# NavList:

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

**Re: Lunar trouble, need help**

**From:**George Huxtable

**Date:**2008 Jul 8, 00:37 +0100

Kent wrote, about the refraction corrections- "It might be easiest to explain by starting with what has to be done when reducing altitudes. In Jeremy's case the UL of the moon was measured. The refraction has to be done for the geocentre of the moon and not on the altitide for the UL." He and I disagree here. In practice, in the case we are considering, the difference in refraction between the Moon's centre and upper limb is pretty infinitesimal: no more than 0.4 arc-seconds. Presumably, Kent is keen on such details because he wants to be completely rigorous, and get the principles right. And it seems to me that he hasn't got the principle right here. I will try to convince him. The light-ray, coming down through the atmosphere, that is being observed with the sextant, is the light that is from the Moon's upper limb. And it's the bend in that ray that constitutes the refraction. Refraction is the difference between the angle at which the light arrives, and the angle at which it would arrive if the Earth had no atmosphere. So when we correct for refraction the observed sextant angle (above the true horizon) of the Moon's upper limb, that then gives us the true elevation of that limb, above the true horizon, as would be seen by that observer if the Earth had no atmosphere. Then the Moon's semidiameter allows for the difference between that true altitude and the Moon's centre; the true difference between them, refraction no longer playing a part. Of course, if working with tables or formula that work with zenith distance rather than altitude, you have to use the complement (to 90�) of the altitude, but the reasoning doesn't change. He continues [with my comments in square brackets]- "Consequently in my way to do the reduction I start with refraction on the UL ..." [all right so far... ] "and then I calculate the difference in refraction for the UL - SD for the moon." [that's the bit that's unnecessary, and indeed wrong]. This is then a correction for achieveing a correct refraction value. In this case the angle between the distance and the vertical is 90d (of course). If George is already from the beginning calculating the refraction for the geocentre [no, I'm not] that is fine but then there is, as I see it, a difficulty coming up later when treating the distance." ==================== Kent continues, about another correction which could be made to the lunar distance- "I all cases there is an angle between the distance line and the vertical used for measuring the altitude. Refraction compresses the body - more on the LL than on the UL - which means that there is a need to correct also the distance for refraction. The body is not circular but compressed in directions apart from th the compression in the vertical. The arguments for this correction is altitude and angle between the distance and the vertical. This correction should be done for the moon and the sun. As an example for altitude 8d 30s and angle of 45d the correction is about 5 arcsec's, while when the angle is 0d, as in altitude reduction, the correction is 10 arcsec's. If the other body is the sun then a similar correction should be used. So it is not negligible to avoid thiscorrection when reducing the distance." [I agree that in principle, this is a correction that might be considered. In Raper, (1864) it's table 53, "correction of the lunar distance for the compression of the vertical semidiameter". And I agree that if one were forced into observing at very low altitudes, such as Kent quotes in his examples, then it might indeed be worth making. But most navigators would do the damnedest to avoid measuring lunars below 15� altitudes, in which case this correction never exceeds 3". In the examples we are considering, it's less than 1".] "If George takes a look in the English reference below and puts this into graph I believe George will agree with me." [It depends on the precision one is hoping to work to, which is limited by the observing instrument, the observer's skills, and the environmental conditions he has to work under. I would ignore such corrections, for observations made in a marine environment. ] "I have three Swedish references and one English: Jeans, Navigation and Nautical Astronomy 1853, page 105, header: Refraction, oulines the need for this correction. Note: I have not searched actively for English referencies." ======================== About another correction, for the contribution to Moon's parallax due to the Earth's oblateness. "George wrote: I'm not familiar with that correction term >which was cos aziumuth x (diff geographic and geocentric latitude>, and perhaps Kent will explain it, or refer to a text that does. But as far as I can estimate, its practical effect in our exercise is less than an arc-second, and I doubt if it can ever work out to be much more than that, so it seems well worth ignoring Firstly I conclude that George does not compensate for the earth oblateness. Unfortunatle I do not have any English reference for this way to correct for earth oblateness, but I have two Swedish. I guess that this way of calculating has been described in the German "Lehrbuch der Navigation" concerning "moondistanzen, strenger metode" from about 1860 (textbook navigation...rigirous method). But I am sure that George os able to do a search amongst English litterature. [The correction I made is from Chauvenet, "Spherical and Practical Astronomy" (1863 and many later reprints), table XIII "Correction of the Moon's eq. parallax" (actually, a reduction)and in text Vol I, page 104 to 126. Kent should take a look at Chauvenet, who provides all the rigour he could ever ask for! He also seems to get everything right. It's also in a table in a modern Norie's "Reduction of the Moon's horizontal parallax", from which I took, in [5530] the value -0.0002�, to slightly tweak the parallax of 0.4622. I agree with Kent that this correction can be worth applying at higher latitudes, but al lat = 14, it was hardly worth bothering with. This corresponds to one of Kent's corrections to parallax due to oblateness, but leaves his second oblateness term unaccounted for. In [5701], Kent describes another correction to parallax for oblateness, which depends on Moon azimuth, and I haven't even considered that one, described by Kent as follows- "- 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." By my rough estimate, that might shift parallax either way by up to 5 arc-sec, so when striving for high accuracy, it could be well worth making. In the present case, it seems to increase parallax by 2". Do I have that right? However, I haven't made any such correction, that depends on Moon's azimuth, and haven't found a reference to one, yet, in text in English. Still looking, though. 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 -~----------~----~----~----~------~----~------~--~---