# NavList:

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

**Re: FW: Re: Chronometer Suggestions**

**From:**Gary LaPook

**Date:**2009 Jan 15, 14:12 -0800

The radius of a sphere on which the great circle is 21,600 NM is 3,437.746 NM (21600/2 Pi) which compares very closely to the mean radius of the various spheroids e.g. Clarke 1866 of 3440..65 NM a difference of 2.319 NM. gl glapook{at}PACBELL.NET wrote: > It may seem counter intuitive that the minute of latitude is longer at > the pole since you are 12 NM closer to the center of the earth at the > pole than at the equator and you would think that the same angle on a > smaller radius would be a shorter arc. The polar radius is 3432 NM, > equatorial radius, 3444 NM. The answer is that the angles are measured > in reference to the geode at that point. Since the surface of the > geode at the pole is "flattened" compared to at the equator, the lines > connecting "straight down" do not come together at the center of the > earth but at some point beyond the center. Since a minute of latitude > is measured between these "straight down" lines, the radius of the arc > is greater than the actual polar radius so the length of the arc is > also longer. > > For celestial navigation purposes, due to the limit of achievable > accuracy, the assumption is that the earth is a perfect sphere with a > circumference of 21,600 NM (360 X 60) which is the length of a great > circle. Such assumptions don't work with GPS due to its high > precision. Sextants altitudes are measured in reference to the local > geode because the sea horizon is determined by the local gravity field > as is the position of the bubble in a bubble octant so the latitudes > determined are actually geodetic latitudes but the difference between > this and geocentric latitude is ignored and are generally treated as > geocentric latitudes. > > gl > > On Jan 15, 12:09 pm, glap...{at}PACBELL.NET wrote: > >> The nautical mile used to be defined, in the U.S., as one minute of >> arc on a sphere having the same area as the earth as defined on the >> Clarke spheroid of 1866 and was 6,080.2 feet. The length of one minute >> of latitude varies from 6,046 feet at the equator to 6,108 feet at the >> poles on this spheroid (I don't know what it is on WGS84.) The length >> of the geographical mile, one minute of longitude on the equator, is >> 6,087 feet. (Bowditch, 1977) >> >> Also see: >> >> http://www.i-DEADLINK-com/bowditch/pdf/chapt02.pdf >> >> gl >> >> On Jan 15, 10:55 am, Lu Abelwrote: >> >> >>> Curiosity question: >>> >>> It's well known that the diameter of the earth across the equator is >>> about 1/300th greater than the diameter across the poles. >>> >>> I would intuitively expect, therefore, that the size of a minute of >>> latitude to change by a like amount. But looking at this graph, there >>> seems to be a 1/60 difference in the size of a minute at the poles vs at >>> the equator. Is there an explanation that this technically competent, >>> but ignorant of the math of the oblate spheroid, person could understand? >>> >>> Also, I assume this graph is for geodetic latitude and not geocentric or >>> parametric latitude? >>> (For people curious about these terms, geodetic latitude is what you get >>> by drawing a line perpendicular to the surface of the earth down to its >>> axis. Due to the flattening of the earth, this line will intersect the >>> earth's axis on the other side of the equator from the observer's >>> position. The other two latitudes are what you get when you draw a line >>> out from the earth's center. This line is not perpendicular to the >>> earth's surface except that the poles and equator) >>> >>> Lu Abel >>> >>> Nicol�s de Hilster wrote: >>> >>>> On NavList 7052 Irv Haworth wrote: >>>> >>>>> "I think it's well known that 1' of arc varies in length as a function >>>>> (cos) >>>>> of the latitude." >>>>> >>>> On which Gary LaPook replied in NavList 7053: >>>> >>>>> That is true for one minute of longitude because parallels of latitude are small circles. >>>>> This is not true for one minute latitude of for any >>>>> other great circle. (Technically these also vary slightly due to the >>>>> oblateness of the earth but these small variations are ignored for >>>>> celestial navigation purposes.) >>>>> >>>> For those who want to know how much exactly that variation is I posted >>>> attached graph of it in NavList 4750 on 24/03/2008. >>>> >>>> ------------------------------------------------------------------------ >>>> >> > > > > --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To unsubscribe, email NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---