# Lecture Notes (19 pages)

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## Lecture Notes

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Lecture Notes

- Pages:
- 19
- School:
- Massachusetts Institute of Technology
- Course:
- 12 215 - Modern Navigation

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12 215 Modern Navigation Thomas Herring Review of Monday Class Latitude and Longitude Simple spherical definitions Geodetic definition For an ellipsoid Astronomical definition Based on direction of gravity Relationships between the types Coordinate systems to which systems are referred Temporal variations in systems 09 20 2006 12 215 Modern Naviation L03 2 Today s class Heights Definition of heights Ellipsoidal height geometric Orthometric height potential field based Shape of equipotential surface Geoid for Earth Methods for determining heights 09 20 2006 12 215 Modern Naviation L03 3 Ellipsoidal heights Calculation of ellipsoid heights from Cartesian XYZ was covered in Lecture 2 The ellipsoid height is the distance along the normal to the reference ellipsoid from the surface of the ellipsoid to the point who height is being calculated While the geometric quantities geodetic latitude and longitude are used for map mapping and terrestrial coordinates in general ellipsoidal height is almost never used although this is changing with the advent of GPS Why is ellipsoidal height not used 09 20 2006 12 215 Modern Naviation L03 4 Orthometric heights The problem with ellipsoidal heights are They are new Ellipsoidal heights could only be easily determined when GPS developed 1980 s Geometric latitude and longitude have been around since Snell optical refraction developed triangulation in the 1500 s Primary reason is that fluids flow based on the shape of the equipotential surfaces If you want water to flow down hill you need to use potential based heights 09 20 2006 12 215 Modern Naviation L03 5 Orthometric heights Orthometric heights are heights above an equipotential surface The equipotential surface is called the geoid and corresponds approximately to mean sea level MSL The correspondence is approximately because MSL is not an equipotential surface because of forces from dynamic ocean currents e g there is about 1m drop over the Gulf stream which is permanently there but

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