The Rooter dragged me to an estate sale. I immediately headed for the garage for the good stuff. I could not believe my eyes for there on the junk table was what appeared to be a mint condition Kollsman MA-2 hand-held sextant complete with a fiberglass carrying case and a power cable. I cut my teeth on one of these and always thought it would be fun to have my own. These sell broken on eBay for $350. Trying not to look interested I asked the lady at the table what it was and what they wanted for it. She said, “Something dad had, you can have it for $50.” Slowly, with my heart racing, I thumbed through my wallet until I came up with the cash. I put the sextant in the case and stashed it in the trunk of my car. The Rooter was wrapping up a marathon haggling session over a Persian rug and got it for $50. We headed home.
The name plate indicated it was an MA-2X. I had never heard of one with an X suffix and nothing came up on Google but I did find the MA-2 Operator's Manual . This was very different from what I thought I had purchased. It seemed much more advanced. The averager mechanical readout had been replaced by a Liquid Crystal Display and there was an access door on the back of the housing where the mechanical average mechanism would have gone. Inside there was a battery compartment labeled CLOCK BAT and several push buttons?
I applied power and heard a motor whirring inside and knew this was something really different because the MA-2 had no motor. I looked through the eyepiece and saw an HH:MM:SS digital clock readout superimposed in the upper left corner. There was no bubble visible so I instinctively reached for the INCREASE BUBBLE knob. Instead of controlling the bubble size it operated an optical zoom and at high magnification it was apparent the image was gyro stabilized. Wow, what do I have here? The X must be for eXperimental. I depressed the average actuator button and the LCD immediately displayed two lines of data. The first looked like the altitude angle as DD: MM. MMM and the second the time as HH: MM: SS. This was many times more accurate than the DD: MM elevation readout of the standard MA-2 mechanical averager and if true it would rival GPS accuracy. I replaced the clock battery and played with the buttons until the clock was synchronized with my “Atomic” clock.
This gave me an idea for a new geocache; but first a primer on celestial navigation.
The navigator does not measure his position directly. Instead measures the difference in his actual position relative to an assumed position. This is the same thing a GPS does and the math is very similar. He measures the star’s angle relative to the celestial horizon. This is called Ho for Height Observed. Ninety degrees minus this angle (90° – Ho) is the great circle distance expressed in degrees from the observer’s position to the point on the Earth where the star is its zenith i.e. directly overhead. This is called the star’s subpoint. Using a celestial almanac and astronomical tables he determines the star’s angle above the celestial horizon as it would be observed from the assumed position. This is called Hc for Height Computed. He also determines the star’s true bearing (Azimuth) as it would be observed from his assumed position.
He plots his assumed position on a chart and draws a line through it at the azimuth to the star. He then computes Δ, the difference between the observed height and the computed height as:
Δ = Ho – Hc
If Δ is a positive number his actual position is closer to the star’s subpoint and if negative it is farther. He converts Δ to distance at the rate of 1852 meters (one nautical mile) per minute of arc and locates the point on the star’s azimuth line at distance Δ from the assumed position. There he constructs a line segment called a Line of Position (LOP) perpendicular to the star’s azimuth line. His actual position is somewhere on that line.
It takes a minimum of two intersecting LOPs to determine actual position but in star navigation it is customary to use three.
Line Of Position (LOP) For One Star
I waited until dark on the eve of The Rooter’s birthday and headed to a location where I was considering placing a cache. I made the following readings:
- Star: Kochab, Ho: 30° 40.404’, Time 2013/03/10-02:00:00 Universal Time
- Star: Regulus, Ho: 42° 46.743’, Time 2013/03/10-02:02:00 Universal Time
- Star: Aldebran, Ho: 48° 58.131’, Time 2013/03/10-02:04:00 Universal Time
At home I computed the following from my assumed position (the coordinates at the top of this page) using astronomical tables:
- Star: Kochab, Hc: 30° 40.494’, Azimuth: 16.6° True, Time 2013/03/10-02:00:00 Universal Time
- Star: Regulus, Hc: 42° 46.455’, Azimuth: 112.1° True, Time 2013/03/10-02:02:00 Universal Time
- Star: Aldebran, Hc: 48° 58.296’, Azimuth: 248.5° True, Time 2013/03/10-02:04:00 Universal Time
You can check your answers for this puzzle on Geochecker.com: Precise or Fuzzy.
If you choose to do a mathematical solution you may want to use the following link: Great Circle Calculator Use Earth model: Spherical (1'=1nm)
FTF Honors go to Elonka