**Back to other Three Dimensional Visualizations**

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

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 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
**X**axis is on the line from the center of the earth._{S} - The
**Z**axis is perpendicular to the satellite's oribital plane._{S} - The
**Y**axis is in the same orbital plane as the_{S}**X**axis, but at a 90° angle from it._{S}

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
**X**axis is parallel to the Equator and points through the Greenwich Meridian (0° longitude). The Greenwich Meridian is also known as the Prime Meridian._{E} - The
**Z**axis is coincident to the conventional terrestrial pole (CTP) which was the mean position of the Earth's rotational axis between 1900 and 1905._{E} - The
**Y**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._{E}

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

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.

- The first step is to mathematically move the satellite in its oribital plane so that it intersects the equator.
- The second step rotates the satellites coordinates so that
**Z**axis is parallel to the_{S}**Z**axis._{E} - 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.
- The final step adjusts the satellite to the true
**X**position._{E}