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Re: Longitude by calculator -theodolite
From: Bruce J. Pennino
Date: 2013 Jun 22, 22:56 -0400

Hi Frank:

I was just trying to see how close I could locate myself with the theodolite. I've done "time sights by calculator" for longitude before and always had excellent results......1-2 minute of longitude from my known location.

BUT....you are quite correct! I just checked all of my previous time sights and the sun was always very much to the east or west! Maybe plus or minus 25-30 degrees. With my posted moon observation data,my procedures, measurements and math seem to be all fine. The moon's Z was at 164-165, and the trig/geometry just causes large errors, as you said. One of these days I'll try to catch an early rising star. Stars are not so easy because there is no internal light on the theodolite and I can't see the cross hairs at twilight. So I must adjust instrument, hold a flashlight and read my watch. Maybe with 30 power magnification I can precompute a star's altitude while there is enough light to skip the flashlight. Vega and Deneb are two candidates. Thanks for insight.

Best regards

Bruce

----- Original Message -----

From: Frank Reed

To: bpennino.ce@charter.net

Sent: Saturday, June 22, 2013 5:26 PM

Subject: [NavList] Re: Longitude by calculator -theodolite

Hi Bruce, Still not entirely sure how you're going about this but I think we're getting warmer. Are you saying that you tried to use the Moon for a traditional time sight to get longitude? If so, you realize that the Moon was nearly South at the time. Time sights become rapidly sensitive to errors in altitude (or latitude) when the object approaches the meridian. Time sights were normally observed when the celestial body was as near as possible to East or West to avoid this issue. With the Moon at an azimuth of 165°, you would expect that an error in altitude would be multiplied by about a factor of 5 in the determination of the longitude. You can figure this out by looking at the equivalent LOPs. Draw an LOP on a "chart" to represent your latitude as input. It's a straight line running east-west, right? Now draw an LOP inclined to that at 15°. This is perpendicular to the Moon's azimuth of 165°. The longitude from a time sight calculation is simply the longitude where the two LOPs cross. But notice what happens if you "wiggle" either of these LOPs. The crossing point shifts by a large distance east-west for a relatively small change in EITHER the input latitude OR the observed altitude. For this specific case, the ratio of the change in longitude to a small change in latitude is just about 5-to-1. The ratio of the change in longitude to a small error in altitude is about 5.1-to-1. Notice that an error of 0.3' in altitude would yield a 1.5' error in longitude. By contrast, if the celestial body were due East or due West, a small change in latitude would have no effect on the longitude. A small change in the observed altitude would have a 1-to-1 impact on the longitude, as you would expect. -FER ---------------------------------------------------------------- NavList message boards and member settings: www.fer3.com/NavList Members may optionally receive posts by email. To cancel email delivery, send a message to NoMail[at]fer3.com ----------------------------------------------------------------

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