NavList:

Gary LaPook writes:

It appears that you ar looking for the "length" of a degree of latitude. For celestial navigation purposes the earth is assumed to be a perfect sphere with a circumference of 21,600 nautical miles; 360º times 60' per degree, with each minute equal to one nautical mile. Since each degree of latitude contains 60' and each minute is equal to one nautical mile then one degree of latitude, for celestial navigation purposes, is exactly 60 nautical miles. Since the nautical mile is defined as exactly 1852 meters, one degree of latitude is 111,120 meters.

Using Mr. de Hilster's figures, the length of one degree of latitude, at 53º north latitude, comes to 111,286.8 meters, a difference of 166.8 meters or a difference of  0.15%. Since one tenth of a nautical mile (one tenth of a minute of measured altitude) is 185.2 meters this difference between the lengths of a degree of latitude is less than can be reasonably measured with a marine sextant and so this difference has no relevance for normal celestial navigation purposes.

It is a different question if you are interested in the latitude of a point as depicted on a chart, its geodetic latitude as compared to its geocentric latitude, as the difference between these two measures of latitude can approach 12 minutes, 12 nautical miles near, 45º latitude. Does this cause a problem for celestial navigation? No, because the latitude determined by celestial observations is actually geodetic latitude, not geocentric latitude. Diagrams found in navigation texts may make this confusing as the diagrams appear to depict geocentric latitude and on small scale diagrams they are indistinguishable. But the altitudes measured with a marine sextant using the natural horizon as a reference point and the altitudes measured with a bubble sextant are all altitudes measured by reference to the local geode as the gravitational field that controls the bubble and which controls the level of the sea works at right angles to the surface of the local geode surface. The latitude determined by such observations are in fact referenced to the local geode and so the latitudes determined by sextant observations are actually geodesic latitudes, the same graticle used to depict points on the chart and so are directly comparable to those points on the chart.

See:

http://en.wikipedia.org/wiki/Latitude


gl


Nicolàs de Hilster wrote:

A degree of latitude of course depends on how you define the surface you
calculate it on. Suppose you want to know it for the WGS'84 ellipsoid
the following applies:

semi major axis (a) = 6378137.000
inverse flattening (Finv) = 298.257223563

the formulas you need for the calculation:
e2=(1/Finv)*2-(1/Finv)^2
mu = a/SQRT(1-e2*SIN(phi)^2)
rho = a*(1-e2)/SQRT((1-e2*SIN(phi)^2)^3)

1" lat = rho*SIN(1/3600)
1" lon = COS(phi)*mu*SIN(1/3600)

If we fill those in for 53 degrees north, the semi major axis and
inverse flattening we get:
e2 = 0.00669437999
mu = 6391797.44772
rho = 6376233.57268

1" lat = 30.913m
1" lon = 18.649m

If you need 1 minute you simply multiply with 60, for one degree
multiply with 3600.

Nicolàs



Lu Abel wrote:
  

This seems quite silly, but I realize that I don't know the "official"
definition of a degree of latitude.

I'm sure most on this list know that the earth is an oblate spheroid --
it's fatter than it is tall.   This means if I cut the earth in half
through its poles, the resulting cross-section looks like an ellipse,
wider than it is tall, rather than a perfect circle.   And this
elliptical cross-section can lead to two possible definitions of a
degree of latitude.

If take a cross-section of the earth and draw an angle one degree up
from the equator, is the place where this line intersects the surface of
the earth the first (degree) parallel?   Or is the first parallel one
ninetieth of the way from the equator to the pole?

Years ago I took an offshore navigation course that taught the various
"sailings," including use of the Meridional Parts table from Bowditch to
determine a rhumb line course when traversing long distances (especially
those with dramatic north-south differences).   (Meridional Parts give
the "stretch" in the latitude scale required at various latitudes to
create a Mercator chart).   As I recollect, the meridional parts down
near the equator are actually slightly less than 1.00000, which would
indicate that the first of my two definitions is the correct one.

I know there are some experts in cartography on the list, I'm sure this
is trivial for them.

Lu Abel

    

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