WO2008118140A2 - Procédés et appareil de contrôle d'excentricité de nœuds synchrones - Google Patents

Procédés et appareil de contrôle d'excentricité de nœuds synchrones Download PDF

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Publication number
WO2008118140A2
WO2008118140A2 PCT/US2007/022322 US2007022322W WO2008118140A2 WO 2008118140 A2 WO2008118140 A2 WO 2008118140A2 US 2007022322 W US2007022322 W US 2007022322W WO 2008118140 A2 WO2008118140 A2 WO 2008118140A2
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satellite
orbit
vector
eccentricity
inclination
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PCT/US2007/022322
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English (en)
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WO2008118140A3 (fr
Inventor
Bernard M. Anzel
Yiu-Hung M. Ho
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The Boeing Company
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Priority to PCT/US2007/022322 priority Critical patent/WO2008118140A2/fr
Publication of WO2008118140A2 publication Critical patent/WO2008118140A2/fr
Publication of WO2008118140A3 publication Critical patent/WO2008118140A3/fr

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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
    • B64G1/242—Orbits and trajectories
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
    • B64G1/26—Guiding or controlling apparatus, e.g. for attitude control using jets

Definitions

  • This invention relates generally to maintaining a position of orbiting satellites, and more specifically, to methods and systems for node-synchronous eccentricity control.
  • Spacecraft such as satellites
  • Earth orbits for a variety of purposes, e.g., weather monitoring, scientific observations and commercial communications. Accordingly, they are maintained in a variety of attitudes and placed in a variety of orbits (e.g., low Earth orbit, transfer orbit, inclined synchronous orbit and geostationary orbit).
  • orbits e.g., low Earth orbit, transfer orbit, inclined synchronous orbit and geostationary orbit.
  • a spacecraft's orbital position is typically defined by the orbit's eccentricity, the inclination of the orbital plane from the Earth's equatorial plane, and the spacecraft's longitude.
  • the spacecraft's orbital period matches the Earth's rotational period, the eccentricity is substantially zero and the spacecraft's orbital plane is substantially coplanar with the Earth's equatorial plane.
  • the principal forces which disturb a spacecraft's position are generated by the gravity of the sun and the moon, the Earth's elliptical shape (triaxiality) and solar radiation pressure.
  • Inclined geosynchronous orbits which are often used for communications to mobile customers are similar to those of geostationary orbits, except, they have a non-zero inclination typically in the range of three to seven degrees.
  • Such satellites pass through the equatorial plane twice each day, once at an ascending node (the portion of the satellite orbit above an equatorial plane), and once at a descending node (the portion of the satellite orbit below an equatorial plane).
  • the motion of satellites in inclined geosynchronous orbits is more complex in practice, due to orbit eccentricity, drift and other perturbing forces.
  • geostationary orbits Due to satellite-to-satellite communication interference issues, satellites in geostationary orbits are assigned to geostationary "slots" that may vary from 0.2 degrees wide to 0.1 degrees wide in longitude near the equatorial plane. Despite their motion, interference is still a problem, and satellites in inclined geosynchronous orbits are also assigned to geostationary "slots" near the equatorial plane, with the same constraints between 0.1 degrees and 0.2 degrees in longitude. These longitude constraints are defined in a latitude range of between 0.1 degrees and 0.2 degrees in the equatorial zone. The constraints in latitude and longitude, are sometimes referred to as defining a "box".
  • Station keeping may be facilitated with thrusters which are directed to generate forces through the spacecraft's center of mass.
  • Attitude control is generally facilitated with momentum and/or reaction wheels whose momentum is periodically “dumped” when the same (or different) thrusters are directed to generate turning moments about the spacecraft's center of mass.
  • Conventional thruster systems typically have sets of thrusters that are aligned in north-south and east-west directions.
  • the north-south thrusters produce north-south velocity changes ( ⁇ V) to control inclination.
  • the east-west thrusters produce an east-west ⁇ V to control drift (change of longitude with time) and eccentricity.
  • the problem associated with maintaining a slot and/or box position is especially critical for current and future generation spacecraft.
  • Such spacecraft often have large solar arrays and solar collectors, and therefore receive a strong solar force.
  • This solar force requires a large steady state eccentricity when a single burn sun-synchronous perigee station keeping strategy is used.
  • This eccentricity is difficult to control efficiently, even when a sun synchronous perigee station keeping strategy, which compresses eccentricity using double burn control maneuvers, is used.
  • the east/west longitude excursion due to eccentricity can take up more than half the width of the slot.
  • Other factors also consume slot width, including drift over the maneuver cycle, maneuver execution error, ⁇ V increments associated with momentum dumping disturbances, orbit determination error, and orbit propagation error.
  • Maintaining a longitudinal position of such a satellite in a synchronous inclined orbit is sometimes referred to as east-west station keeping. Maintaining the inclination of the orbit is sometimes referred to as north-south station keeping. Maintaining the longitudinal position of satellites in a synchronous inclined orbit has been previously performed based on the sun- synchronous strategy introduced above. The sun-synchronous strategy was developed for use with near stationary orbits having near zero inclination. However, north-south station keeping is not required for most mobile communications satellites, which typically have larger inclinations over their lifespan, for example, between three and seven degrees over the life of the satellite.
  • a method for performing east-west station keeping for a satellite in an inclined synchronous orbit comprises averaging a value of a right ascension of the ascending node for an inclination vector directed at the ascending node and associated with the satellite over a period of the control cycle, and managing corrections for the satellite such that an eccentricity vector directed at perigee is substantially collinear with the inclination vector.
  • a satellite including at least one thruster device, a memory device, and a processing device.
  • the thruster device or devices are configured to provide corrections to an orbit of the satellite
  • the memory device includes inclination vector data associated with the satellite over a period of a control cycle for the satellite
  • the processing device is configured to average a value of a right ascension of the ascending node of the orbit with the inclination vector data.
  • the processing device is further configured to manage the at least one thruster device such that an eccentricity vector, directed at perigee of the orbit, is substantially collinear with the inclination vector.
  • a method for removing variations of orbital eccentricity, which are normal to an inclination vector, from the orbit of a satellite comprises determining inclination data over the life of the satellite, and configuring a thruster mechanism for the satellite to maintain a substantial co-linearity between an eccentricity vector of the satellite, directed at perigee of the orbit, with an inclination vector, based on the inclination data, of the satellite.
  • a control system for maintaining a desired equatorial plane crossing position for a satellite.
  • the control system includes a memory device containing inclination vector data for a control cycle of the satellite, and a processing device.
  • the processing device is configured to average a value of a right ascension of the ascending node of the satellite orbit from the inclination vector data.
  • the processing device is further configured to manage one or more thrusters associated with the satellite such that an eccentricity vector of the satellite, directed at perigee of the orbit, is substantially collinear with the inclination vector for the satellite.
  • Figure 1 is a diagram showing an equatorial view of a first spacecraft in a geostationary orbit and a second spacecraft in an inclined geosynchronous orbit.
  • Figure 2 is a polar view of the inclined geosynchronous orbit of the second spacecraft of Figure 1.
  • Figure 3 is an illustration of a ground track associated with an inclined synchronous orbit.
  • Figure 4 includes a plurality of graphs illustrating an accuracy associated with a typical sun- synchronous eccentricity control method for a seven day control cycle.
  • Figure 5 is a flowchart illustrating node synchronous eccentricity control.
  • Figure 6 illustrates the influence of the earth's oblateness and lunar/solar gravity on the inclination vector associated with a satellite over a period of 15 years.
  • Figure 7 illustrates an example of remaining eccentricity vector variation over the 15 year period.
  • Figure 8 illustrates the change in the eccentricity vector required in the control algorithm over the 15 year period.
  • Figure 9 is an illustration of a ground track associated with an inclined synchronous orbit.
  • Figure 10 is a magnified representation of a +/- 0.05 degree latitude and longitude box associated with node synchronous eccentricity control.
  • Figure 11 includes a plurality of graphs illustrating an accuracy associated with the node- synchronous eccentricity control method and a seven day control cycle.
  • Figure 12 is a chart illustrating fuel requirements and three sigma values for sun synchronous eccentricity control and node synchronous eccentricity control.
  • an eccentricity vector is managed throughout the life of the satellite based on an inclination vector associated with the satellite. Management of the eccentricity vector provides an advantage over the standard sun-synchronous eccentricity control currently utilized in satellite station keeping, as longitude variation is minimized using much less thruster fuel.
  • the fuel savings is defined by the ratio, 2/ ⁇ , or about 0.6366, which is about a 36% decrease in fuel consumption over the sun-synchronous eccentricity control method.
  • Figure 1 is a diagram illustrating a first spacecraft 10 in a geostationary orbit 12 and a second spacecraft 14 in an inclined geosynchronous orbit 16 with respect to earth 20, which is shown in an equatorial view.
  • Figure 2 illustrates a polar view of the orbit of satellite 14.
  • the contribution of an orbital eccentricity to the longitudinal variation of the orbit at the equatorial plane of earth 20 is a function of the absolute value of the eccentricity of the orbit and an argument of perigee of the orbit.
  • the argument of perigee is an angle 30 described by the earth center 32, an ascending node 34 (e.g., the crossing of the orbit through the equatorial plane from South to North), and a perigee position 36.
  • the eccentricity vector is directed through the perigee of the orbit.
  • the angle, ⁇ , between the inertial reference, ⁇ , and the ascending node locates the inclination vector 40, ⁇ .
  • the present invention achieves this result by using a station keeping method in which the argument of perigee, ⁇ , is caused to be substantially zero, based on one or more algorithms within the satellite, which, for example, may be stored in a memory and executed by a processing device.
  • a station keeping method in which the argument of perigee, ⁇ , is caused to be substantially zero, based on one or more algorithms within the satellite, which, for example, may be stored in a memory and executed by a processing device.
  • Such a combination referred to herein as a satellite control system, substantially removes the variation of orbital eccentricity that is normal to the inclination vector.
  • the method of the present invention utilizes two velocity increments ( ⁇ V) applied substantially 180 degrees apart along the orbit. These velocity increments, sometimes referred to as velocity changes, are applied to the satellite at substantially six hours before and six hours after the ascending node of the orbit.
  • eccentricity control is based on the sun-synchronous method.
  • This control strategy was originally conceived to point the eccentricity vector, e, in the direction of the sun line, with the proper magnitude and phase, such that a single drift rate correcting velocity change, ⁇ V, cyclically applied, would maintain an e that is substantially synchronous with the sun line. If the more or less constant e magnitude produces a longitude oscillation, or variation, that is too large (e.g., outside of the so- called longitude variation box), a magnitude of e has to be reduced.
  • Reducing a magnitude of e generally necessitates two velocity changes, ⁇ Vs, that are applied approximately 180 degrees apart along the orbit and approximately six hours before and six hours after the sun line of the orbit.
  • the total ⁇ V increases as the e magnitude is reduced.
  • the eccentricity vector 50, e is dependent upon the right ascension (RA) of perigee, ( ⁇ + ⁇ ), where ⁇ is the right ascension of the orbit ascending node, and ⁇ is the orbit argument of perigee.
  • the argument of perigee, ⁇ is not important in the sun-synchronous control of near stationary orbits.
  • the fact that ⁇ varies significantly over a year is due to the 360° motion of the sun right ascension. While this variation in ⁇ produces variations in a latitude vs. longitude phase plane motion, it has minor impact on the goal of containing the phase plane motion inside, for example, a +/- 0.05 degree latitude-longitude box, which is a requirement in at least some known satellite applications.
  • variations in ⁇ have a profound effect on the ability to contain motion within a defined latitude-longitude box.
  • Figure 3 is a diagram depicting a ground track 60 of a typical inclined geosynchronous orbit 16 (also shown in Figure 2).
  • the center 62 of the "figure-8" depicted by the ground track 60 is at the equatorial plane of the earth 20 (shown in Figure 2).
  • the satellite 14 passes through the ground track center 62 twice each day, once at the ascending node 64 and once at the descending node 66.
  • the motion of satellite 14 is more complex in practice, due to orbit eccentricity, drift and perturbing forces.
  • interference is still a problem, as described above, and satellite 14 is therefore still constrained to, for example, the +/-0.05 degree box 68 near the equatorial plane 70.
  • Figure 4 includes a plurality of graphs 80 illustrating an accuracy associated with a typical sun-synchronous eccentricity control method for a seven day control cycle.
  • Graph 82 illustrates a position of a satellite as it passes through the box associated with the equatorial plane over a 15 year cycle.
  • marker 84 indicates the satellite had a position of about +107.335 degrees in longitude and about 0.075 degrees latitude.
  • Overall graph 82 further illustrates a "box" that is +/- 0.1 degree in latitude and +/- 0.05 degrees in longitude.
  • Graph 86 illustrates a distribution of the satellite equatorial plane crossing positions.
  • the mean longitude of the equatorial plane crossing is about 107.304 degrees and the sigma is about 0.014 degrees, providing a three sigma from the mean values of about 0.042 degrees.
  • a minimum eccentricity three sigma value of about 0.026 degrees may be attained using sun synchronous eccentricity control, but requires a much greater fuel mass.
  • the longitude variation for most satellites in synchronous inclined orbits, using the sun- synchronous eccentricity control method, is constrained to +/- 0.1 degree from station longitude.
  • east-west station keeping control is more important for satellites in highly inclined synchronous orbits that must satisfy a +/- 0.05 degree from station longitude constraint.
  • Such satellites have an inclination of about three to seven degrees from the equatorial plane, but still must satisfy a +/- 0.05 degree latitude-longitude box constraint.
  • These satellites spend a very small fraction of each day within such a +/- 0.05 degree latitude-longitude box.
  • the longitude (E-W) variation need only be confined to within +/- 0.05 degree of center only when the latitude (N-S) variation is within +/- 0.05 degree of the equatorial plane.
  • a satellite in a highly inclined synchronous orbit does not require latitude (N-S) control due to the desire to conserve station keeping fuel.
  • E-W longitude
  • the satellite may be injected, for example, into an approximately six degree inclined orbit with an ascending node of about 335°.
  • the ascending node of the inclination vector 40, ⁇ will monotonically increase approximately 60 degrees or an average of about four degrees per year.
  • the eccentricity vector 50, e is made to track the direction of the inclination vector 40, ⁇ . This condition is sometimes referred to herein as maintaining a colinearity between the eccentricity vector 50 and the inclination vector 40.
  • Figure 5 is a flow diagram illustrating a process 150 for performing east-west station keeping for a satellite in an inclined synchronous orbit.
  • process 150 a value of a right ascension of the ascending node for an inclination vector associated with the satellite is averaged 152 over a period of the control cycle of the satellite and corrections for the satellite are managed 154 such that an eccentricity vector associated with the satellite rotates at substantially the same rate as the inclination vector.
  • a control program which maintains the colinearity of the eccentricity vector with the inclination vector. Maintaining the colinearity of the eccentricity vector with the inclination vector is sometimes referred to as being node synchronous. As such, the methods and systems described herein are sometimes referred to as node-synchronous eccentricity control.
  • solar forces provide the dominant perturbation of the eccentricity vector, e.
  • the solar forces cause the eccentricity vector to trace out a circle in the phase plane (hl,kl).
  • the period of this motion is one year and the radius of the circle is about 0.00054 radians for a solar radiation force (SRF) that is equal to 750 milli-newtons (mnt) and a satellite mass of about 3400 kilograms.
  • SRF solar radiation force
  • the maximum eccentricity is minimized by properly initializing the satellite 14, which centers the circle at (0,0).
  • the control program for satellite 14 includes two predominately tangential corrections, which are separated in right ascension, producing a change in the eccentricity vector, ⁇ e, normal to the direction which is colinear with the inclination vector 40, ⁇ .
  • the magnitude of ⁇ e is ideally equal but opposite to the component of the eccentricity vector to be negated.
  • the portion of the eccentricity vector that remains after the negation is colinear with the inclination vector and varies approximately sinusoidally with a period of one year and amplitude of 0.00054 (using example given above).
  • a complete cancellation of the normal component is unrealizable, however, by performing daily corrections, the pointing variation can be reduced to about +/-0.5 degree. For a weekly correction frequency, the pointing variation is reduced to about +/- 3.5 degrees.
  • the ascending node of the inclination vector advances at an average rate of about four degrees per year.
  • the eccentricity vector can be made to track the inclination vector most closely by adjusting the magnitudes of the cyclic corrections in the eccentricity vector just enough so that, on the average, the eccentricity vector rotates at substantially the same rate as the inclination vector.
  • Input to the computational algorithms specify the known value of the inclination vector right ascension of the ascending node averaged over the period of the satellite control cycle.
  • the change in the eccentricity vector during this period (without considering maneuvers) is computed from a perturbation model. Only the normal component change in the eccentricity is considered for correction. Using this method, two corrections are usually necessary.
  • the thruster firing durations and locations along the orbit are easily computed and they occur about six hours before and six hours after the node crossing time. Some variation in this node crossing time occurs if the thrusters do not provide purely tangential ⁇ Vs (i.e., the thruster geometry may include residual ⁇ V coupling). The remaining variation maximums in the eccentricity vector are minimized by proper orbit initialization.
  • FIG. 7 An example of the remaining eccentricity vector variation over the 15 year cycle is shown in Figure 7.
  • Figure 8 illustrates the change in the eccentricity vector required in the control algorithm over the same 15 years where Hl and Kl are Cartesian coordinates of the eccentricity vector.
  • Figure 9 is an illustration of a "figure 8" ground track associated with an inclined synchronous orbit where the eccentricity vector is non-zero.
  • Figure 10 is a magnified representation of the 0.1 degree latitude and longitude box (+/- 0.05 degree).
  • Figure 11 includes a plurality of graphs 200 illustrating the improved accuracy associated with the above described node-synchronous eccentricity control methods as compared to the sun-synchronous eccentricity control method over a seven day control cycle.
  • Graph 202 illustrates positions of a satellite as it passes through the box associated with the equatorial plane over a 15 year cycle. For example, marker 204 indicates the satellite had a position of about 107.32 degrees in longitude and about -0.0125 degrees in latitude.
  • Overall graph 202 further illustrates a "box" that is +/- 0.1 degree in latitude and +/- 0.05 degrees in longitude.
  • Graph 206 illustrates a distribution of the satellite equatorial plane crossing positions.
  • the mean longitude of the equatorial plane crossing is about 107.302 degrees and the sigma is about 0.0065 degrees, an improvement over the sun-synchronous control method, providing a three sigma value of 0.0195 degrees.
  • Figure 12 is a chart 250 that summarizes an amount of fuel utilized and the resulting longitudinal control for the node synchronous eccentricity control method described herein, for a typical sun synchronous eccentricity control method and for a sun synchronous control method that provides a minmal eccentricity in the orbit of a satellite.
  • the required tangential component velocity changes ( ⁇ Vs) utilizing minimum eccentricity sun-synchronous eccentricity control is about 80.8 meters per second (about 5.2 meters per second per year), about 63.8 meters per second (about 4.2 meters per second per year) utilizing a typical sun synchronous eccentricity control method, and about 54.0 meters per second (about 3.5 meters per second per yea)r using the node synchronous eccentricity control methods described herein.
  • This difference increases the station keeping life by about 57 percent. More directly, the amount of thruster fuel to provide a station keeping life of about
  • station keeping using typical sun-synchronous eccentricity control will require about 111.7 kilograms of thruster fuel (141.8 kilograms to maintain a minimum eccentricity), while station keeping using node synchronous eccentricity control will require about 94 kilograms of fuel, while maintaining a ⁇ longitude, for a seven day correction cycle, of about 0.020 degree as compared to 0.042 degree for a typical sun-synchronous eccentricity control method.
  • utilization of a minimum eccentricity sun synchronous control method can maintain a three sigma ⁇ longitude of about 0.026 degrees, about 37% more fuel is required than is required to maintain a three sigma ⁇ longitude of about 0.020 degrees using node synchronous eccentricity control.
  • the above described methods are desirable for use by entities that operate, design or manufactures satellites for inclined synchronous orbits as the significant fuel savings allows more on-station life, more payload capability, or a combination of the two.
  • GEM GeoMobile
  • the node synchronous eccentricity control method translates primarily into higher dry mass capability for the spacecraft, which is critical since GEM typically do not have XIPS orbit raising capability.
  • mass is critical.
  • the methods and systems described herein are valuable to this market as they represent a significant improvement over currently utilized station keeping methods. The end results of utilizing such systems and methods include, a savings in mass associated with the spacecraft, savings and potentially millions of dollars in savings due to launch vehicle compatibility.

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  • Engineering & Computer Science (AREA)
  • Remote Sensing (AREA)
  • Chemical & Material Sciences (AREA)
  • Combustion & Propulsion (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)
  • Radio Relay Systems (AREA)

Abstract

La présente invention concerne un procédé pour effectuer le maintien de station est-ouest d'un satellite en orbite synchrone inclinée. Le procédé comprend le calcul de la moyenne d'une valeur d'ascension correcte du nœud ascendant pour un vecteur d'inclinaison associé au satellite sur une période du cycle de commande, et le contrôle des corrections pour le satellite de sorte qu'un vecteur d'excentricité, orienté au niveau d'un périgée, soit sensiblement colinéaire avec le vecteur d'inclinaison.
PCT/US2007/022322 2007-10-18 2007-10-18 Procédés et appareil de contrôle d'excentricité de nœuds synchrones WO2008118140A2 (fr)

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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2014189893A3 (fr) * 2013-05-20 2015-04-02 Kratos Integral Holdings, Llc Commande d'excentricité pour satellites géostationnaires
EP2896570A1 (fr) * 2014-01-10 2015-07-22 The Boeing Company Procédés et appareil pour commander une pluralité de satellites au moyen de contrôle d'excentricité de noeuds synchrones
CN106909166A (zh) * 2017-03-01 2017-06-30 北京航天自动控制研究所 升交点赤经参数的修正方法及装置
CN112607065A (zh) * 2020-12-23 2021-04-06 长春工业大学 一种基于电推进系统的高精度相位控制方法

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US5669585A (en) * 1992-06-02 1997-09-23 Mobile Communications Holdings, Inc. Elliptical orbit satellite, system, and deployment with controllable coverage characteristics
US6305646B1 (en) * 1999-12-21 2001-10-23 Hughes Electronics Corporation Eccentricity control strategy for inclined geosynchronous orbits
EP1288760A1 (fr) * 2001-09-04 2003-03-05 Centre National D'etudes Spatiales Procédé de contrôle d'orbite autonome d'un satellite, et satellite en orbite contrôlé de facon autonome

Patent Citations (3)

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Publication number Priority date Publication date Assignee Title
US5669585A (en) * 1992-06-02 1997-09-23 Mobile Communications Holdings, Inc. Elliptical orbit satellite, system, and deployment with controllable coverage characteristics
US6305646B1 (en) * 1999-12-21 2001-10-23 Hughes Electronics Corporation Eccentricity control strategy for inclined geosynchronous orbits
EP1288760A1 (fr) * 2001-09-04 2003-03-05 Centre National D'etudes Spatiales Procédé de contrôle d'orbite autonome d'un satellite, et satellite en orbite contrôlé de facon autonome

Cited By (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2014189893A3 (fr) * 2013-05-20 2015-04-02 Kratos Integral Holdings, Llc Commande d'excentricité pour satellites géostationnaires
JP2016525978A (ja) * 2013-05-20 2016-09-01 クラトス インテグラル ホールディングス，エルエルシー 静止衛星のための離心率制御
US9487309B2 (en) 2013-05-20 2016-11-08 Kratos Integral Holdings, Llc Eccentricity control for geosynchronous satellites
AU2014268743B2 (en) * 2013-05-20 2018-02-15 Kratos Integral Holdings, Llc Eccentricity control for geosynchronous satellites
EP2896570A1 (fr) * 2014-01-10 2015-07-22 The Boeing Company Procédés et appareil pour commander une pluralité de satellites au moyen de contrôle d'excentricité de noeuds synchrones
US9309010B2 (en) 2014-01-10 2016-04-12 The Boeing Company Methods and apparatus for controlling a plurality of satellites using node-synchronous eccentricity control
CN106909166A (zh) * 2017-03-01 2017-06-30 北京航天自动控制研究所 升交点赤经参数的修正方法及装置
CN106909166B (zh) * 2017-03-01 2020-05-08 北京航天自动控制研究所 升交点赤经参数的修正方法及装置
CN112607065A (zh) * 2020-12-23 2021-04-06 长春工业大学 一种基于电推进系统的高精度相位控制方法

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