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Modeling Earth as an Ellipsoid

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First published at 06:05 UTC on April 11th, 2024.

#math
#geometry
#science

Math Easy Solutions

MES

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In this video I model the Earth as an ellipsoid as used by the World Geodetic System of 1984 (WGS-84) since it is a more accurate model than a sphere. The Earth is not perfectly spherical but instead is more squished vertically by about 21.6 km: the distance from the center to the Poles is 6356.523 km while the distance to the equator is larger at 6378.137 km. The parallels or circular lines of equal latitude are the horizontal circular traces of the ellipsoid. The meridians or elliptical lines of equal longitude are the vertical elliptical traces of the ellipsoid. I plot this all out using GeoGebra's 3D and 2D graphing calculators (the 2D traces turn into cylinders in 3D so I had to also use the 2D graphing calculator).

GeoGebra 3D graphing calculator: https://www.geogebra.org/3d/tabys4ec
GeoGebra 2D graphing calculator: https://www.geogebra.org/calculator/hte4yr46

Time stamps:

- Exercise 1: Modeling Earth as an Ellipsoid: 0:00
- Solution to (a): Earth's Ellipsoid Equation: 1:09
- Solution to (b): Parallels or Circular Lines of Equal Latitude: 6:26
- Note: Using GeoGebra's 2D (not 3D) calculator to plot 2D circles: 10:37
- Solution to (c): Meridians or Elliptical Lines of Equal Longitude: 11:58

Full video below:

- Cylinders and Quadric Surfaces: https://youtu.be/k4EyLr4uOUA
- HIVE video notes: https://peakd.com/hive-128780/@mes/cylinders-and-quadric-surfaces
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EfmYwT81SebJnU1Ny8Fc5u
- Infinite Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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