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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Captain Cook's Sep 07th, 1773 Lunar revisited**

**From:**Paul Hirose

**Date:**2012 Jul 20, 16:47 -0700

Antoine Couëtte wrote: > From Ulietea Harbour (S 16°45'33" W151°29'48") the Moon Upper Limb Height was 43°29'0 at time UT = 17h02m55s0 and the Moon was in Azimuth 312°9. I am computing this way with the Moon first since most likely the Moon Height is the most reliable one for refraction correction and also for the reasons given in my previous post on this subject. I also computed a time sight with the Moon, at the same assumed position (S16°45.55' W151°29.80' +5 meters), atmosphere conditions (78° F at observer, altimeter setting 29.92), dip (3' 50"), and ∆T (+16.4 s). Results (UT1): 17:07:19 Couëtte lunar distance 17:02:55 Couëtte time sight 17:03:18 Hirose time sight At my time the observed altitude of the Sun (corrected for semidiameter, refraction, etc.) is 17.1' more than the predicted altitude. The observed lunar distance is .9' less than the predicted distance. The Astronomical Almanac table in Section K says ∆T = +16 at 1773.0 and also at 1774.0, so +16.4 s is reasonable. My computation confirms that Antoine's assumed position, the lunar distance, and the altitudes cannot all be correct: -00.004' observed - predicted lunar distance +41.95' Moon altitude observed - predicted -39.69' Sun altitude observed - predicted The above data are based on his assumed position and the time he computed from the lunar distance (with extreme accuracy). For the Sun and Moon observed altitudes I used the angles he gave, less 3' 50" for dip. I also solved for time and position: 17:07:18.5 S16°45.55' W151°29.80' initial values 17:05:54.8 S16°30.65' W151°53.78' Hirose solution 17:06:04.9 S16°22.4' W151°53.8' Couëtte "Second Solution" Kermit's solution makes the observed and computed lunar distances virtually identical. That's good. But the observed Sun altitude is 3.8' less than the computed value, and the Moon altitude 3.9' less. Not that my solution is much help. The computed angles match the observations to .01', but the position is tens of miles away from the modern coordinates of the anchorage. I have followed Alex's contributions with interest. His idea that perhaps the date was wrong seemed good enough to check out. But I discovered the lunar rate of 12°/day removes ambiguity. Given a lunar distance and approximate date, but no information on the observer's position, you can still compute a date and time accurate to about 2 hours. Simply assume the angle is geocentric. The parallax error will be 1° at most. As for his theory that the altitude observations were not simultaneous with the lunars, the Moon and Sun altitude rates were -10.7 and +14.1 '/min, respectively, and the observed - computed were +42.0' and -39.7'. This implies the altitudes were shot 3 or 4 minutes before the mid time of the lunars. But I wonder, were the observers that dumb? Isn't it more logical, and just as easy, to shoot 5 lunars, 2 altitudes, then 5 more lunars? Here is the full output from my lunar program, where I start with Kermit's values and let it solve for time and position. Ephemeris is the JPL DE422, their latest long term ephemeris, successor to DE406. IAU 2006 precession and 2000A nutation models. GRS80 ellipsoid. The "observed" altitudes are actually 3' 50" less than the observed angles to correct for dip. My program does not automatically apply that correction. Program Lunar2, by Paul S. Hirose. Initial conditions. estimated time: 1773-09-07 17:07:18.52 UT1 1773-09-07 17:07:34.88 TT (Gregorian) JD 2368884.5 + 0.713598 (TT) 16.400 seconds delta T estimated position: -16°45.55' -151°29.80' north lat, east lon 5 meters above ellipsoid atmosphere: 25° C (78° F) at observer 1013.3 mb (29.92" Hg) altimeter setting 1012.7 mb (29.90" Hg) actual pressure Moon altitude observation: 43°25.17' observed upper limb altitude 0.97' refraction 14.93' unrefracted semidiameter 43°09.26' unrefracted altitude of center 42°27.31' predicted altitude 0°41.95' intercept 311°56.18' predicted azimuth Sun altitude observation: 12°34.57' observed lower limb altitude 4.02' refraction 15.89' unrefracted semidiameter 12°46.43' unrefracted altitude of center 13°26.13' predicted altitude - 0°39.69' intercept 79°35.88' predicted azimuth Moon to Sun predicted separation angle: 106°21.42' center to center, unrefracted 3.58' refraction 106°17.84' center to center, refracted 14.93' Moon near limb refracted semidiameter 15.84' target near limb refracted semidiameter 105°47.07' Moon near limb to Sun near limb 105°47.07' observed angle - 0°00.004' observed - predicted unrefacted separation angle rate: -16" per minute (topocentric) 77% of total angular velocity -------------------- Solution, after 3 iterations. corrected time: 1773-09-07T17:05:54.84 UT1 1773-09-07T17:06:11.24 Terrestrial Time 16.400 seconds delta T corrected position: -16°30.65' -151°53.78' north lat, east lon 53° LOP crossing angle geocentric coordinates (true equator and equinox): 3h52m13.08s +15°39'46" Moon RA and dec. 14.77' apparent semidiameter 11h05m49.32s + 5°48'19" Sun RA and dec. 15.89' semidiameter 6h06m34.36s local apparent sidereal time geocentric separation angle and rate: 105°58.01' center to center -27.1" per minute 85% of total angular velocity illumination conditions: 79.9° 12.8° Sun unrefracted az, el 306.2° Moon to Sun position angle (0 = 12 o'clock) 73.5° Moon phase angle (0 = full, 180 = new) position angles: 306.2° Moon to Sun 37.1° Sun to Moon recommended limbs: Use Moon upper limb. Use Moon near limb. Moon altitude observation: 43°25.17' observed upper limb altitude 0.97' refraction 14.93' unrefracted semidiameter 43°09.26' unrefracted altitude of center 43°09.26' predicted altitude 0°00.00' intercept 312°25.26' predicted azimuth Sun altitude observation: 12°34.57' observed lower limb altitude 4.02' refraction 15.89' unrefracted semidiameter 12°46.43' unrefracted altitude of center 12°46.43' predicted altitude 0°00.00' intercept 79°53.91' predicted azimuth Moon to Sun predicted separation angle: 106°21.56' center to center, unrefracted 3.72' refraction 106°17.84' center to center, refracted 14.93' Moon near limb refracted semidiameter 15.84' target near limb refracted semidiameter 105°47.07' Moon near limb to Sun near limb 105°47.07' observed angle 0°00.000' observed - predicted unrefacted separation angle rate: -16" per minute (topocentric) 77% of total angular velocity -- I filter out messages with attachments or HTML.