# Geodetic Surveying: Aligning Satellite Axes with Terrestrial Axes

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:

• Press the green cube labeled "1" to view the first rotation.
• Press the blue cube labeled "2" to animate the second rotation.
• Press the yellow cube labeled "3" to animate the third rotation.
• Press the gray cube labeled "4" to complete the final rotation.

• Press the red cube labeled "R" to reset it to the original rotation.

## Satellite Coordinates 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.
• The XS axis is on the line from the center of the earth.
• The ZS axis is perpendicular to the satellite's oribital plane.
• The YS axis is in the same orbital plane as the XS axis, but at a 90° angle from it.

## Earth's Coordinate System

For the earth's coordinate system, all axes are designated with a subscript E. In this coordinate system:
• The origin (0,0,0) corresponds with the mass center of the earth.
• The XE axis is parallel to the Equator and points through the Greenwich Meridian (0° longitude). The Greenwich Meridian is also known as the Prime Meridian.
• The ZE axis is coincident to the conventional terrestrial pole (CTP) which was the mean position of the Earth's rotational axis between 1900 and 1905.
• The YE axis lies in the Earth's equatorial plane and is perpendicular to the X and Z axes and creates a right-handed Cartesian 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.