Method for adjusting the orbital path of a satellite

A method for adjusting the path of a satellite to limit a risk of collision with items of debris each having a date of closest pass with the satellite is disclosed including: propagating at least one orbit from the reference path of the satellite according to at least one manoeuvre to the farthest date of closest pass; determining a probability of collision for each item of debris according to the at least one orbit; determining at least one overall probability according to the set of probabilities determined; selecting the lowest overall probability from among the at least one overall probability obtained; determining a command for the satellite including the manoeuvre associated with the lowest overall probability.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a National Phase of International Application Number PCT/IB2021/055117 filed Jun. 10, 2021, which designated the U.S. and claims priority benefits from French Application Number FR2005476 filed May 25, 2020, the entire contents of each of which are hereby incorporated by reference.

TECHNICAL FIELD OF THE INVENTION

The present invention relates to a method for adjusting the orbital path of a satellite in order to reduce a probability of collision of the satellite with a cloud of space debris. More particularly, the present invention relates to a method for determining one or more manoeuvres of the satellite orbiting the earth to reduce the probability of collision of the satellite with the cloud of orbital debris, that is, with all the orbital debris of the cloud.

PRIOR ART

Sequential debris avoidance strategies for a satellite based on a single manoeuvre on the opposite side of the orbit of a piece of debris are known in prior art. This strategy was adapted to the chemical propulsion satellite and considering the former population of tracked debris.

The current context is marked by an increase in mega constellation projects, where up to 1000 satellites can be operated. In addition, the number of tracked debris could increase from 20,000 to 100,000 objects when the detected radar surface of the debris is reduced from 10 centimetres to 5 centimetres. These two phenomena will create multi-debris conjunctions, where several pieces of debris have to be avoided.

In the case of electrically propelled satellites, space debris avoidance becomes more complex than for chemically propelled satellites. This is because the low thrust associated with electric propulsion does not usually enable avoidance to be performed in a single manoeuvre.

In addition, due to the low thrust associated with electric propulsion, satellite station-keeping manoeuvres are much more frequent. Therefore, to avoid mission disruption, hold manoeuvres can only be located in a dedicated location. In this way, hold manoeuvres will not be planned when the satellite is required for other purposes. Finally, in order to avoid operators commanding all hold manoeuvres, it is essential to calculate these hold manoeuvres with an automatic process.

To this end, sequential debris avoidance strategies by a satellite can no longer be applied.

DISCLOSURE OF THE INVENTION

The present invention aims to remedy these drawbacks with a completely new approach.

To this end, according to a first aspect, the present invention relates to a method for adjusting a satellite orbital path to limit a risk of collision with a cloud of space debris, each piece of debris including a date of closest passage with the satellite, the method including the steps of: determining a reference path of the orbit of the satellite from an initial time instant until the date of closest passage furthest from the initial time instant; determining an ephemeris of state transition data representative of the reference path of the orbit of the satellite; propagating, according to the determined ephemeris of state transition data, at least one first alternative orbit of the reference orbit of the satellite according to at least one first avoidance manoeuvre related to the satellite performed during at least one free manoeuvre time slot, and from at least one manoeuvre time instant of the at least one free manoeuvre time slot until the date of closest passage furthest from the initial time instant; analytically determining an individual probability of collision on each date of closest passage for each piece of debris according to the at least one first alternative orbit of the satellite; determining at least one overall probability of collision according to all the individual probabilities of collision determined according to the at least one first alternative orbit of the satellite related to the at least one first avoidance manoeuvre; selecting at least one first lowest overall probability of collision from the at least one overall probability obtained; determining a command of the satellite including at least the first manoeuvre related to the first lowest overall probability of collision selected.

The invention is implemented according to the embodiments and alternatives set out below, which are to be considered individually or in any technically operative combination.

Advantageously, the determination of a reference path of the orbit of the satellite can be determined according to a free drift propagation of the orbit of the satellite.

Advantageously, the step of propagating at least one first alternative orbit, the step of analytically determining an individual probability of collision and the step of determining at least one overall probability of collision, may be repeated iteratively along a plurality of directions of the at least one first avoidance manoeuvre so as to obtain a first plurality of alternative orbits related to a first plurality of avoidance manoeuvres and to evaluate a first plurality of overall probabilities of collision related to each of the alternative orbits related to the first plurality of avoidance manoeuvres.

Advantageously, each avoidance manoeuvre may comprise an initial value of maximum velocity variation allowed during the avoidance manoeuvre.

Advantageously, the method may comprise a step preceding the step of determining a command of the satellite, comprising adjusting the velocity variation of the at least one first avoidance manoeuvre of the command when the at least one previously selected lowest overall probability is less than a critical probability threshold of collision, so as to obtain at least one first overall probability of collision as close as possible to or equal to the critical probability threshold of collision.

Advantageously, the step of propagating at least one first alternative orbit, the step of analytically determining an individual probability of collision and the step of determining at least one overall probability of collision can be repeated according to a plurality of free manoeuvre slots of the satellite so as to obtain a second plurality of alternative orbits and to evaluate a second plurality of overall probabilities of collision related to the second plurality of alternative orbits.

Advantageously, the step of determining a command of the satellite may comprise a step of determining at least one second manoeuvre of the command of the satellite, said second manoeuvre being combined with the first manoeuvre related to the first lowest overall probability of collision, the at least one second manoeuvre producing a second alternative orbit enabling the calculation of a second lowest overall probability of collision according to the step of propagating the at least one first alternative orbit, the step of analytically determining an individual probability of collision, the step of determining at least one overall probability of collision and the step of selecting a first lowest overall probability of collision from the at least one overall probability obtained.

Advantageously, the determination of the second manoeuvre of the satellite command may include the step of determining a reference path of the orbit and the step of determining an ephemeris of state transition data according to which the reference path of the satellite is the path of the first alternative orbit of the satellite related to the first lowest overall probability of collision.

Advantageously, the ephemeris of state transition data may be an ephemeris of state transition matrix.

According to a second aspect, the present invention relates to a computer program product comprising instructions which, when the program is executed by a computer, cause the computer to implement the steps of the method described above.

According to a third aspect, the present invention relates to an information storage medium storing a computer program comprising instructions for implementing, by a processor, the method described above, when said program is read and executed by said processor.

DESCRIPTION OF THE EMBODIMENTS

According toFIG.1andFIG.2, a satellite10orbiting the Earth12and a cloud of space debris d1, d2, d3, dicomprising a plurality i of space debris d1, d2, d3, dialso orbiting the Earth12are represented. The satellite10orbits the earth12along its reference orbit Xref. Each piece of space debris d1, d2, d3, diof the cloud of debris comprises its own orbital path Xd1, Xdi. Each piece of space debris d1, d2, d3, d4, diis associated with an individual probability P1, Piof collision with the satellite12, each of the individual probabilities P1, Piof collision being evaluated according to a date specific to each piece of debris, called the date of closest passage TCA1, TCAi, that is, the date on which the distance between the average paths of the satellite10and each piece of debris d1, d2, d3, diconsidered individually is the shortest.

It is known to evaluate an individual probability Piof collision between a satellite10and a single piece of space debris d1in several ways according to the thesis presented and defended on December 10, two thousand and fifteen by Romain Serra, entitled “Opérations de proximité en orbite: évaluation du risque de collision et calcul de manoeuvres optimales pour l'évitement et le rendez-vous”, said thesis being publicly accessible especially via the “archives-ouvertes.fr” website under the reference tel-01261497. It will be noted in particular that a probability Piof collision between a satellite and a single piece of debris d1can be evaluated both according to a numerical integration calculation and according to an analytical formula in the form of a convergent series with positive terms.

According toFIG.3, a method for adjusting the orbital path of a satellite in order to reduce a probability of collision of the satellite with a cloud of space debris comprises determining the individual probability Piof collision of each piece of debris d1, d2, d3, diof the cloud with the satellite12, each individual probability P1, Piof collision having been evaluated according to its date of closest passage TCA1, TCAi.

To this end, the method for adjusting the orbital path of the satellite10requires the calculation of the probability of collision of the satellite10with the entire cloud of debris d1, d2, d3, di. In the following, the probability of collision of the satellite10with the cloud of debris will be referred to as the overall probability Pgof collision. The overall probability Pgof collision according to the invention can be determined from all the individual probabilities P1, Piof collision previously estimated, each on their date of closest passage TCA1, TCAi. Assuming that the probability calculation relating to an overall non-collision of the satellite10with the cloud of debris d1, d2, d3, dican be determined by the following formula:

1-P⁢g=∏i(1-P⁢i)
the overall probability Pgof collision according to the invention is determined according to the formula:

For the purpose of evaluating, on a given initial date t0, the individual probability Piof collision between a satellite10and a single piece of space debris d1, it is necessary to be able to determine as precisely as possible the orbital position and the covariance of the orbital position that the satellite and the single piece of debris would have on the date of closest passage TCA1 according to the data of the orbital position and the covariance of the orbital position of the satellite and the single piece of debris on the initial date t0.

According to the invention, it is necessary that the data on the orbital positions and covariance of the orbital positions of the debris d1, d2, d3, diof the cloud on the date of their closest passage TCA1, TCAiwith the satellite are previously known data, provided by space debris monitoring agencies such as, for example and in a non-limitative manner, the American organisation CSOpC (Combined Space Operations Center), or the international organisation SDA (The Space Data Association).

According to the invention, it is necessary to determine an ephemeris of data enabling the propagation of a state difference, also called ephemeris of state transition data, enabling a projection of the orbital position X(t) and of the covariance Cov of the orbital position of the satellite10on the dates of closest passages TC1, TCAi.

In particular, it is possible to be able to propagate the relative motion of a satellite using a state transition matrix.

According toFIG.4, one solution consists in performing a free drift propagation of the orbit of the satellite10, that is, without manoeuvring the satellite10, once from the initial date t0of determination of the overall probability Pgof collision until the date of closest passage TCAlastfurthest from the initial date t0of a piece of debris d1, d2, d3, diof the cloud. In this respect, two ephemerides are determined, namely an ephemeris of the reference orbit Xrefof the satellite10and an ephemeris of the state transition matrix ϕ(t, t0) corresponding to the path of the reference orbit Xref. This determination especially makes it possible to calculate all the state transition matrices ϕ(tn, tm)

According toFIG.5, the first satellite10orbiting the Earth12is in communication with a control centre14of the satellite10via a radio frequency communication means16. The control centre14of the satellite10may be configured to command orbital path manoeuvres of the satellite10especially by commanding thrusts of the satellite10according to a variation of the orbital velocity ΔV of the satellite10in a direction {right arrow over (d)} of the thrust. According toFIG.5, an example of a period of revolution of the satellite10around the Earth, also called the orbital period of the satellite10around the Earth12, is represented schematically by a discontinuous circle formed by several arcs of circle. Each arc represents a time slot that can be dedicated to an operation of the satellite10. As a non-limiting example, and according toFIG.5, the orbital period of satellite10may comprise two time slots for charging a battery for powering the satellite10, two other time slots for correcting the attitude of satellite10if necessary, another time slot for a mission to photograph the Earth12, and finally two other time slots available for any other operations of the satellite. In the following, the available time slots will be referred to as free manoeuvre slots Sl1, Sl2.

According to the invention, the method for adjusting the orbital path of the satellite10consists in determining the manoeuvre or manoeuvres necessary to command the satellite10during the free slot or slots Sli, in order to simultaneously avoid all the debris d1, d2, d3, diof the cloud when the initial overall probability Pg0of collision of the satellite10with the cloud of debris d1, d2, d3, diis greater than a critical probability threshold Pthof collision; the initial overall probability Pg0of collision of the satellite10being determined according to the reference orbit Xrefof satellite10.

According to the invention, in general, the term time slot may comprise simply an occasional date on which it is possible to command an orbital path adjustment manoeuvre of the satellite10.

Known prior art enabling the determination of one or more avoidance manoeuvres for a single piece of debris at a time is not contemplatable. Indeed, in the context of avoidance of a cloud of debris d1, d2, d3, diis not possible to determine an avoidance manoeuvre for a first piece of debris d1of the cloud without taking account of the other debris d2, d3, diof the cloud. In addition, the calculation time of the cumulative avoidance manoeuvre for each of the debris would be too heavy and not fast enough for the avoidance of the cloud of debris d1, d2, d3, di.

According to the invention, a fast propagation based on the state transition matrix ϕ(t, t0) and the ephemeris of the reference orbit Xrefof the satellite10enables the calculation of the effect of a manoeuvre during any of the free manoeuvre slots Sl1, Sliof the satellite10. The ephemerides will be used in the optimisation process to test a large number of possible thrust directions in order to calculate the effect on the overall probability Pgof a manoeuvre during any of the free manoeuvre slots Sl1, Sliof the satellite10.

The ephemerides of the orbit of the satellite10can be considered as a reference path that does not take account of the manoeuvre under consideration. The idea of calculating the real path is to modify this reference path by means of the ephemerides of the state transition matrix ϕ(t, t0).

To this end, the method for adjusting the orbital path of the satellite10comprises determining a first manoeuvre ΔV.{right arrow over (d)} and a free slot Slnenabling the execution of the first manoeuvre ΔV.{right arrow over (d)} so as to best optimise the overall probability Pgof collision, that is, preferably to obtain an overall probability Pgof collision less than or equal to the critical probability threshold Pthof collision.

To this end, according toFIG.6, each free manoeuvre slot Sl1, Sliis associated with a maximum velocity variation ΔV. The maximum variation ΔVmax of the velocity may be related for example and in a non-limiting manner either to the duration of the free manoeuvre slot Sl1, Slior to the maximum energy consumption of the electric propulsion device of the satellite10allowed for a manoeuvre. It will also be necessary according to the invention, that a minimum variation of the velocity of the satellite10is defined, this minimum variation being related to the minimum thrust energy required by the satellite10to perform a change of orbit of the satellite10.

According toFIG.7, several examples of orbits of the satellite10deviating from its reference orbit Xrefas a result of manoeuvre operations are represented. A first avoidance orbit X11of satellite10deviating from the reference orbit Xrefis represented. Said first avoidance orbit X11follows a first avoidance manoeuvre ΔVmax1.{right arrow over (d)}11commanded at a first manoeuvre time instant t_Sl1associated with the first free manoeuvre slot Sl1. The reference orbit Xrefof the satellite10before the first manoeuvre ΔVmax1.{right arrow over (d)}11at the manoeuvre time instant t_Sl1is directly determined according to the reference orbit Xrefdetermined at the manoeuvre time instant t_Sl1, and denoted as Xref(t_Sl1). More particularly, this orbit Xref(t_Sl1) can be determined by using the reference orbit Xrefby interpolating it into the generated ephemerides.

The determination of the first avoidance orbit X11(t_Sl1) evaluated at the manoeuvre time instant t_Sl1following the first avoidance manoeuvre ΔVmax1. {right arrow over (d)}11can be calculated by updating the reference orbit Xref(t_Sl1) at the manoeuvre time instant t_Sl1according to the first avoidance manoeuvre ΔVmax1.{right arrow over (d)}11. For Cartesian elements, this corresponds to performing a velocity increment ΔVmax1with the direction {right arrow over (d)}11of the manoeuvre expressed in the reference frame associated with these Cartesian elements. For Keplerian, circular and equinoctial elements, the Gaussian equation provides this delta state. In all cases, the calculation of the orbital deviation created by the first avoidance manoeuvre ΔVmax1.{right arrow over (d)}11can be written: ΔX11(t_Sl1)=F(ΔVmax1.{right arrow over (d)}11, Xref(t_Sl1)). Knowing the state transition matrices ϕ(TCAi, t0) and ϕ(t_Sl1, t0) determined previously, the orbital deviation ΔX11(TCAi) of the satellite10on each of the dates of closest passages TCAican be determined according to the formula:
ΔX11(TCAi)=ϕ(TCAi,t_Sl1)ΔX11(t_Sl1)=ϕ(TCAi,t0)ϕ(t_Sl1,t0)−1ΔX11(t_Sl1)

In order to be able to calculate all individual probabilities of collision Pibetween satellite10according to its first avoidance orbit X11following the first avoidance manoeuvre ΔVmax1.{right arrow over (d)}11, and all debris d1, d2, d3, diof the cloud according to their respective date of closest passage TCAi, it is necessary to determine the first avoidance orbit X11(TCAi) on each of said dates of closest passages TCAi. In this respect, the reference orbit Xref(TCAi) can be determined on each of the dates of closest passage TCAiby interpolating this reference orbit Xref(TCAi) into the ephemerides generated according to each of the dates of closest passage TCAi. Finally, the first avoidance orbit X11(TCAi) on each of said dates of closest passages TCAican be determined according to the formula:
X11(TCAi)=Xref(TCAi)+ΔX11(TCAi)

In order to be able to calculate all individual probabilities of collision Pibetween the satellite10according to its first avoidance orbit X11following the first avoidance manoeuvre ΔVmax1.{right arrow over (d)}11, and all the debris d1, d2, d3, diof the cloud according to their respective date of closest passage TCAi, it is necessary to determine the covariance COVTCAiof the orbital position of the satellite on each of said dates of closest passages TCAi. Knowing the state transition matrix ϕ(TCAi, t0) determined previously, and the covariance COVt0of the orbital position of the satellite10on the initial date0, the determination of the covariance COVTCAiprojected to each of the dates of closest passage TCAiis determined by the following formula:
covTCAi=ϕ(TCAi,t0)×covt0×ϕ(TCAi,t0)t

The first avoidance orbit X11of satellite10after the first avoidance manoeuvre ΔVmax1.{right arrow over (d)}11, being determined on each date of closest passage TCAi, as well as the covariance COVTCAion each date of closest passage TCAi, the orbit of each piece of debris d1, d2, d3, diand their covariance on their date of closest passage TCAibeing also known, the method for adjusting the orbital path of the satellite10may comprise determining all the individual probabilities of collision Pibetween the satellite10according to its first avoidance orbit X11following the first avoidance manoeuvre ΔVmax1.{right arrow over (d)}11, and all debris d1, d2, d3, diof the cloud according to their respective date of closest passage TCAi. To this end, the overall probability Pg11of collision related to the first avoidance manoeuvre ΔVmax1.{right arrow over (d)}11performed during the first free manoeuvre slot SL1can be calculated and compared with a critical probability threshold Pthof collision.

According toFIG.7, the method for adjusting the orbital path of the satellite10may comprise determining the overall probability Pgof collision as a function of different directions {right arrow over (d)} of a manoeuvre performed during the same free manoeuvre slot SL1and according to a given orbital velocity variation ΔV of the satellite10. According toFIG.7, a second avoidance orbit X21of the satellite10representing an alternative to the first orbit X11is represented. This second orbit, called second alternative avoidance orbit X21is obtained after the application of a second alternative avoidance manoeuvre ΔVmax1.{right arrow over (d)}21different from the first avoidance manoeuvre ΔVmax1.{right arrow over (d)}11during the same first free manoeuvre slot SL1. This so-called second alternative avoidance manoeuvre ΔVmax1.{right arrow over (d)}21differs from the first avoidance manoeuvre ΔVmax1. {right arrow over (d)}11in that the direction {right arrow over (d)}21applied to the thrust of the satellite10according to the same orbital velocity variation ΔVmax1differs from the first direction {right arrow over (d)}11. In this respect, a second alternative avoidance orbit X21(TCAi) of the satellite10on all dates of closest passage TCAiis also determined in the same way as described for the first avoidance orbit X11(TCAi). Knowing also the covariance COVTCAifor each of the dates of closest passage TCAi, a second alternative overall probability Pg12of collision related to the second alternative avoidance manoeuvre ΔVmax1.{right arrow over (d)}21performed during the first free manoeuvre slot Sl1can be calculated and compared with the critical probability threshold Pthof collision and also with the overall probability Pg11of collision related to the first avoidance manoeuvre ΔVmax1.{right arrow over (d)}11performed during the first free manoeuvre slot Sl1.

According toFIG.7, the method for adjusting the orbital path of the satellite10may comprise determining an overall probability Pgof collision as a function of the positioning in time of a manoeuvre ΔV{right arrow over (d)}. In other words, the overall probability Pgof collision is also a function of the free manoeuvre slot Sl1, Sliduring which a manoeuvre is performed. According toFIG.7, a third alternative avoidance manoeuvre ΔVmaxi.{right arrow over (d)}1iperformed during any of the free slots Slidistinct from the first free slot Sl1of manoeuvre is represented. To this end, a third alternative avoidance orbit X1i(TCAi) of the satellite10specific to each of the dates of closest passage TCAiis also determined in the same way as described for the first avoidance orbit X11(TCAi). Also knowing the covariance COVTCAifor each of the dates of closest passage TCAi, a third alternative overall probability Pg1iof collision associated with the third avoidance manoeuvre ΔVmaxi.{right arrow over (d)}1iperformed during said any of the free slots Slidistinct from the first free manoeuvre slot Sl1can be determined and compared with the critical probability threshold Pthof collision and also with the lowest overall probability Pgof collision determined during the first free manoeuvre slot Sl1.

In the same way as previously described, the method for adjusting the orbital path of the satellite10may comprise determining the overall probability Pgof collision as a function of different directions {right arrow over (d)} of a manoeuvre performed during any free slot Sliand according to a given orbital velocity variation ΔV of the satellite10. According toFIG.7, a fourth alternative avoidance orbit X2iof the satellite10deviating from the reference orbit Xrefat the manoeuvre time instant t_Sli representing an alternative of the previously described third alternative avoidance orbit X1iis represented. This fourth alternative avoidance orbit X2iis obtained after the application of a fourth alternative avoidance manoeuvre ΔVmaxi.{right arrow over (d)}2idifferent from the third alternative avoidance manoeuvre ΔVmaxi.{right arrow over (d)}1iassociated with the previously described third alternative avoidance orbit X1i. This so-called fourth alternative avoidance manoeuvre ΔVmaxi.{right arrow over (d)}2idiffers from the third alternative avoidance manoeuvre ΔVmaxi.{right arrow over (d)}1iin that the direction {right arrow over (d)}2iapplied to the thrust of the satellite10according to the same orbital velocity variation ΔVmaxidiffers from the direction {right arrow over (d)}1iof the third alternative avoidance manoeuvre ΔVmaxi.{right arrow over (d)}1i. In this respect, a fourth alternative avoidance orbit X2i(TCAi) of the satellite10related to the fourth alternative avoidance manoeuvre ΔVmaxi.{right arrow over (d)}1iis also determined on all dates of closest passages TCAiin the same way as described for the first avoidance orbit X11(TCAi). Knowing also the covariance COVTCAifor each of the dates of closest passage TCAi, a fourth alternative overall probability Pg2iof collision related to the fourth alternative avoidance manoeuvre ΔVmaxi.{right arrow over (d)}2iperformed during said any of the free slots Slidistinct from the first free manoeuvre slot Sl1can be calculated and compared with the critical probability threshold Pthof collision and also with the third alternative overall probability Pg1iof collision related to the third alternative avoidance manoeuvre ΔVmaxi.{right arrow over (d)}1iperformed during the same free slot Sli.

According to the determination of one or more overall probabilities of collision Pgas described inFIG.7, under the hypothesis that at least one of the determined overall probabilities of collision Pgwould be less than or equal to the critical probability threshold Pthof collision, then a single avoidance manoeuvre ΔVmax.{right arrow over (d)} performed during a single free slot Sliwould enable collision avoidance of the satellite10with all the debris d1, d2, d3, diof the cloud. According to this hypothesis, several strategies of the method for adjusting the orbital path of satellite10are possible.

A first strategy may consist in determining the first manoeuvre ΔV.{right arrow over (d)} enabling collision avoidance, that is, the avoidance manoeuvre ΔV.{right arrow over (d)} for which the overall probability Pgof collision associated with this manoeuvre, and thus the free slot Sliassociated with the manoeuvre, is less than or equal to the critical probability threshold Pthof collision. In order to determine the collision avoidance manoeuvre ΔV.{right arrow over (d)}, it will be necessary, for example, to first set a parameter of orbital velocity variation ΔV of the satellite10, for example and preferably according to its maximum value ΔVmaxiallowed during the free slot Sliunder consideration and to vary the direction {right arrow over (d)} of the manoeuvre. This operation is repeated on all the slots until a manoeuvre ΔVmaxi.{right arrow over (d)} is obtained that enables an overall probability less than or equal to the critical probability threshold Pthof collision to be obtained. The choice of the maximum allowed value ΔVmaxiof orbital velocity variation is a relatively relevant choice to obtain a lower overall probability Pgwith orbital velocity variations ΔV less than the maximum variation ΔVmaxi.

In the case of an overall probability Pgobtained strictly less than the critical probability threshold Pthof collision, a reduction in the maximum velocity variation ΔVmaxis possible in order to obtain an overall probability Pgof collision preferably equal to, or very close to, the critical probability threshold Pthof collision. In this way, the energy required for the identified manoeuvre will be reduced to a minimum.

It will be necessary according to the invention, that the determination of an orbital velocity variation ΔV combined with a determination of manoeuvre direction {right arrow over (d)} can be performed, for example and in a non-limiting manner, by dichotomy algorithms or Brent methods. It should be noted that a velocity variation ΔV may be associated with an optimal manoeuvre direction {right arrow over (d)}.

A second strategy may consist in determining, over a free slot Sliunder consideration, the avoidance manoeuvre ΔV{right arrow over (d)} enabling the lowest overall probability Pgof collision as a function of all possible manoeuvre directions {right arrow over (d)}, the orbital velocity variation ΔV of the manoeuvre preferably also being set to the maximum velocity variation ΔVmaxiallowed on the free slot Sliunder consideration. If the free slot Sliunder consideration does not make it possible to obtain an overall probability Pgless than or equal to the critical probability threshold Pthof collision, the determination should be repeated on another free slot Sli. In case this other free slot Slienables an overall probability Pgless than the critical probability threshold Pthof collision, a reduction in the maximum orbital velocity variation ΔVmaxof the manoeuvre ΔVmax{right arrow over (d)} determined is possible in order to obtain an overall probability Pgof collision preferably equal to, or even very close to, the critical probability threshold Pthof collision.

A third strategy may consist in determining, over all the previously identified free slots Sli, the avoidance manoeuvre ΔV{right arrow over (d)} enabling the lowest overall probability Pgof collision as a function of all the directions {right arrow over (d)} of possible manoeuvres for each free slot Sli, the orbital velocity variation ΔV of the manoeuvre also preferably being set to the maximum velocity variation ΔVmaxiallowed for each free slot Sli. Similarly to the first strategy, in the case where the identified avoidance manoeuvre ΔV{right arrow over (d)} enables an overall probability Pgless than the critical probability threshold Pthof collision, a reduction in the maximum orbital velocity variation ΔVmaxof the manoeuvre ΔVmax{right arrow over (d)} determined is possible in order to obtain an overall probability Pgof collision preferably equal to, or even very close to, the critical probability threshold Pthof collision.

It is well understood that other strategies for determining a collision avoidance manoeuvre ΔV{right arrow over (d)} according to the description inFIG.7are possible, so that the invention is not limited to the three examples of collision avoidance strategy previously described.

According to the invention, it is also likely that a single avoidance manoeuvre ΔV{right arrow over (d)} may not be sufficient to avoid a collision between the satellite10and all the debris of the cloud. In other words, it is also likely, according to the invention, that a single manoeuvre ΔV{right arrow over (d)} may not enable an overall probability Pgof collision less than or equal to the critical probability threshold Pthof collision to be obtained.

To this end, according toFIG.8, a first avoidance manoeuvre ΔVmax1.{right arrow over (d)}11and a second avoidance manoeuvre ΔVmaxi.{right arrow over (d)}5iof the satellite10following the first avoidance manoeuvre ΔVmax1.{right arrow over (d)}11are represented, the combination of the first avoidance manoeuvre ΔVmax1.{right arrow over (d)}11with the second avoidance manoeuvre ΔVmaxi.{right arrow over (d)}5ienabling avoidance of the collision of the satellite10with the debris d1, d2, d3, diof the cloud. More particularly, the first avoidance manoeuvre ΔVmax1.{right arrow over (d)}11represented is the first avoidance manoeuvre ΔVmax1.{right arrow over (d)}11represented inFIG.7for which a first avoidance orbit X11deviating from the reference orbit Xrefhas been determined. It will be necessary to hypothesise that of all the manoeuvres ΔV{right arrow over (d)} estimated in accordance with the description inFIG.7, the first avoidance manoeuvre ΔVmax1.{right arrow over (d)}11commanded at the first manoeuvre time instant t_Sl1associated with the first free manoeuvre slot Sl1has been identified as the avoidance manoeuvre ΔVmax1.{right arrow over (d)}11for obtaining the lowest overall probability Pgof collision11in comparison with the determination of all other estimated overall probabilities of collision Pgassociated with the manoeuvre alternatives ΔV{right arrow over (d)} performed from the reference orbit Xrefas described inFIG.7. It will also be necessary to assume according toFIG.8that the overall probability Pgof collision11associated with said first avoidance manoeuvre ΔVmax1.{right arrow over (d)}11is greater than the critical probability threshold of collision Pthr. To this end, it is necessary to determine at least one second avoidance manoeuvre ΔVmax1.{right arrow over (d)}5iof the satellite10following the first avoidance manoeuvre ΔVmax1.{right arrow over (d)}11so as to reduce the overall probability Pgof collision with the objective of obtaining in the end an overall probability Pgof collision at least equal to, or even less than, the critical probability threshold Pthrof collision. It will be necessary to name this second manoeuvre as the second avoidance manoeuvre ΔVmaxi.{right arrow over (d)}5iin the following description of the invention.

According toFIG.8, a second avoidance orbit X5iin continuity with the first avoidance orbit X11is represented. This second orbit X5i, called second avoidance orbit X5i, follows the second avoidance manoeuvre ΔVmaxi.{right arrow over (d)}5icommanded at any of the free slots Slidistinct from the first free manoeuvre slot Sl1. The first avoidance orbit X11of the satellite10at the manoeuvre time instant t_Slibefore the second avoidance manoeuvre ΔVmaxi.{right arrow over (d)}5iis directly determined, since it has been previously determined according to the description inFIG.7. The first avoidance orbit X11of the satellite10at the manoeuvre time instant t_Slibefore the second avoidance manoeuvre ΔVmaxi.{right arrow over (d)}5iis denoted as X11(t_Sli).

The determination of the second avoidance orbit X5i(t_Sli) evaluated at the manoeuvre time instant t_Slifollowing the second avoidance manoeuvre ΔVmaxi.{right arrow over (d)}5ican be calculated by updating the first orbit X11(t_Sli) at the manoeuvre time instant t_Sliaccording to the second avoidance manoeuvre ΔVmaxi.{right arrow over (d)}5i. For Cartesian elements, this corresponds to the second avoidance manoeuvre ΔVmaxi.{right arrow over (d)}5iin the inertial reference frame. For Keplerian, circular and equinoctial elements, the Gaussian equation provides this delta state. In all cases, the calculation of the orbital deviation created by the second avoidance manoeuvre ΔVmaxi.{right arrow over (d)}5ican be written: ΔX5i(t_Sli)=F(ΔVmaxi.{right arrow over (d)}5i, X11(t_Sli)). In the same way as described inFIG.4, considering that the first orbit X11is a new reference orbit with respect to the second avoidance manoeuvre ΔVmaxi.d5i, the orbital deviation ΔX5i(TCAi) of the satellite10on each of the dates of closest passages TCAican be determined according to the formula:
ΔX5i(TCAi)=ϕ(TCAi,t_Sli)ΔX5i(t_Sli)=ϕ(TCAi,t_Sl1)ϕ(t_Sli,t_Sl1)−1ΔX5i(t_Sli)

In order to be able to calculate all individual probabilities of collision Pi between the satellite10according to its second avoidance orbit ΔX5i(t_Sli) following the second avoidance manoeuvre ΔVmaxi.{right arrow over (d)}5i, and all debris d1, d2, d3, diof the cloud according to their respective date of closest passage TCAi, it is necessary to determine the second avoidance orbit X5i(t_Sli) on each of said dates of closest passages TCAi. In this respect, the first avoidance orbit X11(TCAi) can be determined on each of the dates of closest passage TCAiby interpolating this first avoidance orbit X11(TCAi) into the ephemerides generated according to each of the dates of closest passage TCAi. Finally, the second avoidance orbit X5i(t_Sli) can be determined on each of said dates of closest passages TCAiaccording to the formula:
X5i(TCAi)=X11(TCAi)+ΔX5i(TCAi)

The second avoidance orbit X5iof the satellite10after the second avoidance manoeuvre ΔVmaxi.{right arrow over (d)}5ias well as the orbital covariance COVTCAiof the satellite10being determined on each date of closest passage TCAi, the orbit of each piece of debris d1, d2, d3, diand their covariance on their date of closest passage TCAibeing also known, the method for adjusting the orbital path of satellite10may comprise determining all the individual probabilities of collision Pi between the satellite10according to its second consecutive orbit X5ifollowing the second avoidance manoeuvre ΔVmaxi.{right arrow over (d)}5i, and all debris d1, d2, d3, diof the cloud according to their respective date of closest passage TCAi. To this end, the overall probability Pg5iof collision related to the second avoidance manoeuvre ΔVmaxi.{right arrow over (d)}5iperformed during said any of the free slots Slidistinct from the first manoeuvre slot Sl1can be calculated and compared with a critical probability threshold Pthof collision.

Similarly toFIG.7, the method for adjusting the orbital path of the satellite10may comprise determining a plurality of other overall probabilities Pgof collision according to a plurality of further second alternative avoidance manoeuvres ΔV{right arrow over (d)} in combination with the first avoidance manoeuvre ΔVmax1.{right arrow over (d)}11, each representing an alternative of the second ΔVmaxi.{right arrow over (d)}5iavoidance manoeuvre represented inFIG.8; these other second alternative avoidance manoeuvres ΔV{right arrow over (d)} being according to another free manoeuvre execution slot Sliand/or along another manoeuvre direction {right arrow over (d)} than the second avoidance manoeuvre ΔVmaxi.{right arrow over (d)}5ias represented inFIG.8. Each of the overall probabilities of collision Pgeach related to one of the other second alternative avoidance manoeuvres ΔV{right arrow over (d)} can be compared with the critical probability threshold Pthof collision and with all other overall probabilities of collision Pgrelated to the other second avoidance manoeuvres ΔV{right arrow over (d)}.

To this end, according toFIG.8, under the hypothesis of at least one overall probability Pgof collision, related to a second avoidance manoeuvre ΔV{right arrow over (d)} less than or equal to the critical probability threshold Pthof collision, it will be necessary according to the invention and in a non-limiting manner, to be able to determine the second avoidance manoeuvre ΔV{right arrow over (d)} enabling the avoidance of the collision of the satellite10with all the debris d1, d2, d3, diof the cloud according to at least one of the three strategies of the method for adjusting the orbital path of the satellite10similar to the three strategies described in the preceding paragraphs relating toFIG.7.

In the case of an overall probability Pgstrictly less than the critical probability threshold Pthof collision after the application of the second avoidance manoeuvre ΔVmaxi.{right arrow over (d)}5ifollowing the first avoidance manoeuvre ΔVmaxi.{right arrow over (d)}11, a reduction in the maximum velocity variation ΔVmaxis possible in order to obtain an overall probability Pgof collision preferably equal to, or even very close to, the critical probability threshold Pthof collision. In this way, the energy required for the identified second avoidance manoeuvre ΔV{right arrow over (d)} will be reduced to a minimum.

According to the invention, and in accordance with the description inFIG.7andFIG.8, the first avoidance manoeuvre and the second avoidance manoeuvre may each be manoeuvres performed on any of the free slots Sli, the free slot Sliassociated with the second avoidance manoeuvre being distinct from that associated with the first avoidance manoeuvre. More particularly, according to a strategy with two or more avoidance manoeuvres, and it is possible, according to the method for adjusting the orbital path of the satellite10, to determine a second avoidance manoeuvre to be performed on a free slot Sliprior in time to the free slot Sliof the first manoeuvre. In other words, according to the method for adjusting the orbital path of the satellite10, it is possible to determine a first avoidance manoeuvre to be performed on a free slot Slilater in time than the free slot of the second avoidance manoeuvre Sli, said second avoidance manoeuvre being determined later than the first manoeuvre.

To this end, in general, a first orbit X1(t) from a first avoidance manoeuvre ΔVmax.{right arrow over (d)}1relating to the reference orbit Xref, determined on any of the free slots Sli, serving as a new reference orbit relative to a second avoidance manoeuvre ΔV.{right arrow over (d)}2, should be able to be evaluated also for the free slot or slots Sliprior to said any of the free slots Sliassociated with the first manoeuvre. To this end, and in general, the first avoidance orbit X1(t_Sli<t) at all manoeuvre time instants t_Slirelating to the free slots prior to the first avoidance manoeuvre ΔVmax.{right arrow over (d)}1orbit is determined by interpolation of the ephemerides related to the reference orbit Xref.

To this end, it will be necessary for the method for adjusting the orbital path of a satellite10to command the avoidance manoeuvres to the satellite10not in the order of determination of the avoidance manoeuvres, but according to a time sequential execution of manoeuvres according to the time location of free slots Sliassociated with the determined collision avoidance manoeuvres.

According toFIG.9, a non-limiting example of the application of a strategy for determining free slots Sl1, Sliand avoidance manoeuvres required to avoid a collision of the satellite10with the cloud of debris d1, diis represented. To this end, a hypothesis is made that 5 free manoeuvre slots Sl1, Sl2, Sl3, Sl4, Sl5are available in order to be able to carry out the avoidance manoeuvres in such a way as to obtain an overall probability Pgof collision less than or equal to the critical threshold Pthof collision. As a non-limiting example, the critical threshold of collision Pthis set to Pth=0.0005.

According toFIG.9, three lines representative of three determinations D1, D2, D3 of three avoidance manoeuvres required for collision avoidance between the satellite10and the cloud of debris d1, diare represented. A fourth determination line D4 represents the optimisation of the parameters of the third manoeuvre, that is, the velocity variation ΔV and the direction {right arrow over (d)} of the thrust so as to obtain an overall probability Pgof collision equal to the critical threshold Pthof collision, equal to Pth=0.0005.

The first determination D1 consists in determining a first avoidance manoeuvre ΔV.{right arrow over (d)} on any of the five free manoeuvre slots Sl1, Sl2, Sl3, Sl4, Sl5enabling a first lowest overall probability to be obtained. To this end, in a manner similar to that described throughFIG.7, a plurality of manoeuvres on each free slot, each along a plurality of directions related to the manoeuvre thrust and according to a maximum velocity variation ΔV related to each free manoeuvre slot Sl1, Sl2, Sl3, Sl4, Sl5is evaluated. According to this first determination D1, the first manoeuvre to obtain the first lowest overall probability Pg1of collision is one of the manoeuvres evaluated on the third free slot Sl3, along a first direction {right arrow over (d)}3and according to the maximum velocity variation ΔV3max allowed during the third free slot Sl3. As a non-limiting example, the first overall probability Pg1of collision obtained has a value equal to Pg1=0.001. As this value of first overall probability Pg1following the first avoidance manoeuvre ΔV3max.{right arrow over (d)}3={right arrow over (ΔV3)}max is not less than or equal to the critical threshold of Pthof collision, a second collision avoidance manoeuvre has to be determined.

According toFIG.9, the second determination D2 consists in determining a second avoidance manoeuvre ΔV.{right arrow over (d)} on any of the four free manoeuvre slots Sl1, Sl2, Sl4, Sl5distinct from the third slot already determined for the first avoidance manoeuvre {right arrow over (ΔV3)}max enabling a second lowest overall probability Pg2to be obtained, by taking account of the effect of the first manoeuvre {right arrow over (ΔV3)}max. To this end, in a manner similar to that described throughFIG.8, a plurality of avoidance manoeuvres on each of the four free manoeuvre slots Sl1, Sl2, Sl4, Sl5remaining available, is evaluated along a plurality of directions related to the manoeuvre thrust and according to a maximum velocity variation ΔV related to each free manoeuvre slot Sl1, Sl2, Sl4, Sl5remaining. According to this second determination D2, the second avoidance manoeuvre enabling the second lowest overall probability Pg2of collision to be obtained is one of the avoidance manoeuvres evaluated on the second free slot Sl2, along a second direction {right arrow over (d)}2 and according to the maximum velocity variation ΔV2max allowed during the second free slot Sl2. As a non-limiting example, the second overall probability Pg2of collision obtained has a value equal to Pg2=0.0007. As this value of second overall probability Pg2following the combination of the first manoeuvre {right arrow over (ΔV3)}max and the second avoidance manoeuvre {right arrow over (ΔV2)}max is not less than or equal to the critical threshold of collision Pth, a third collision avoidance manoeuvre has to be determined.

According toFIG.9, the third determination D3 consists in determining a third avoidance manoeuvre ΔV.{right arrow over (d)} on any of the three free manoeuvre slots Sl1, Sl4, Sl5still available, enabling a third lowest overall probability Pg3to be obtained by taking account of the combined effect of the first avoidance manoeuvre {right arrow over (ΔV3)}max and the second avoidance manoeuvre {right arrow over (ΔV2)}max. To this end, in a manner similar to that described throughFIG.8, a plurality of avoidance manoeuvres on each of the three free manoeuvre slots Sl1, Sl4, Sl5remaining available, is evaluated along a plurality of directions related to the thrust of the avoidance manoeuvre and according to a maximum velocity variation ΔV related to each free manoeuvre slot Sl1, Sl4, Sl5remaining. According to this third determination D3, the third avoidance manoeuvre enabling the lowest third overall probability Pg3of collision to be obtained is one of the manoeuvres evaluated on the fifth free slot Sl5, along a fifth direction {right arrow over (d)}5 and according to a maximum velocity variation ΔV5max allowed during the fifth free slot Sl5. As a non-limiting example, the third overall probability Pg3of collision obtained has a value equal to Pg2=0.0003, that is, a value below the critical threshold of Pthof collision.

According toFIG.9, a fourth determination D4 consists in adjusting the parameters of the third manoeuvre so as to obtain a third overall probability Pg3of collision equal to the critical threshold of Pthof collision, namely Pth=0.0005. In this respect, a velocity variation value ΔV5optless than the maximum velocity variation ΔV5max allowed, and combined with a fifth direction {right arrow over (d)}5_opt optimised with respect to the optimal velocity variation ΔV5optis obtained.

According toFIG.9, a collision avoidance command C of the satellite10with all the debris d1, diof the cloud comprises the combination of the three determined avoidance manoeuvres {right arrow over (ΔV3)}max, {right arrow over (ΔV2)}max, {right arrow over (ΔV5)}optperformed according to a time order related to the three free slots associated with said three manoeuvre. In other words, the collision avoidance command C includes a first command C1 comprising the execution during the second free slot Sl2of the second determined avoidance manoeuvre {right arrow over (ΔV2)}max, then the collision avoidance command C includes a second command C2 comprising the execution during the third free slot Sl3 of the first determined avoidance manoeuvre {right arrow over (ΔV3)}max, and finally, the collision avoidance command C includes a third command C3 comprising the execution during the fifth free slot Sl5of the third determined avoidance manoeuvre {right arrow over (ΔV5)}opt.

Optionally, and according to the invention, in order to confirm the result obtained, namely the determination of manoeuvres of the satellite enabling collision avoidance between the satellite and all the debris of the cloud, preferably a numerical calculation of the path of the satellite10including all the identified manoeuvres can be performed.

Indeed, the propagation used to evaluate the avoidance manoeuvres on the overall probability Pgof collision, called fast propagation based on the ephemeris of the state transition matrix ϕ(t, t0) and on the ephemeris of the reference orbit Xrefof satellite10, is a simplified propagation. As a result, the overall probability Pgof collision may be slightly different from an overall probability of collision determined according to numerical orbit propagation determinations, for example and in a non-limiting manner, from the orbital parameters of satellite10. To ensure that this overall probability Pgof collision is close to the critical probability threshold of collision Pth, a numerical propagation taking account of the previously estimated manoeuvres should be performed and the overall probability of collision recalculated.

If, however, the operation of calculating the overall probability Pgof collision based on a numerical propagation of the orbit of the satellite10, especially comprising the avoidance manoeuvres determined previously, results in an overall probability Pgof collision greater than the critical probability threshold Pthof collision, it would be necessary, according to the invention, to resume the determination of additional avoidance manoeuvres according to the method for adjusting the orbital path of the satellite10described inFIGS.7and8, from a new reference orbit relating to the orbit of the satellite determined numerically.

A simpler solution than that based on a verification of the calculation of the overall probability Pgof collision by a numerical calculation of the propagation of the orbit of the satellite corrected according to the avoidance manoeuvres determined previously, simply consists in setting a sufficiently low critical probability threshold of collision Pthin order to compensate for the uncertainties of the so-called fast propagation solution.

According toFIG.10, a non-limiting example of a flowchart relating to the method100for adjusting the orbital path of the satellite10comprises several steps.

The first step consists in determining110a reference path of the orbit Xrefof the satellite10from an initial time instant t0until the date of closest passage TCA1, TCAifurthest from the initial time instant t0. Preferably, according to the invention, the determination110of the reference path of the orbit Xrefof the satellite10is determined according to a free drift propagation of the orbit Xrefof the satellite10.

The first step is associated with a second step relating to the determination120of an ephemeris of a state transition matrix ϕ(t, t0) representative of the reference path of the orbit Xrefof the satellite10. This first step is essential to the invention. It makes it possible especially to calculate all the state transition matrices ϕ(tn, tm) required for the method for adjusting the orbital path of the satellite.

The determined state transition matrix ϕ(t, t0) enables a step130of propagating at least one first alternative orbit X1iof the reference orbit Xrefof the satellite10according to at least one first avoidance manoeuvre ΔV.{right arrow over (d)} related to the satellite10performed during at least one free manoeuvre time slot Sl1, and from at least one manoeuvre time instant t_Sl1of the at least one free manoeuvre time slot Sl1until the date of closest passage TCAifurthest from the initial time instant t0.

The propagation of the at least one first alternative orbit X1iof the satellite10enables a step of analytically determining140an individual probability Piof collision on each date of closest passage TCA1, TCAifor each piece of debris d1, direlated to at least the first alternative orbit X1iof the satellite10.

The method100for adjusting the orbital path of the satellite10, in accordance with the description inFIG.3, comprises a step of determining150at least one overall probability Pgof collision according to all the individual probabilities Piof collision determined according to the at least one first alternative orbit X1iof the satellite10related to the at least one first avoidance manoeuvre ΔV.{right arrow over (d)}. This step of determining150at least one overall probability Pgof collision is followed by a step of selecting160at least one first lowest overall probability Pgof collision from the at least one determined overall probability Pgof collision.

Preferably, the method100comprises an initial step according to which each avoidance manoeuvre ΔV.{right arrow over (d)} comprises an initial value of maximum velocity variation ΔVmax allowed during the avoidance manoeuvre ΔV.{right arrow over (d)}. The method100preferably also comprises a step of adjusting170the velocity variation ΔV of the at least one first avoidance manoeuvre ΔV.{right arrow over (d)} when the selected at least first lowest overall probability Pgis less than a critical probability threshold Pthof collision, so as to obtain at least one first overall probability Pgof collision as close as possible to or equal to the critical probability threshold Pthof collision. The adjustment of the velocity variation ΔV may also be associated with an adjustment of the direction {right arrow over (d)} of the manoeuvre.

The method also includes a step of determining180a command C of the satellite10including at least the first manoeuvre related to the first lowest overall probability Pgof collision selected so as to best minimise the risk of collision of the satellite10with the cloud of debris.

Preferably, the step of propagating130alternative orbits is repeated several satellite times by a step of multiple iterations190on the direction {right arrow over (d)} of the avoidance manoeuvre ΔV.{right arrow over (d)} so as to obtain a first plurality of alternative orbits X1irelated to a first plurality of avoidance manoeuvres ΔV.{right arrow over (d)} and to evaluate a first plurality of overall probabilities of collision Pgrelated to each of the alternative orbits related to the first plurality of avoidance manoeuvres ΔV.{right arrow over (d)}.

Preferably, the step of propagating130alternative orbits is also repeated several times by a step of multiple iterations200according to a plurality of free manoeuvre slots Sl1, Sliof the satellite10so as to obtain a second plurality of alternative orbits X1iand to evaluate a second plurality of overall probabilities Pgof collisions related to the second plurality of alternative orbits X1i.

According toFIG.10, the step of determining180a command C of the satellite10may comprise a plurality of additional steps230,240,250,260,270,290, and300similar to the steps preceding the step of determining180a command C, for defining a step of determining280the command C of the satellite10for which at least one second avoidance manoeuvre combined with the first manoeuvre related to the first lowest overall probability Pgof collision is also determined. The at least one second manoeuvre is the second manoeuvre related to a second lowest probability of collision determined according to the steps230,240,250,260,270,290, and300of the method.

According toFIG.10, the step of determining280the command C of the satellite10for which at least one second avoidance manoeuvre combined with the first manoeuvre related to the first lowest overall probability Pgof collision is also determined, may include the steps210,220of the method for which the reference path of the satellite10is the path of the first alternative orbit X1iof the satellite10related to the first lowest overall probability Pgof collision. The path of the first alternative orbit X1iof satellite10could be numerically re-evaluated taking account of the first avoidance manoeuvre. The path of the first alternative orbit X1iof satellite10will serve as a new reference path, and enable the generation of new ephemerides of the state transition matrix ϕ(t, t0).

According toFIG.11, a device400for implementing the method for adjusting the orbital path of the satellite10may comprise an information processing unit402of the processor type such as, for example and in a non-limiting manner, a processor specialised in signal processing, or a microcontroller, or any other type of circuit enabling software-type instructions to be executed. The device400also includes random access memory404associated with the information processing unit402. The information processing unit402is configured to execute a program, also called a computer program, comprising instructions implementing the method100for adjusting the orbital path of a satellite10described above. The instructions are loaded into the random access memory of the device400from any type of storage media406such as, for example and in a non-limiting manner, a non-volatile type memory or an external memory such as a removable storage memory card. The instructions may also be loaded via a connection to a communications network.

Alternatively, the computer program, comprising instructions implementing the method100for adjusting the orbital path of the satellite10, may also be implemented in hardware form by a machine or by an application-specific integrated circuit or by a programmable logic array type electronic circuit.

It should be understood that the detailed description of the subject matter of the invention, which is given for illustrative purposes only, does not in any way constitute a limitation, as the technical equivalents are also comprised in the scope of the present invention.