# NavList:

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

**Re: Lunar trouble, need help**

**From:**Kent Nordstr�m

**Date:**2008 Jul 5, 13:19 +0200

Georeg wrote [5635]: The next point of issue is the Moon parallax. Kent writes "It is unclear how George measured his local parallax" It's simple enough. See navlist [5530]. We agree precisely on the figure for Moon HP, quoted by Kent to be 56m 36.5s, and by me, from Skymap, to be .9435�, which works out as 56.61', or 56m 36.6. Can't expect much better than that! Yes, I have taken the moon's HP from Umland. But it might be a little confusion here so let me try to explain how I calculate the moon's parallax. Firstly, George is right about the value. The error in calculation is on me (very embarassing) but the good news is that the model seems to calculate correct. I used 61d 41m 4,19s as (wrong) input data which gave 26m 50.39s. The input should have been 60d 41m 04,19s. When using this the parallax will be 26m 42,3s (George 26m 44s). So it seems that we don't have a disagrement here. What my model does is as per below. As can be seen the calculation includes two corrections for earth flatness (maybe a better English term is oblateness?): - find the azimuth to the moon - find the difference between the geographic and geocentric latitude - multiply this difference with cosine for the azimuth The azimuth is approx. 111d and the diff. between the latitudes is 5m 45s. The product is +2m 6,46s, which gives a "local altitide" of 60d 38m 57,73s + 2m 6,46s = 60d 41m 04,19s to be used for parallax calculation. Due to the earth oblateness the value is added to the true local altitude if the azimuth is greater than 90d (the moon is pointing away from the pole), otherwise the value is negative. Next is a small correction to the moon's HP with the arguments latitude and HP. This gives a "HP" of 56m 36s - correction 0,78s = 56m 35,22s. Now the parallax is calculated as arcsine (sine "HP" x cosine "local altitide") = arcsine ( sine 56m 35,22s x cosine 60d 41m 04,19s ) = 27m 42,3s (George 27m 44s). Geroge wrote: Kent has ignored the augmentation factor, which allows for the fact that an observer is significantly closer to the Moon, when it's high in the sky, than when its near the horizon. Indeed, he has taken "augmentation of Moon's semidiameter" into account, in making an exact calculation of Moon's altitude corrections (but when that has little or no influence on the final lunar distance) but neglected to do so in correcting the lunar distance for semidiameters (when it's crucial). I am not sure I understand this comment. So again let me try to explain what my model does for the moon. The measured altitude is corrected for dip and the moon's semi-diameter: 61d 05m 16,4s - dip 10m 10,9s - SD 15m 25s = 60d 39m 40,5 s. To this two corrections are done: - augmentation of -13,3 s. The minus sign depends on the measurement of the UL. - refraction correction of + 0,34s (diff .in refraction form UL to geocentre). For finding the apparent distance (what I believe George defines as d) my model does the following: Obs. distance + corr. for index error +/- SD for the moon +/-SD for the sun (if used) +/- corr. for augmentation of the moon +/- refraction correction for the moon +/- refraction correction for the sun (if used). The correction for augmentation is based on the arguments moon's semi-diameter and apparent altitude. Is this what George means... "but neglected to do so in correcting the lunar distance for semidiameters (when it's crucial)."??? Is the "augmentation factor "someting else? Georeg wrote: Kent doesn't hasn't yet told us what actual values he puts in for his Sun and Moon refraction, or his Sun parallax, and we need to know these for a comparison (or at least, know how they are somehow to be included into the lunar distance calculation.). My input data were: - moon's refraction -29,82s - sun's refraction -1m 21s - sun parallax 7,3s Kent N ----- Original Message ----- From: "George Huxtable"To: Sent: Wednesday, July 02, 2008 10:49 PM Subject: [NavList 5635] Re: Lunar trouble, need help I can see why the Kent's correction to the lunar distance for semidiameters differs, by a fraction of an arc-minute, from my own. We agree about Sun semidiameter, but differ, a bit, about the Moon's. Kent used- Sun SD: 15m 45s Moon SD: 15m 25s whereas mine were (translated into the same units)- Sun SD. 15m45s Moon SD (as seen from Earth's centre) 15m 25s Moon SD (augmented, to allow for altitude of 61 and-a-bit degrees) 15m 39s. Kent has ignored the augmentation factor, which allows for the fact that an observer is significantly closer to the Moon, when it's high in the sky, than when its near the horizon. Indeed, he has taken "augmentation of Moon's semidiameter" into account, in making an exact calculation of Moon's altitude corrections (but when that has little or no influence on the final lunar distance) but neglected to do so in correcting the lunar distance for semidiameters (when it's crucial). Kent has simply taken the semidiameters from Henning Umland's website, but as Umland doesn't know the altitude at which the Moon was being measured (because it depends on where the measurement is being made from), that correction has be applied next, by him. If Kent recalculates, taking augmentation into account, I suggest that he will find perfect agreement between us, at least as far as the lunar distance corrected for semidiameters. Perhaps we can draw a line under that one, and go on to the next discrepancy between us. =============================== The next point of issue is the Moon parallax. Kent writes "It is unclear how George measured his local parallax" It's simple enough. See navlist [5530]. We agree precisely on the figure for Moon HP, quoted by Kent to be 56m 36.5s, and by me, from Skymap, to be .9435�, which works out as 56.61', or 56m 36.6. Can't expect much better than that! Now, if we're bothered to, we can make the correction for the reduction in the Moon's HP on account of the spheroidal shape of the Earth, described by Kent as "Earth flattening". At such a low latitude of 15�, this amounts to only .01' (taken from a table in a modern Norie's), so we end up with a corrected HP of 56.60' Then multiply that by cos alt, to get the actual parallax at that altitude. True altitude of the Moon's centre, after allowing for dip and semidiameter, I get to be 60.6523�, or 60� 39' 08' in Kent's notation. This gives me Moon parallax of 27.74', or 27' 44". That has to be compared with the figure Kent quotes of 26m 50.39s. There's a significant difference here, of getting on for a whole minute, so my next question is : exactly how did Kent arrive at a Moon parallax of 26m 50.39, starting from an HP of 56m 36.5s? Kent doesn't hasn't yet told us what actual values he puts in for his Sun and Moon refraction, or his Sun parallax, and we need to know these for a comparison (or at least, know how they are somehow to be included into the lunar distance calculation.). Did Kent's final figure, for cleared lunar distance, come from some tables, or from a log-trig calculation, or a computer / calculator program, or what? Details would be of interest. George. contact George Huxtable at george@huxtable.u-net.com or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To unsubscribe, email NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---