## 1. Introduction

Tail Probe is a spin-stabilized spacecraft spinning around the main axis of the maximum moment of inertia. The angle between the spin axis and direction towards the Sun should not exceed a certain value.

As this angle increases with the rate of about 1^{o}/day (because of the Earth orbital motion) the attitude control system periodically (once per ~7 days) restores the direction of the spin axis to the Sun.

To know the spacecraft attitude for a given time we use a matrix `N` to transform any vector `V` from the Geocentric Solar-Ecliptic (**GSE**) coordinate system to the Spacecraft Construction (**S/C**) coordinate system

`V`_{S/C} = `N` * `V`_{GSE}

or a matrix `M` for the inverse transformation

`V`_{GSE} = `M` * `V`_{S/C}

The both systems **S/C** and **GSE** are spacecraft-centered ones.

#### The **GSE** coordinate system:

- X
_{G} axis is directed to the Sun,

- Z
_{G} axis is directed to the North Pole of Ecliptic,

- Y
_{G} axis supplements the right three.

#### The **S/C** coordinate system:

- X
_{S} axis is the spacecraft struclural axis which is close to the spin axis and to the main axis of the maximum moment of inertia `X`_{m},

- Y
_{S} axis is the structural axis close to the axis of the intermediate moment of inertia `Y`_{m},

- Z
_{S} axis is the structural axis close to the axis of the minimum moment of inertia `Z`_{m}.

By attitude sensors data processing the attitude coefficients arrays have been obtained. It gives the possibility to calculate matrixes `N`,`M` for a given time.