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Geodetic Surveying: Aligning Satellite Axes with Terrestrial Axes

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This VRML animation demonstrates the four rotations needed to align the coordinate system of a satellite with the axes of the earth.

3D Animation

You will need a VRML 2.0 viewer to see the illustration below. Please download the Cortona vrml plug-in.

Click here for the VRML Animation Within the animation you will see three buttons:

Satellite Coordinates

Satellite in Orbit labelled with axes, orbital plane and equitorial plane

Satellite in Orbit
Y axes not labelled

Each satellite in orbit has its own three dimensional coordinate system. In the satellite system all axes are designated with a subscript s.

Earth's Coordinate System

For the earth's coordinate system, all axes are designated with a subscript E. In this coordinate system:

Note that this coordinate system is also called the Conventional Terrestrial system.


Aligning the Satellite Coordinate Systems

To align the satellite coordinate systems with the earth's coordinate system you will need to perform the following mathematical conversions to position and rotate the satellite.

  1. The first step is to mathematically move the satellite in its oribital plane so that it intersects the equator.
  2. The second step rotates the satellites coordinates so that ZS axis is parallel to the ZE axis.
  3. The third step moves the satellite along the equator to the vernal point (♈) or the point where the sun crosses the equator in the spring.
  4. The final step adjusts the satellite to the true XE position.

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