The Dynamical Attitude Model (DAM) is a simulation software developed to achieve a detailed understanding of the Gaia attitude. Its main characteristic is that it takes into account at the same time physical effects and internal hardware components controlling the satellite. This attitude will be used as input for the Gaia data simulations by CU2.

By "attitude" we mean the orientation of the satellite and its rotation state. The attitude is characterised by a 7-component array which is recorded for time-step (1 second). This array is composed of:

• A quaternion that defines the rotation of the Scanning Reference System (SRS, attached to the spacecraft) with respect to the ICRS. Quaternions are 4-dimensional normalised vectors, a generalisation of the complex numbers very convenient for specifying rotations.
• A 3-dimensional vector that defines the spacecraft angular rate in the SRS.

Currently the model implements the following effects:

• A copy of the on-board AOCS (Attitude and Orbit Control System) algorithms.
• Thruster performance.
• Torque due to the solar radiation pressure on the Deployable Solar Array.
• Thermal infra-red emission from the surface of Gaia.
• Impact of micro-meteoroids.
• Clanks (discontinuities in the attitude).

All these effects can be modified by means of changing some input parameters, for instance thruster capabilities or micro-meteoroid characteristics. And since the code is very modular, more disturbances could be implemented in the future. The simulation considers the satellite to be a rigid body, for which the motions are described by the Euler equation. It takes about 1 week of computing time to simulate 5 years of spacecraft attitude.

These plots show 6h of spacecraft attitude. This simulation includes a micro-meteoroid impact that produces a spike in these plots at about t=15500 seconds.

• Top left: angular distance between the actual attitude and the demanded one. Deviations from nominal values are well within the requirement limits except for when there is a hit. It must be lower than 60 arcsec during 99.73% of the time.
• Top right: angular rate error. It is the difference between the actual rate and the demanded rate. Attitude requirements impose that it must be lower than 2 mas/s (AL) and 10 mas/s (AC) during 99.73% of the time.
• Bottom left: scan phase (angular position of the Sun in the XY plane of the SRS), scan phase derivative, and solar aspect (angular distance to the Z(SRS) axis, always close to 45 degrees).
• Bottom right: this plot shows how thrusters are commanded in order to counteract disturbances. The vertical axis is measured in LSB. 1 LSB (Least Significant Bit) is equivalent to 0.1 µN, and thrusters are commanded in units of 10 LSB. Thrusters are installed in opposite pairs: thrusters 1 and 3 control mainly the X(SRS) axis, thrusters 2 and 4 control mainly the Y(SRS) axis, and thrusters 5 and 6 control the Z(SRS) axis. Note that no more than three thrusters are active at the same time, opposite thruster pairs never work at the same time (because it would be inefficient), and thrusters 5 and 6 are always commanded with very little force because the torque due to the solar radiation pressure is small in the Z(SRS) axis.

For more information, please refer to:

• Accurate Modelling the Attitude of the Gaia Satellite
• Modelling the Attitude Noise of the Gaia Spacecraft. A Simplified Approach

This work is being developed by Daniel Risquez and Anthony Brown (both from Leiden Observatory), Floor van Leeuwen (IoA) and Ralf Keil (ZARM).

[Published: 13/07/2011]