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This paper is dedicated to the development of a model of the attitude dynamics for a nonideal Simple Solar Photon Thruster (SSPT) and to the analysis of sailcraft motions with respect to their centre of mass. Derivation of the expressions for force and torque due to solar radiation that is valid for the case, when there is a misalignment of the SSPT axis with the sun direction, is followed by study of sailcraft dynamics and stability properties. Analysis of stability shows that an ideally reflecting sail is unstable, while for a sailcraft with nonideal collector, the symmetry axis is stable with respect to the Sun direction for large variety of system parameters. The motion around symmetry axis is always unstable and requires an active stabilizer.

Solar sails are attractive spacecrafts for long missions, for they create a propulsion effort using freely available solar radiation pressure. The initial concepts of such vehicle have been proposed in the 1920s [

The large majority of these studies are focused on the analysis of the Flat Solar Sail (FSS); its principal element is a large flat surface formed by a reflecting membrane. Control of FSS orbital motion is performed by turning the entire sail with respect to the sunlight direction. As a result, the radiation pressure on the surface changes, enabling the control of the vehicle trajectory. Attitude dynamics of such sailcraft are studied, for example, in [

Another possible scheme for a sailcraft is the Solar Photon Thruster (SPT). Its main idea is to separate the functions of collecting and reflecting the incoming light. Even though the SSPT's general scheme has been proposed long ago [

The SPT can be either Simple SPT (SSPT) or Dual Reflector SPT (DR SPT) depending on the system of smaller mirrors used. The SSPT is provided with two main elements, the Collector C and the Director mirror D [

Several versions of DR SPT structure (see, e.g., [

Previous studies [

In [

Figure

Scheme of a Simple Solar Photon Thruster.

In [

A force and torque model for SSPT has been developed in [

To calculate the vectors of force and torque due to solar radiation on the SSPT, consider a parabolic surface (collector) shown in Figure

Scheme of reflections on SSPT with axis misalignment.

Suppose that the incoming sunlight has the direction

A fraction

In (

Then, the light is reflected by the director whose orientation can be described by the normal to its surface

Force and torque transmitted by the light hitting the director are, respectively, as follows:

The reflection of the light at the director produces force and torque that can be written, respectively, as

The interaction of the light beam caught by the element

The total force actuating on the sailcraft due to sunlight radiation pressure can be obtained by integration as follows:

After integration, one gets

Here,

For the case when the ideally reflecting SSPT is completely aligned with the sun direction (

These expressions for the solar radiation force acting on SSPT have been used previously to study orbital transfer problems for SSPT and FSS [

Calculation of the total torque due to the light pressure results in the following expressions:

These models for force and torque are used later on to study the attitude dynamics of SSPT.

Consider the problem of a SSPT attitude dynamics on a heliocentric orbit. This analysis is done using two right Cartesian reference frames located at the SSPT center of mass

Mutual orientation of these frames can be described by the orthogonal matrix

At the heliocentric trajectories, the characteristic values of the angular acceleration due to orbital motion and gravity-gradient torque are much smaller than those created by cm-cp offset. Taking into account only the latter effect, the equations of attitude motion can be written as

The direction of sunlight is

Solution (

Assuming that the attitude motion of SSPT occurs in the vicinity of the equilibrium orientation, (

Analyzing linearized system (

For stability of zero equilibrium position of system (

As one can see,

This condition is satisfied for all possible values of

Writing condition (

For a sailcraft with an ideal collector, the surface optical parameters are [

So, for all geometries of the sail, the

For a sailcraft with an ideally black film in collector, the surface optical parameters are [

Condition (

For sailcraft with general properties of the film, condition (

Condition (

The stability of

In this paper, a new model for force and torque actuating on a compound solar sail is developed and used to study sailcraft motions. The attitude dynamics of a SSPT is studied for the case when the collector film possesses nonideal optical properties and the sailcraft symmetry axis is not aligned to the sun-sailcraft direction. Analysing the sailcraft stability, one can see that the solar radiation pressure destabilizes an ideal sail, but non-ideal collector film contributes to stabilization, resulting in stability, of its symmetry axis for all orientations of director when collector focal distance is large enough. However, an active control system is always necessary to guarantee stabilization of the sailcraft orientation with respect to the collector’s symmetry axis.

The authors declare that they have no conflict of interests.

This research is supported by the Brazilian program “Science without Borders” and Project ODySSea (PTDC/CTESPA/098030/2008) funded by the Portuguese Foundation for Science and Technologies (FCT), the Portuguese Operational Program for Competitiveness Factors (COMPETE), the Portuguese Strategic Reference Framework (QREN), and the European Regional Development Fund (FEDER).