Satellite deorbiting system

Abstract

A device to stabilize and deorbit a satellite includes a pair of coplanar masts, each one carrying at least one membrane forming an aerobraking web. The masts are fixed to the satellite along non-parallel axes. Each mast is provided on the opposite end of the satellite with a mass to generate a gravity gradient. The end of each mast is fixed to the satellite. The masts form, with the bisectrix between the masts, a fixed angle to align the bisectrix with the satellite speed vector at any altitude.

Claims

1. A satellite stabilization and deorbiting device to stabilize and deorbit a satellite, comprising a pair of coplanar masts, each coplanar mast carrying at least one membrane to form an aerobraking sail, said coplanar masts are fixed to the satellite along non-parallel axes, said coplanar masts form a fixed angle, a first end of each coplanar mast is fixed to the satellite, and a second end of said each coplanar mast is provided with a mass, the fixed angle and each mass being configured to generate a gravity gradient resulting in a restoring torque for aligning a bisectrix of the fixed angle with a satellite velocity vector at any altitude.

2. A satellite comprising the satellite stabilization and deorbiting device as claimed in claim 1, wherein the bisectrix between the two coplanar masts carrying the aerobraking sails is an axis of a satellite principal system of axes of an inertia matrix of the satellite; and wherein an inertia I.sub.z along the bisectrix is between inertia values on other two axes of the satellite principal system of axes.

3. The satellite stabilization and deorbiting device as claimed in claim 1, wherein said each coplanar mast carries two membranes in a form of panels disposed in a V to form the aerobraking sails.

4. The satellite stabilization and deorbiting device as claimed in claim 3, wherein the panels are rectangular panels, one of longer sides of each rectangular panel is fixed to said each coplanar mast.

5. The satellite stabilization and deorbiting device as claimed in claim 3, wherein an angle between the panels on a same coplanar mast is between 70 to 110.

6. The satellite stabilization and deorbiting device as claimed in claim 3, wherein the V has a same orientation for the two coplanar masts.

7. A method of sizing the coplanar masts, and determining masses m and an angle of the satellite as claimed in claim 2, comprises steps of: determining, by trajectory calculation tools, a minimum effective aerobraking sail area to deorbit the satellite in a predetermined time; dividing the minimum effective aerobraking sail area across said two coplanar masts of length L with an angle 2 between said two coplanar masts; placing a mass m at an end of each coplanar mast; positioning said two coplanar masts at an arbitrary location on the satellite; selecting the satellite principal system of axes such that its axis Z is the bisectrix of an angle between said two coplanar masts; calculating and diagonalizing the inertia matrix of the satellite; reproducing an approach by successive iterations that varies installation locations of said coplanar masts, the lengths of said coplanar masts, the masses m and the angle , so that: the axis Z of the satellite principal system of axes is also the bisectrix of said coplanar masts; and the inertia I.sub.Z on the axis Z of the satellite principal system of axes has an intermediate value between a minimum value and a maximum value on the other two axes of the satellite principal system of axes; and selecting values of the masses m, the lengths of said coplanar masts and the angle that minimizes a total mass of the aerobraking sails while maintaining robustness of the selected values, such that variations of parameters around the selected values do not change attitudes of the satellite with the aerobraking sails.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Other features and advantages of the invention will become apparent on reading the following description of one nonlimiting embodiment of the invention given with reference to the drawings, which show:

(2) FIG. 1: a first example of a prior art spherical aerobraking structure;

(3) FIG. 2: a second example of a prior art aerobraking structure;

(4) FIG. 3: a typical deorbiting curve;

(5) FIG. 4: a diagram showing the gravity gradient principle applied to a satellite;

(6) FIG. 5: a diagram showing a satellite according to the invention;

(7) FIGS. 6A to 6C: views of satellites in gravity gradient stabilized positions according to three ranges of angles at high altitude;

(8) FIGS. 6D to 6F: views of satellites in aerobraking stabilized positions according to the three ranges of angles from FIGS. 6A to 6C at low altitude;

(9) FIG. 7: a rear view of the satellite in its direction of movement; and

(10) FIG. 8: a view of one embodiment of a mast useable in the invention.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

(11) The problem that the invention proposes to solve is that the satellite has to have a stable position that at high altitude enables the largest possible aerobraking area in the plane perpendicular to the axis of the trajectory of the satellite.

(12) The operating principle of the device of the invention is based on the gravity gradient as shown diagrammatically in FIG. 4 for a satellite S provided with a mast at the end of which is a mass M and in an orbit O at a distance DT from the center of the Earth.

(13) To understand the various embodiments of the invention, it is appropriate to define three systems of axes: A system of axes linked to the orbit of the satellite, termed the local orbital system of axes at the center of mass of the satellite; A first system of axes linked to the satellite, termed the satellite system of axes, used to describe the geometry of the satellite and its properties, also at the center of mass of the satellite; A second system of axes linked to the satellite, termed the satellite principal system of axes, again at the center of mass of the satellite.

(14) FIG. 4 shows the local orbital system of axes, which includes:

(15) The axis L, which connects the center of the Earth to the center of mass of the satellite (yaw of the satellite is relative to this axis).

(16) The axis R, tangential to the trajectory of the satellite (roll of the satellite is relative to this axis).

(17) The axis T perpendicular to the other two (pitch of the satellite is relative to this axis).

(18) For an aerobraking sail to be as effective as possible it must be substantially in a plane perpendicular to the axis R, although rotation about that axis is acceptable.

(19) The satellite system of axes is an arbitrary system of axes the center of which is placed at the center of mass of the satellite and used to describe the geometry of the satellite in a simple manner. For FIG. 5, for example, for a satellite of cubic shape, a satellite system of axes has been chosen such that each axis is perpendicular to one of the faces of the satellite; here this system of axes has also been chosen so that the bisectrix of the two sails 10 and 11 is the axis z of that system of axes.

(20) In this system of axes it is then possible to calculate the inertia matrix of the satellite as a function of its distribution of mass.

(21) If (x.sub.i, y.sub.i, z.sub.i) are coordinates of a point of mass mi of the satellite, then in this satellite system of axes the inertia matrix is conventionally written as follows:

(22) $\stackrel{\_}{I}=\left[\begin{array}{ccc}-I_{\mathrm{Ox}}& -I_{\mathrm{xy}}& -I_{\mathrm{xz}}\\ -I_{\mathrm{xy}}& I_{\mathrm{Oy}}& -I_{\mathrm{yz}}\\ -I_{\mathrm{xz}}& -I_{\mathrm{yz}}& I_{\mathrm{Oz}}\end{array}\right]=\left[\begin{array}{ccc}\underset{i}{\overset{}{.Math.}}{m}_i\left(y_i^2+z_i^2\right)& -\underset{i}{\overset{}{.Math.}}{m}_i{x}_i{y}_i& -\underset{i}{\overset{}{.Math.}}{m}_i{x}_i{z}_i\\ -\underset{i}{\overset{}{.Math.}}{m}_i{x}_i{y}_i& \underset{i}{\overset{}{.Math.}}{m}_i\left(x_i^2+z_i^2\right)& -\underset{i}{\overset{}{.Math.}}{m}_i{y}_i{z}_i\\ -\underset{i}{\overset{}{.Math.}}{m}_i{x}_i{z}_i& -\underset{i}{\overset{}{.Math.}}{m}_i{y}_i{z}_i& \underset{i}{\overset{}{.Math.}}{m}_i\left(x_i^2+y_i^2\right)\end{array}\right],$

(23) The satellite principal system of axes, which includes points with coordinates (X, Y, Z) is obtained by seeking the principal directions of the inertia matrix of the satellite. In this system of axes, which is deduced from the satellite system of axes by a rotation, the inertia matrix at the center of mass of the satellite is a diagonal matrix of the following type:

(24) $\mathrm{Id}=\left[\begin{array}{ccc}{I}_X& 0& 0\\ 0& I_Y& 0\\ 0& 0& I_Z\end{array}\right]$

(25) The inertia values I.sub.X, I.sub.Y, I.sub.Z are generally different and can therefore be classified according to their value I.sub.minimum<I.sub.intermediate<I.sub.maximum.

(26) Considering the above diagonal inertia matrix Id of the satellite in the satellite principal system of axes, the known condition for gravity gradient stabilization of the attitude of the satellite is reflected in the fact that: the axis of the inertial principal system of axes for which the inertia value is I.sub.intermediate is aligned with the axis R of the local orbital system of axes; the axis of the inertial principal system of axes for which the inertia value is I.sub.maximum is aligned with the axis T of the local orbital system of axes; the axis of the inertial principal system of axes for which the inertia value is I.sub.minimum is aligned with the axis L of the local orbital system of axes.

(27) In other words, because of the effect of the gravity gradient, the satellite has tipped until it has reached the stable position indicated above.

(28) The gravity gradient therefore produces a restoring torque toward a stable attitude position of the satellite. Oscillations about the equilibrium position being naturally damped and dissipated by the flexible appendages (masts, sails), sloshing of the residual fluids in the tanks and atmospheric friction.

(29) As shown in FIG. 5, the satellite 100 includes two coplanar masts 10, 11 at an angle to a straight line segment 12 perpendicular to a plane P of placement of the masts on the satellite; the straight line segment 12 is the bisectrix of the angle between the two masts 10 and 11.

(30) The present invention causing the gravity gradient stable position and the aerodynamic stable position to coincide, the loss of efficacy linked to changes of attitude of the satellite depending on the altitude and to a lack of stability is avoided.

(31) The parameters that can be adjusted for the masts 10, 11 are the angle : angle of deployment of the mast relative to the vertical to the plane of placement of the mast on the satellite, the length L of the masts, the mass m at the mast ends producing the gravity gradient.

(32) With the given inertia values of the satellite, as a function of the angle , the length of the masts and the mast end mass, it is possible to obtain three stable configurations of the satellite. Referring to FIGS. 6A to 6C, three ranges of deployment angles of the masts correspond to three gravity gradient stabilized positions at high altitude: the position from FIG. 6A, first angle range 1 for which the masts are oriented upward in the direction opposite the direction DT of the center of the Earth; the position from FIG. 6B, second angle range 2 for which the masts are oriented in a direction opposite the direction V of movement of the satellite, the plane containing the masts being oriented in the direction DT of the Earth; and the position from FIG. 6C, third angle range 3 with the masts in a plane inclined relative to the direction V of movement of the satellite and relative to the direction DT of the center of the Earth.

(33) Referring to FIGS. 6D to 6F, at low altitude, because of the aerodynamic braking, three new stable positions are obtained. In FIGS. 6D to 6F the masts are oriented toward the rear of the satellite relative to its direction of movement.

(34) It is seen that only the second range, FIG. 6B, can ensure a stable position at high altitude, identical to the aerodynamic position, FIG. 6E, the other two ranges leading to tipping between the gravity stabilized regimes of FIGS. 6A, 6C and the aerodynamic stabilization regimes of FIGS. 6D and 6F, respectively.

(35) For a given mast length and a given satellite inertia, and if it is well chosen, the angle therefore makes it possible to achieve coincidence of the aerodynamic and gravity gradient regimes.

(36) The length L of the masts makes it possible to fix the deployed aerodynamic area and the gravity gradient torque.

(37) The mass m at the end of the mast makes it possible to adjust the gravity gradient torque stabilizing the attitude of the satellite.

(38) Considering a typical satellite 100a of the Myriad class represented diagrammatically in FIG. 5A and the dimensions and the masses of which constitute a parallelepiped-shape body 1 m1 m0.6 m including two small solar panels p1, p2 0.6 m1 m, a mass of 183 kg, but with no aerobraking sails, the inertial principal axes X, Y, Z are approximately as shown with the axis X in the direction of the solar panels, the axis Z perpendicular to the plane containing said panels and the axis Y perpendicular to the other two.

(39) In this system of axes the principal inertia matrix of the satellite is then as follows:

(40) $I=\left[\begin{array}{ccc}19& & \\ & 31& \\ & & 58\end{array}\right]\mathrm{kg}.Math.m^2$

(41) In this case, because of the effect of the gravity gradient, the stable position of the satellite is not that with the axis z aligned with the axis R, but that with the axis y aligned with the axis R, and the two solar panels have no aerodynamic braking effect.

(42) Consider now a satellite 100 according to the invention including two masts 10, 11, as indicated in FIG. 5B, 4.90 m long, each carrying a mass m of 1.8 kg at its free end and each carrying a 600 g sail 4.9 m long and 0.6 m wide.

(43) Different positions of equilibrium in the local orbital system of axes are distinguished on varying the angle of deployment of the masts relative to the bisectrix 12 between the masts along the axis Z.

(44) TABLE-US-00001 = 20 = 47.5 = 80 Satellite 118 78 33 principal 146 157 163 system 81 134 184 of axes inertia

(45) The above table gives typical inertias about the satellite axes for different values of angle in the satellite principal system of axes. That principal system of axes suffers a rotation about the axis z relative to the geometrical system of axes from FIG. 5A because of the aerobraking sails. This rotation in roll relative to the trajectory of the satellite is ignored in the calculations because it is not a problem in relation to braking the satellite.

(46) This table shows that there are three possible situations at high altitude: For a low angle , it is the axis X of the satellite that is parallel to the velocity axis of the satellite on its trajectory, axis R in FIG. 4; For an intermediate angle, it is the axis Z that is parallel to the axis R; For a high angle, it is axis Y that is parallel to the axis R.

(47) More comprehensive calculations show that it is possible at high altitude to identify three types of attitude of the satellite depending on the deployment angle . These attitudes are shown diagrammatically in FIGS. 6A to 6C for constant mast length, value of the mass at the mast end and sail area.

(48) As indicated above, for their part FIGS. 6D to 6F represent, under the same conditions, the attitude of the satellite at low altitude because of the effect of aerodynamic drag.

(49) It emerges from the calculations that two angle values .sub.1 and .sub.2 therefore define ranges that lead to three different behaviors of the satellite with its sails: For <1: There is tipping of the satellite on entering the aerodynamic regime according to FIGS. 6A and 6D; For .sub.2: The satellite will maintain the same stable attitude at high and low altitude according to FIGS. 6B and 6E; For .sub.2: The satellite will be reoriented relative to the yaw axis according to FIGS. 6C and 6F.

(50) For the above satellite data, .sub.1=33, .sub.2=62.

(51) The angle of inclination of the masts relative to their bisectrix is therefore chosen between .sub.1 and .sub.2 (33 and 62 for the satellite of this example), which makes it possible to make the gravity gradient position at high altitude coincide with the aerodynamic position at low altitude by optimizing this angle, because the larger the angle the greater the aerodynamic area presented.

(52) Finally, and in the case of the satellite from the chosen example, an angle of deployment of the masts of 47.5 has been adopted that makes it possible to ensure a margin of robustness in the face of inertia uncertainties.

(53) The effective aerodynamic area in the equilibrium position is then 6.94 m.sup.2. Compared to the prior art solution which, for the same Myriad family satellite, the same additional mass and identical masts and membranes, is not stabilized in attitude and has a mean aerodynamic area of only 5.1 m.sup.2, the invention makes it possible to increase the aerodynamic area of the satellite by 36% without increasing the onboard mass.

(54) FIG. 7 shows the stabilized satellite 100 with its masts 10, 11 and the panels 13, 13, 14, 14 deployed. The panels are provided in known manner by membranes and form aerobraking sails. In this Figure the satellite is seen from behind relative to its trajectory. The production of the deployment masts and the aerobraking membranes is based on inflatable masts, for example polyimide-aluminum laminate masts 120 that are stiffened by an increase in pressure as shown in FIG. 8. The architecture of the aerobraking system is made up of two masts 10, 11 and four aerobraking membranes 13, 13, 14, 14: each sail is optimized to take into account any oscillations of the satellite about the axis z.

(55) This type of deorbiting system can be installed for deorbiting purposes on any LEO satellite at an orbit below 850 km because above that altitude the atmosphere is too tenuous to slow the satellite sufficiently, necessitating an active device to bring it down in a time compatible with space requirements.

(56) It is also clear that for each satellite the angles 1 and 2, the length of the masts, the masses at their end, the area of the sails must be adapted using calculations such as those described above.

(57) The method for determining the dimensions of the masts, the masses m and the angle of the invention is as follows: Known trajectory calculation tools such as by way of nonlimiting example the Stella tool from ONES (Centre National des Etudes Spatiales, France) are used to determine a minimum effective area of the sail, i.e. the projection perpendicular to the trajectory of the aerobraking sail necessary and sufficient to enable deorbiting of the satellite within a chosen time; this time is 25 years maximum according to the laws and codes of good practice in this field; When this area has been determined, it is divided between two coplanar masts of length L with an angle 2 between them; A mass m is disposed at the end of each mast; The pair of masts is placed at an arbitrary location on the satellite; A satellite system of axes is chosen such that its axis z is the bisectrix of the angle between the two masts; The inertia matrix of the satellite is calculated and then diagonalized; The approach is reproduced by successive iterations that vary the location for installation of the masts, their length, the masses m and the angle , so that: aThe axis Z of the satellite principal system of axes is also the bisectrix of the masts; bThe inertia I.sub.Z in that system of axes has the intermediate value I.sub.intermediate; Values of the masses m, the mast lengths and the angle are chosen that make it possible to minimize the total mass of the sails whilst ensuring a certain robustness of the solution, i.e. that small variations of the parameters about the values adopted do not change the attitudes of the satellite with its sails.

(58) Under these conditions, according to the method of the invention, the axis Z is aligned with the velocity vector of the satellite both at high altitude by the action of the gravity gradient and at low altitude by the action of the aerodynamic force applied to the sails.

(59) The method of the invention is not limited to the calculations and characteristics of the satellite given by way of example and may notably be applied to satellites up to 500 kg in low Earth orbit (LEO).