# Geodetic Surveying: Pole Alignments for the Precession

Similar to a spinning top, the earth's north pole wobbles in a circular motion once every 26,000 years. In 1905, scientists agreed on a fixed position for the celestial coordinate system. Thus, the instantaneous position of the earth's poles and equator are titlted with respect to the celestial coordinate system's pole and equator.

This VRML animation demonstrates the three rotations needed to align the actual position of the earth's north pole and equator with the agreed upon position of the celestial equator and north pole.

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

## Celestial Coordinates

Precessed versus Celestial Poles
Y axes not labelled

Unlike terrestrial coordinates, the axes of the celestial coordinate system, here called the Mean Right Ascension (MRA) system are as follows:

• The origin (0,0,0) corresponds with center of the earth.
• The ZMRA axis is the celestial north pole.
• The XMRA axis is on the celestial equator and points to the constellation Aries at a given time.
• The YMRA axis is in the celestial equators but at a 90° angle from XMRA.

## Aligning Precessed and Celestial Poles

Because the celestial equator "moves" around the earth (due to wobble of the earth in orbit), the position of the XMRA axis changes depending on the time (signified as τ or Greek "tau") when observations are made.

• XMRA(τ) is the position of the XMRA at the observation time τ.
• XMRA0) is the position of the XMRA recorded in an almanac for an initial time or τ0.

To align the precessed pole and equatorial plane with the celestial poles and equator you will need to perform the following mathematical conversions to position and rotate the axes.

1. The first rotation aligns the earth's X axis with the the XMRA0) record in an almanac.
2. The second step aligns the celestial and earth's equator and north pole pole to the celestial pole at ZMRA. Note that ZMRA(τ) and ZMRA0) will be the same.
3. The final step moves rotates the coordinates around the pole from XMRA0) to XMRA(τ).