A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Lunar longitudes, not by lunar distance.
From: George Huxtable
Date: 2009 Aug 9, 15:03 +0100
From: George Huxtable
Date: 2009 Aug 9, 15:03 +0100
Thanks to Geoffrey for some useful comments, paricularly about viewing high objects in a theodolite, such as Polaris from Northern Europe. Although Polaris will be lower in San Diego, the Moon altitude will be higher. Will that cause a difficulty? I've just had a chat with Clive Sutherland, Navlist member in the next village to mine, who has theodolites, fiddles with and modifies them, and knows a lot about them. An alternative to an expensive instrument with the light path bent through 90� where the axes intersect, such as the Wild, is to fit an eyepiece with a reflecting prism, on the same lines as a star-diagonal as fitted to a telescope, though this may obstruct some movements. I omitted to mention that a theodolite would be needed that possessed illumination, not only for the scales, but the cross-wires also. Geoiffrey added- "the error in azimuth goes as the tangent of the error in vertical alignment of the theodolite. So, if the theodolite is 1 minute off vertical and you are looking at an object at an altitude of 45 degrees, the error in azimuth could be up to 1 minute. "For azimuths, the correction is the semi-diameter divided by the cosine of the altitude." Indeed, that would be the case, if we were measuring azimuths, but we're simply timing the Moon as it passes a vertical line, so the correction is constant in time, independent of altitude. I would expect a reasonable instrument on a firm base could be set to vertical to rather better that 1 minute, but in this case it doesn't matter much. As long as the reference star chosen is close to the altitude of the Moon, the tilt matters little. It doesn't even matter much, for establishing the time difference to deduce GMT, whether the telescope tilts exactly in the plane of the meridian. For observing the reference star's time of meridian passage, to get local time for determining longitude, then that does matter. George. contact George Huxtable, at firstname.lastname@example.org or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. ----- Original Message ----- From: "Geoffrey Kolbe"
To: Sent: Sunday, August 09, 2009 11:08 AM Subject: [NavList 9431] Re: Lunar longitudes, not by lunar distance. George wrote [NavList 9430] >All he needs to do, once it's been placed firmly on a well-set tripod, is >to >set up his instrument so that its vertical axis is truly vertical, for >which >the built-in levels should be quite adequate. Then to set it so that its >telescope swings in a near-meridian plane. One way to do this is to >establish North (in the Northern hemisphere), by bisecting the most-Eastern >and most-Western azimuth swings of Polaris. However, that's only possible >at >certain times of year; at others, two different stars may have to be used, >but this presents no problem now that stars have been catalogued so >precisely. Then swing by 180� to look Southwards. A couple of practical points are worth noting (again, as Hanno is new to the list) in the use of transit theodolites for measuring azimuth. First is that for altitudes greater than about 50 degrees, it is usually not possible to get your eyeball behind the telescope using a standard transit theodolite. I think Hanno says he lives in San Diego, whose latitude is low enough that he will be able to see Polaris without difficulty using a standard transit theodolite. Here in Northern Europe, it would not be possible to do so. There are so called 'broken' theodolites, where the viewing is done along the axis about which the telescope and vertical scales rotate. There is a 45 degree mirror which redirects the view up the telescope. There is no limit to the altitude one can view using such a theodolite, the most famous example of which is the Wild T4 - but you won't find one of those on ebay! What you do find quite commonly on ebay are theodolites for tracking weather balloons. These are 'broken' theodolites and would be excellent for CN alt/az measurements - except that their scales are quite coarse, usually in degrees only I think, judging by what I can see from the ebay pictures. Second, is that the error in azimuth goes as the tangent of the error in vertical alignment of the theodolite. So, if the theodolite is 1 minute off vertical and you are looking at an object at an altitude of 45 degrees, the error in azimuth could be up to 1 minute. Luckily, standard transit theodolites are self limiting in this regard - see my first point above. Third and final point. As George mentioned, when doing measurements on the sun or moon, it is usual to take a measurement as the edge of the body (top of bottom for altitudes, sides for azimuth) touches the appropriate cross hair and then make a correction to get the centre of the body. For altitudes, the correction (to first order) is simply the semi-diameter of the body. For azimuths, the correction is the semi-diameter divided by the cosine of the altitude. With both these last two points, it can be seen that it is advantageous to observe bodies of low altitude to avoid significant errors in azimuth. Geoffrey Kolbe --~--~---------~--~----~------------~-------~--~----~ NavList message boards: www.fer3.com/arc Or post by email to: NavList@fer3.com To unsubscribe, email NavListemail@example.com -~----------~----~----~----~------~----~------~--~---