Aerobraking satellite deorbiting system

Abstract

A satellite deorbiting device including an aerobraking surface including a satellite attitude control device with gravity gradient, the device with gravity gradient including at least one mast carrying the aerobraking surface, a first end of which is secured to the satellite and the second end of which is provided with a mass, such that the mast is oriented in a direction opposing that of the planet around which the satellite orbits.

Claims

1. A satellite deorbiting device comprising an aerobraking sail wherein it includes a gravity gradient satellite attitude control device for holding attitude of the satellite, the gravity gradient device including at least one mast carrying the aerobraking sail and a first end of which is secured to the satellite and a second end of which is provided with a mass, such that said mast orients itself in a direction opposite the direction of the planet around which the satellite orbits, and the aerobraking sail including at least two sails made of membranes deployed with and extending along a length of the mast, where each of the at least two sails has a length substantially equal to the length of the mast.

2. The satellite deorbiting device as claimed in claim 1, wherein the gravity gradient device is adapted to return the aerobraking sail to a direction perpendicular to the trajectory of the satellite.

3. The satellite deorbiting device as claimed in claim 1, wherein the aerobraking sail is such as to retain an effective aerobraking area whatever the orientation of the satellite about an axis parallel to the satellite/planet center direction.

4. The satellite deorbiting device as claimed in claim 1, wherein the aerobraking sail includes three sails disposed around said axis at 120.

5. A satellite comprising a deorbiting device as claimed in claim 1.

6. A method of producing a satellite as claimed in claim 5, the method comprising: defining the location and the direction of installation of the mast intended to support the aerobraking sail on the satellite; modeling the re-entry of the satellite using a modeling tool so as to determine an altitude at which the satellite flips during re-entry that corresponds to the maximum altitude to complete re-entry of the satellite in a given time and determine, based on a flipping point, a length m of the mast and the mass at an end of the mast; determining, by successive iterations and approximations, an area S.sub.aero of the sail, based on the length m of the mast and a mass at the end of the mast, such that a flipping point effected from the determined length m of the mast and the mass at an end of the mast is approximately situated at the altitude determined with the chosen total re-entry duration; and providing the device comprising the sail of determined area S.sub.aero, the mass having a determined minimized total mass, and the mast of determined length m; wherein the sail has one, two or three panels having a length substantially equal to the mast of determined length m and the determined area S.sub.aero.

7. The method as claimed in claim 6, wherein the iterations are effected using the equations $\stackrel{.fwdarw.}{C^{\mathrm{gg}}}=-\frac{3}{R^3}*\left(\left[I\right],\stackrel{.fwdarw.}{\mathrm{Zo}}\right)\stackrel{.fwdarw.}{\mathrm{Zo}};$ $\stackrel{.fwdarw.}{F}=-\frac{\mathrm{Saero}}{m}{C}_D{V}^2\frac{\stackrel{.fwdarw.}{V}}{V};$ and C.sub.aero=F.D.cos (.sub.y).

8. The method as claimed in claim 6, wherein the mast is defined perpendicular to the surface of the satellite having the greatest area.

9. The method as claimed in claim 6, wherein the mast is defined with its axis passing through the center of mass of the satellite.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

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

(2) FIG. 1 is a graph showing the correlation between the variation of density at a given altitude as a function of the solar flux;

(3) FIG. 2 is a graph showing the minimum and maximum densities of the atmosphere as a function of altitude according to solar activity minima/maxima;

(4) FIG. 3 is a graph of deorbiting with the roost unfavorable altitude as a function of time for a given satellite;

(5) FIG. 4 is a diagrammatic view of the principle of stabilization by gravity gradient applied to a satellite;

(6) FIG. 5 is a diagrammatic view of a satellite utilizing the gravity gradient stabilization principle;

(7) FIG. 6 is a graph representing the pitch angle of a satellite according to the disclosed embodiment as a function of altitude;

(8) FIG. 7 is a graph representing the re-entry profile of a satellite according to the disclosed embodiment;

(9) FIG. 8 is a diagrammatic perspective view of a satellite constructed in accordance with the principle of the disclosed embodiment;

(10) FIG. 9 is a graph representing the inclination of a satellite according to the disclosed embodiment as a function of solar activity and taking into account the balance between the restoring torque created by the gravity gradient and the torque created by the aerodynamic force on an aerobraking sail of said satellite;

(11) FIG. 10 is the illustration of a special case of FIG. 9;

(12) FIG. 11 is a plan view of an example of an aerobraking sail for a satellite of the disclosed embodiment;

(13) FIG. 12 is a perspective view from the side of the sail from FIG. 11;

(14) FIG. 13 is a satellite including a sail according to FIGS. 11 and 12;

(15) FIG. 14 is an example of materials for the production of a mast according to the disclosed embodiment; and

(16) FIG. 15 is a sectional view of an aerobraking sail membrane applicable to the disclosed embodiment.

DETAILED DESCRIPTION

(17) The principle of the disclosed embodiment consists in equipping a satellite with a deorbiting system that is deployed at the satellite end of life and combines a deorbiting sail and a gravity gradient device to maintain said sail in a position generating a high drag adapted to brake the satellite and therefore to cause it to lose altitude.

(18) The device stabilizes the satellite at end of life by means of the gravity gradient device, the sail and the gravity gradient device being designed so that the sail is the most perpendicular to the trajectory despite the flipping torque caused by drag. The disclosed embodiment also has the object of designing the sail and the gravity gradient device so that the denser the residual atmosphere the more the sail departs from this perpendicular position but remains within the stable range of the system.

(19) The gravity gradient device more particularly consists of a mast fixed to the satellite and a remote mass at the opposite end of the mast to the satellite.

(20) The sail and the gravity gradient device are ideally combined; for example, this can be the case of the sail of the type described in the document FR 2 897 843 A1 that extends along a mast that is deployed when it is required to begin the deorbiting of a satellite. The mass of the gravity gradient device enabling the stabilization of the satellite during deorbiting is placed at the end of the mast carrying the aerobraking sail.

(21) Moreover, the disclosed embodiment also concerns the operation of the gravity gradient aerobraking sail during the evolution of the orbit of the satellite as it descends.

(22) According to FIG. 4 gravity gradient stabilization consists in applying to the mast M fixed to the satellite S a force Z.sub.0 in the direction opposite the satellite-Earth direction T.

(23) The theory of the gravity gradient is illustrated below with reference to FIG. 5.

(24) The gravity gradient torque {right arrow over (C.sup.gg )} exerted on a satellite is given by:

(25) $\stackrel{.fwdarw.}{C^{\mathrm{gg}}}=-\frac{3}{R^3}*\left(\left[I\right],\stackrel{.fwdarw.}{\mathrm{Zo}}\right)\stackrel{.fwdarw.}{\mathrm{Zo}}$ With: : gravity constant, R: Satellitecenter of the Earth distance, Z.sub.0: unit vector of the local orbital system of axes, according to the Earth satellite direction, axis T, [I]: inertia matrix of the satellite in the system of axes of the satellite that comprises principal inertia axes {right arrow over (x)}{right arrow over (y)}{right arrow over (z)} as defined in FIG. 8, the axis z extending in the opposite direction to the mast.

(26) There is obtained in this way a restoring torque toward a stable attitude position of the satellite. Oscillations about the equilibrium position are naturally damped and dissipated by the flexible appendages (masts, sails), sloshing in the tanks and atmospheric friction.

(27) FIG. 5 shows a satellite of mass m1 including a deployed aerodynamic surface along a mast 21 and a mass m2 at the mast end.

(28) The gravity gradient pushes the mast into alignment with the Earth direction T, the mast taking up a position on the opposite side to the Earth relative to the body of the satellite.

(29) When the satellite is provided with an aerobraking sail having a direction parallel to the mast and an aerodynamic surface perpendicular to the direction of the satellite velocity, the deployed aerodynamic surface is almost normal to the velocity vector of the satellite and creates a maximum braking force.

(30) The braking force F is given by the equation:

(31) $\stackrel{.fwdarw.}{F}=-\frac{\mathrm{Saero}}{m}{C}_D{V}^2\frac{\stackrel{.fwdarw.}{V}}{V},$ with: : atmospheric density, S.sub.aero: aerobraking aerodynamic area (perpendicular to the trajectory of the satellite), also termed the effective braking area, m: satellite mass, C.sub.D: aerodynamic coefficient, V: satellite velocity.

(32) The aerobraking torque is then: C.sub.aero=F.Math.D.Math.cos(.sub.y), D being approximately the half-length of the mast; .sub.y being the angle between the mast and the Earth-satellite direction, equilibrium angle of the satellite subject to the aerobraking torque C.sub.aero and the gravity gradient torque {right arrow over (C.sup.gg)}.

(33) Equilibrium is then established between the gravity gradient torque and the torque linked to the application of the drag force at the aerodynamic center. The concept of stabilization of the sail therefore makes it possible to maximize the use of the available aerobraking area, stabilizing the satellite and avoiding flipping of the satellite on itself. The satellite has a total aerodynamic area varying with the pitch angle .sub.y. In an approximate manner:
S.sub.aero=S1.Math.cos(.sub.y)+S2.Math.sin(.sub.y) with: S1: principal aerobraking area (S.sub.satellite+S.sub.deployed); S2: secondary area after flipping of the satellite; typically S1>10*S2.

(34) It is clear that when the atmospheric density increases the force F increases and likewise the pitch angle .sub.y, which reduces S.sub.aero.

(35) Finally, by stabilizing the satellite using the gravity gradient device, the variations of the product *S.sub.aero are reduced, which makes it possible to obtain partial decoupling of the braking performance of the satellite and solar activity at a given altitude. The variation of the deorbiting time therefore depends less on the solar cycle and on average the deorbiting prediction is improved.

(36) The combination of an aerobraking sail and a gravity gradient device will therefore ensure a deorbiting time minimizing the spread of the re-entry time regardless of the phasing of the date at which deorbiting begins and solar cycles or the intensity of solar cycles.

(37) FIG. 6 gives an example of variation of the pitch angle curve (pitch deg) with altitude for a mean residual atmosphere profile with plotted on the abscissa axis the altitude in km and on the ordinate axis the inclination in pitch expressed in degrees.

(38) This table is for a 250 kg satellite equipped with an 8 m high deorbiting mast including a sail with three panels 8 m high, 0.55 m wide and each with a mass of 0.54 kg disposed around the mast at 120.

(39) It is found that the higher the atmospheric density, the less the gravity gradient torque is able to compensate the drag torque: the angle .sub.y increases and the satellite flips until .sub.y reaches 90. The satellite in its orbit has then reached a second equilibrium position and then has a constant aerodynamic area S.sub.aero, (S2) that is smaller whatever the increase of atmospheric pressure.

(40) It is therefore found that in this situation the concept of stabilization of the sail also makes it possible to maximize the use of the available aerobraking area even if the satellite flips on itself.

(41) Moreover, the so-called flipping altitude at which this second equilibrium position is reached is also a criterion for the dimensions of the aerobraking area. FIG. 7 shows the variations of altitude in apogee 3 and perigee 4 of a stabilized satellite with plotted on the abscissa axis time expressed in years and on the ordinate axis the altitude in km. The flipping point 5 must occur at a sufficiently low altitude, between 500 and 550 km and typically of the order of 525 km, where the atmospheric braking is sufficiently high to guarantee re-entry in a few years (3-5 years maximum) and for the solar activity variation to have negligible impact on the re-entry time of the satellite having a constant aerodynamic area (S2). The adjustment of this tipping altitude is effected by the design values for the mast length parameter and the mast end mass parameter.

(42) A concrete satellite example is given hereinafter by way of example and with reference to FIG. 8.

(43) The reference situation is a 250 kg satellite 50, a 9 m mast 51 and a 3.5 kg mast end mass 52. The panels forming the sail notably represented deployed in FIGS. 11 to 13 are rectangular panels extending along the mast that are 9 m=0.55 m each with a mass of 0.54 kg. The body of the satellite measures 1 m1 m0.6 m and in the example includes two small solar panels 53 that are 1 m0.6 m. The restoring torque of the gravity gradient in this case approximately 1 mN.Math.m.

(44) FIG. 9 makes it possible to determine the inclination I of the satellite in degrees as plotted on the ordinate axis (0 to 100 degrees in 10 steps) relative to the altitude A in km (100 km to 900 km in 100 km steps) as a function of solar activity taking account of the equilibrium between the restoring torque of the gravity gradient and the torque created by the aerodynamic force on the membrane of the sail.

(45) The curve 8 in this figure corresponds to minimum solar activity and the curve 9 corresponds to maximum solar activity. Between these two curves lies the range of inclination of the satellite 10. The point 6 corresponds to tipping of the satellite in minimal atmosphere (minimum solar activity) and the point 9 corresponds to tipping with maximum atmosphere (maximum solar activity).

(46) FIG. 10 corresponds to the inclination of a satellite taking the example of deorbiting starting at 725 km with an atmosphere of medium density over a rising solar activity cycle. The inclination of the satellite as a function of its altitude is given considering deorbiting over slightly more than one solar cycle with a first activity maximum 12 and a second activity maximum 11 between the start 14 of deorbiting and the end 6 of deorbiting.

(47) As a function of this data, the mast end mass is adjusted to make it possible to ensure tipping at an altitude between 500 and 550 km in the case of medium solar activity.

(48) These values are given by way of example, a precise calculation being required for each situation as a function of the date of starting deorbiting and the parameters of the satellite.

(49) FIGS. 11 and 12 show a 9 m long mast 21 of the type discussed above. The mast carries a mast head mass 25 and a deorbiting sail here comprising three membranes 22, 23, 24 disposed around the mast at 120 for both gravity gradient stabilization and deorbiting.

(50) The mast can be an inflatable mast for example utilizing the technology known from the document FR 2 877 315 A1 for deploying it for the purpose of deorbiting the satellite.

(51) The sail comprises three 9 m0.55 m panels extending along the mast and disposed around the mast at 120. These panels are produced with membranes having a mass of 0.54 kg which ensures effective braking whatever the yaw angle of the satellite, compensating the absence of stability in rotation about the mast. This configuration achieves a maximum aerodynamic area of 9.6 m.sup.2 including 9 m.sup.2 of membrane area and 0.6 m.sup.2 for the satellite when solar activity is at a minimum with a total deployed area of 16.2 m.sup.2.

(52) It is however possible to provide only two membranes disposed in a V with an angle between them making possible a compromise between the effective braking area and the stabilization of the satellite about an axis passing through the mast.

(53) A solution with a cylindrical sail but with lower optimization in terms of deployed area can be considered.

(54) FIG. 13 shows a satellite 20 provided with two solar panels 26 and equipped with the mast and the sail from FIGS. 11 and 12.

(55) The following materials are used to manufacture the mast and the membranes:

(56) As shown in FIG. 14 the mast is an inflatable mast that is made from an aluminum/polyimide film laminate (registered trademark Kapton) 130 m thick with a 250 g/m.sup.2 coating of SiOx to provide protection against the atomic oxygen present in low Earth orbit.

(57) It includes from the interior toward the exterior a first internal polyimide film 30, a first polyester adhesive 31, an aluminum foil 32, a second polyester adhesive 33, a second polyimide film 34 and the silicon oxide coating 35.

(58) The aerodynamic membrane 22 shown in section in FIG. 15 includes an aluminum/polyimide film (aluminum/Kapton) laminate approximately 40 to 80 m thick with a 100 g/m.sup.2 coating of SiOx.

(59) From one face to the other the membrane comprises a SiOx coating 41, a first polyimide film 43 12 to 15 microns thick, a layer 43 of glue 10 to 15 microns thick, an aluminum foil 14 to 15 microns thick, a second layer 45 of glue, a second polyimide film 46 and a second SiOx coating layer 47.

(60) The disclosed embodiment can be applied to satellites of 100 to 500 kg in LEO out to a maximum altitude of approximately 850 km.

(61) Depending on the mass of the satellite and its flight altitude, the deorbiting time is obtained by adjusting the height of the deployed mast and the mast end mass to ensure stabilization of the attitude by gravity gradient and tipping at an altitude below 550 km.

(62) The disclosed embodiment as defined by the claims is not limited to the example represented in the figures, and in particular the position of the mast can be modified and pass or not pass through the center of mass of the satellite.

(63) The method of defining a deorbiting sail of a satellite according to the disclosed embodiment is as follows (it is assumed that the satellite is known in terms of mass and geometry, which inter alia defines its aerobraking area S2 at low altitude, for all attitudes of the satellite; it is also assumed that the aim is to guarantee re-entry in less than 25 years, and that the altitude of the satellite is of the 800 km type):

(64) the location and the direction for installation of the mast intended to support the aerobraking sail are defined, the mast being typically, but not necessarily, perpendicular to the surface of the satellite having the greatest area S2, and the axis of the mast possibly but not necessarily passing through the center of mass of the satellite to simplify the calculations;

(65) satellite re-entry is modeled using a known tool such as the Stella tool from CNES, which makes it possible to determine the maximum altitude that makes it possible to guarantee an end of re-entry in less than 3 to 5 years; in other words, the tipping altitude of the satellite;

(66) successive iterations and approximations are then used to determine the area S.sub.aero of the sail, the length m of the mast and the mass at its end to guarantee:

(67) that the tipping point is situated approximately at the altitude previously determined;

(68) that the total duration of re-entry is that expected;

(69) the solutions are chosen that make it possible to minimize the total mass of the device comprising the sail plus the mass and the mast; and

(70) the real sail is then defined with one, two or three panels so that it has the length of the mast and the area S.sub.aero defined previously.

(71) The iterations are performed with a software tool of the Stella type from CNES and using equations for gravity gradient torque and aerodynamic torque of the type referred to above.

(72) It should be noted that it is possible in accordance with the disclosed embodiment to aim for re-entry times shorter than 25 years and different initial altitudes. It is then necessary to adapt the duration of the various phases accordingly, given that the person skilled in the art knows that very short re-entry times from a high altitude are not reasonably possible with a sail of acceptable area and mass.