Earth geodesics | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-06-15

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Geodesics_on_an_ellipsoid


00:01:49 1 Geodesics on an ellipsoid of revolution
00:06:38 1.1 Equations for a geodesic
00:07:33 1.2 Behavior of geodesics
00:07:52 1.3 Solution of the direct and inverse problems
00:15:24 1.4 Differential properties of geodesics
00:22:57 1.5 Envelope of geodesics
00:26:35 1.6 Area of a geodesic polygon
00:30:33 2 Geodesics on a triaxial ellipsoid
00:35:43 2.1 The triaxial coordinate system
00:43:48 2.2 Jacobi's solution
00:44:06 2.3 Survey of triaxial geodesics
00:47:00 3 Applications
00:56:15 4 See also
00:57:46 5 Notes
01:01:34 6 References
01:01:55 7 External links
01:03:26 Jacobi's solution
01:10:05 Survey of triaxial geodesics
01:10:30 0, and Z
01:11:28 0, and α1
01:13:22 ω1 and ω
01:16:14 0 and Z
01:16:35 0, which goes through all 4 umbilical points, is exponentially unstable.  If it is perturbed, it will swing out of the plane Y
01:17:31 −β1 between the cusps.
01:17:37 Applications
01:20:04 See also



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SUMMARY
=======
The study of geodesics on an ellipsoid arose in connection with geodesy
specifically with the solution of triangulation networks.  The
figure of the Earth is well approximated by an
oblate ellipsoid, a slightly flattened sphere.  A geodesic
is the shortest path between two points on a curved surface, analogous
to a straight line on a plane surface.  The solution of a triangulation
network on an ellipsoid is therefore a set of exercises in spheroidal
trigonometry (Euler 1755).
If the Earth is treated as a sphere, the geodesics are
great circles (all of which are closed) and the problems reduce to
ones in spherical trigonometry.  However, Newton (1687)
showed that the effect of the rotation of the Earth results in its
resembling a slightly oblate ellipsoid and, in this case, the
equator and the meridians are the only simple
closed geodesics.  Furthermore, the shortest path between two points on
the equator does not necessarily run along the equator.  Finally, if the
ellipsoid is further perturbed to become a triaxial ellipsoid (with
three distinct semi-axes), only three geodesics are closed.