Determining Geodetic Latitude and Longitude
- Oldest way is by using instruments
o For observing positions of Celestial bodies,
o Technique: establish celestial lines of position (east-west, north-
south) by comparing the predicted positions of celestial bodies with
their observed positions.
- Sextant – tool used to measure the angle of a celestial body above the earth’s
o Nautical navigators used to find their way using the moon, planets and
stars, including our sun
- Since Earth rotates on an axis defined by North and South poles, stars in the
northern hemisphere’s night sky appear to move slowly in a circle centered
on Polaris (the North Star).
o Navigators need to only located Polaris to find North.
- In Southern Hemisphere, latitude is harder to find because four stars are
used to interpolate due south as there is no equivalent to Polaris over the
South pole. Navigators use a small constellation called Crux Australis (the
o Finding South = more complicated because the Southern Cross is a
collection of 5 stars that are part of the constellation Centaurus.
o 4 stars form cross, the 5 is dim = offset about 30 degrees below the
center of the cross
- The prime meridian at 0 degree longitude passes through Greenwich,
England. Therefore, each hour difference between your time and that at
Greenwich, called Greenwich mean time or GMT, is roughly equivalent to
15 degree of longitude from Greenwich
o To determine geodetic longitude, compare you local time with
Greenwich Mean Time and multiply by 15 degree of longitude for each
hour of difference.
- Before = difficult to determined longitude
o 1762 – clock was portable enough and used accurate enough for
o Chronometer was set to Greenwich Mean Time before departing on a
o Longitude of distant local found by noting GMT at local noon (highest
point of the sun in the sky, found with a sextant). The time difference
was multiplied by 15 to find the longitude Properties of the Graticule
- Circumference of the authalic and other spheres
o Using spheres leads to simpler calculations, specially working with
small-scale maps of countries, continents, or the entire earth.
o The value of the earth’s spherical circumference used is called
Authalic sphere is a sphere with the same surface area as a
o Other properties of oblate ellipsoid:
Rectifying sphere, is where the length of meridians from
equator to pole on the ellipsoid equals one-quarter of the
This sphere is a little over three-tenths of a percent larger in
surface area than the WGS84 ellipsoid (authalic sphere).
The values are really close to each other, difference by
less than two-tenths of a percent
- Spacing of parallels
o Important to know how to define distance as there may be different
definitions for the words, i.e, what they mean.
o There is a 15% difference in the number of statute and nautical miles
o Statute miles are what we use for land distances in the United States.
o Nautical miles are used worldwide for maritime and aviation
o A Statute mile is about 1,609 meters and Nautical mile is 1,852
meters exactly (about 1.15 statute miles)
o Original Nautical mile was defined as 1 minute of latitude measured
north-south along a meridian.
o Oblate ellipsoid are not spaced equally, but decrease slightly from
pole to the equator.
- Converging meridians
- The precise spacing of meridans at a given latitude is found by:
o 69.09 miles (111.20 Km) / deg. X cosine(latitude)
o Example: at 45degree north or South of the equator, for example,
cosine (45degree) = 0.7071. Therefore, the length of a degree of
69.09 x 0.7071 = 48.85 Statute miles (111.20 x 0.7071 = 78.63
- Great and Small circles
o A great circle is the largest possible circle that could be drawn on the
surface of the spherical earth. Its circumference is that of the sphere,
and its center is the centere of the earth so that all great circles divide
the earth into halves. o The prime meridian and the 180 deg. Meridian at the opposite side of
the earth (called the antipodal meridian) form a great circle dividing
the earth into eastern and western hemispheres.
A great circle is the shortest route between any two points on
the earth and hence great circle routes are fundamental to
o Any circle on the earth’s surface that intersects the interior of the
sphere at any location other than the center is called a small circle.
- Quadrilaterals are areas bounded by equal increments of latitude and
longitude, 10deg. By 10deg.
- The equation cosine(latitude) gives the aspect ratio (with/height) of any
- A quadrilateral centered at 45deg N will have aspect ratio of 0.07071,
whereas, 60deg. N = 0.5. [2:1 ratio]
Graticule Appearance on Maps
- Small-scale maps
o World or continental maps such as globes and worldatlas sheets
normally use coordinates based on an authalic sphere.
Before computers, it was easier to make them from
The difference in the plotted positions of spherical and
corresponding geodetic parallels become negligible on maps
that cover so much area.
The scale to a world wall map approx. 18 inches high
and 36 inches wide
- Large-scale maps
o Parallels and meridians are shown in different ways on different types
Topographic maps in U.S and other countries have TICK
MARKS showing the location of the graticule.