICK” at tangency. At “TICK”, the Notekeeper hits “lap” button, records minutes, seconds and tenths of seconds; he hits “lap” button again to continue stopwatch and again records the horizontal angle as he heard it from the Observer. ✓ Repeat for eight more observations (or at least, sufficient for three complete D&R sets). ✓ Notekeeper stops stopwatch at moment of final observation and records last set of minutes and seconds. He then notes the daily hourly time and makes sure that the subtraction of his start time and his ending time equals the duration of the session’s set of minutes and seconds. Observer makes a Reverse backsight check. Field Notes: Hour-Angle Sunshot

This Observer has made 3 D-R sets on the sun. He also noted the DUT correction as well as a stopwatch correction.

Back in the office, both corrections are applied and the angle sets averaged. Note the Lat/Long of the observation station, also the magnetic bearing to the backsight.

This poor Having an survey schlupp HP-41 at the who observed in time, he then the field then keyed EKSI’s computed his program into it own sun shots and used it to in the office. He calculate all decided to six observa- compute each tions. field observation This sheet separately and represents the then average calculations the results. for Observa- Notice that the tion No. 1, angle right is the with average same as the first of the six angle right from shown below. the field notes. First, you have to find it! (Also, remember compass and co-latitude).  Polaris, a circumpolar star, traces a 1°± arc around the North Pole.  During its counter-clockwise circumpolar path, it is directly aligned with True North at “Upper Culmination” and at “Lower Culmination” when it is exactly on line between the Surveyor’s Zenith (Meridian) and the North Pole. Then all the Surveyor has to do is sight it.  However, it is moving quickly then, being at Culmination only for an instant. It is easier for the Surveyor to track it when it is near Eastern or Western Elongation (90° from Culmination).  It crosses every Meridian once during each Sidereal Day.  The distance around the circle from the Surveyor’s Meridian to Polaris is called the Local Hour Angle (LHA).  The distance around the circle from the Greenwich (or Prime) Meridian to Polaris is called the Greenwich Hour Angle (GHA). This is the angle that is/was published in the EKSI Ephemeris.  We are here at 39°29’± North Latitude. The Co-Altitude (90° minus angle up from Horizon) to Polaris is approximately 50°41’. …is the conical wobbling movement of Earth’s axis that causes a 23.4º circle (the angle of the Ecliptic) to be scribed onto the Celestial Sphere. Astronomers theorize that precession has a period of 26,000 years. If any of you are still surveying in the Year 27985 A.D., you will have to sight the star Vega (in the constellation Lyra) as the North Pole, instead of Polaris. Here in 2017 A.D., wasn’t it considerate of God to give us Land Surveyors here in the Northern Hemisphere the star Polaris to aim at? Professor a short- Porter W. wave radio. McDonnell, Jr. from his He also 1975 class on wants two Celestial sets D&R, Observations with first at Penn State B.S. from Mont Alto. close to 0° Note that and the he has this second B.S. form set up from close for the use of to 90°. This is one …it notes the of the Local computation Magnetic sheets from Declination the and also Appalachian computes Chapter’s the Mapping Polaris Angle for observation conversion of 2003. of the True This sheet North not only Azimuth to computes MD Grid the North Azimuth. bearing to the backsight…. Here’s one possibility:  https://celnav.de/longterm.htm  This long term almanac calculates Greenwich Hour Angle (GHA) and Declination for the Sun and Polaris.  However, you need to calculate DT by the formula DT = 32.183 sec. + (TAI-UTC) – DUT1  For this, use the USNO Multiyear Interactive Computer Almanac (MICA) or consult the USNO website Any other questions or comments? of grateful indebtedness to the following Land Surveying giants for the use of their instructions, programs and data

 Robert E. Angle, LS  Professor Porter McDonnell, Penn State University, Mont Alto Campus  Professor Jim Mask, Catonsville Community College  Dr. R. Ben Buckner, Ohio State University  Drs. Elgin, Knowles & Senne (EKSI) for their Celestial Observation Handbook and Ephemeris  U.S. Naval Observatory (USNO) Our profession of Land Surveying is intimately connected with the sky’s celestial bodies and their movements. There is very much that we have not mentioned in these presentations, but what we have seen should be enough to challenge you to perform your own celestial measurements from this constantly moving, constantly changing platform of observation we call “Earth”. Now let’s all go outside and perform a sun shot!