Optimal Transfer Orbit Trajectory Using Electric Propulsion

1. Technical Field

This invention relates to an apparatus and method of translating a spacecraft from an injection orbit to a geosynchronous orbit in a time efficient manner while optimizing the energy required for injecting a particular payload.

2. Discussion

In order to place a spacecraft in geosynchronous orbit about a central body, such as the earth, the spacecraft is first launched into an injection orbit by the spacecraft launch vehicle. From this injection orbit, the spacecraft is translated through a series of orbits to the geosynchronous orbit. In order for the spacecraft to translate from its injection orbit to geosynchronous orbit, propulsion thrusters fire to exert a force on the spacecraft and move it through the transfer orbit.

There are a number of strategies for translating a spacecraft from its injection orbit to geosynchronous orbit. In a first strategy, a launch vehicle injects the spacecraft to an elliptical orbit having an apogee greater than the geosynchronous orbit, defined as a supersynchronous orbit. Once the spacecraft has reached supersynchronous orbit, propulsion thrusters are fired when the spacecraft is in a predetermined orientation and in proximity to apogee or perigee. Firing the propulsion thrusters at apogee to create thrust in the direction of orbital velocity raises perigee, and firing the propulsion thrusters at perigee to create thrust in a direction opposite the orbital velocity lowers apogee. These apogee and perigee firings or burns translate the spacecraft from supersynchronous orbit to geosynchronous orbit. In a second strategy, the spacecraft is injected into an elliptical orbit having an apogee less than the geosynchronous, defined as a subsynchronous orbit. Once the spacecraft is in subsynchronous orbit, the propulsion thrusters are once again fired when the spacecraft is in proximity to apogee or perigee and in a predetermined orientation. Firing at apogee to create thrust in the direction of orbital velocity raises perigee, and firing at perigee to create thrust in the direction of orbital velocity raises apogee. The apogee and perigee burns cause the spacecraft orbit to spiral out to the geosynchronous orbit. Such a spiraling-out mission using a specific type of thruster is described in Meserole, J. "Launch Costs to GEO Using Solar Powered Orbit Transfer Vehicles." American Institute of Aeronautics and Astronautics (AIAA) Paper 93-2219, AIAA/SAE/ASME/ASEE 29th Joint Propulsion Conference and Exhibit (Jun. 28-30, 1993).

Because the launch vehicle injects the spacecraft into either a subsynchronous or supersynchronous orbit, the spacecraft must include its own propulsion system to effect a translation from injection to geosynchronous orbit and to perform orientation and other stationkeeping maneuvers. This raises several considerations for selecting a particular injection orbit translation strategy. Ideally, an injection orbit is selected so that the weight of the spacecraft without fuel, the dry weight, is maximized. The dry weight generally includes the weight of the instrumentation and the underlying spacecraft structure for the instrumentation. Optimizing dry weight requires a trade-off between the capability of the launch vehicle, how high above the earth the spacecraft can be launched, and the propulsion system of the spacecraft, the on-board thrusters and fuel carried by the spacecraft to translate from injection orbit to geosynchronous orbit and perform stationkeeping maneuvers. Greater injection orbits, i.e., higher apogees, reduce the amount of propellant expended by the spacecraft propulsion system to achieve geosynchronous orbit. On the other hand, the capability or payload capacity of the launch vehicle decreases with an increase in the targeted apogee altitude, so that a more powerful launch vehicle is required to inject a spacecraft having the same mass to an injection orbit having a higher apogee. Thus, in order to optimize the weight of the spacecraft at arrival in geosynchronous orbit, defined as the beginning of life weight (BOL), there is a trade-off between the capability of the launch vehicle and the amount that the propulsion thrusters need to be fired. Of course, the more that the propulsion thrusters are fired, more propellant mass is required, leaving less mass allocated to useful pay load?

Further adding to the above considerations is that there are two types of spacecraft propulsion thrusters, electric and chemical. Chemical propulsion thrusters provide the required thrust for translating the spacecraft from injection orbit to geosynchronous orbit and are capable of exerting a substantial force on the spacecraft. However, chemical propulsion thrusters expend a great deal of mass (propellant) in achieving a predetermined orbit orientation. Electric propulsion thrusters, on the other hand, create significantly less thrust than the chemical propulsion thrusters, but they expend much less mass (propellant) in doing so. That is, electric propulsion thrusters use propellant (mass) much more efficiently than chemical propulsion thrusters. Using electric and chemical propulsion thrusters to effect translation from injection orbit to geosynchronous orbit is described in Forte, P. "Benefits of Electric Propulsion for Orbit Injection of Communication Spacecraft." American Institute of Aeronautics and Astronautics (AIAA) Paper 92-1955, 14th AIAA International Communication Satellite Systems Conference & Exhibit (Mar. 22-26, 1992). A combined electric and chemical propulsion system is also described in Free, B. "High Altitude Orbit Raising with On-Board Electric Power." International Electric Propulsion Conference Paper 93-205, American Institute of Aeronautics and Astronautics (AIAA)/AIDA/DGLA/JSASS 23rd International Electric Propulsion Conference (Sept. 13-16, 1993).

Because chemical propulsion thrusters exert a much higher force than electric propulsion thrusters, they enable translation from injection orbit to geosynchronous orbit in a substantially shorter period of time than electric propulsion thrusters. Furthermore, current transfer orbit strategies for translating a spacecraft from injection orbit to geosynchronous orbit fail to describe a viable burn strategy using electric propulsion thrusters exclusively to translate the spacecraft to geosynchronous orbit. Moreover, substitution of electric propulsion thrusters in chemical propulsion thrusters transfer orbit strategies would require an unacceptable transfer orbit duration (TOD).

Electric propulsion thrusters also introduce yet another consideration, that of stationkeeping and maneuvering. Because electric propulsion thrusters expend substantially less propellant for a given thrust than chemical propulsion thrusters, and that thrust is relatively low compared to chemical propulsion thrusters, they are more desirable for stationkeeping and on-station maneuvers. Because stationkeeping maneuvers require minimal thrust to reposition the spacecraft, electric propulsion thrusters perform stationkeeping using much less mass (propellant) than chemical propulsion thrusters.

The trade-off remains that by using chemical propulsion systems and chemical transfer orbit strategies to achieve geosynchronous orbit, a substantial portion of the spacecraft mass is allocated to propellant for the chemical thrusters. This mass may be traded into a decreased required launch vehicle capability, or, alternatively, traded for increased payload for the same launch vehicle capability or a combination thereof. However, using electric propulsion thrusters to execute chemical propulsion transfer orbit strategies would result in an unacceptably long transfer orbit duration. Thus, it is desirable to provide a transfer orbit apparatus and strategy using electric propulsion thrusters which provides acceptable transfer orbit duration for a given launch vehicle capability and a given payload.

This invention is directed to an apparatus and method for translating a spacecraft launched into an injection orbit about a central body and oriented in a predetermined attitude to a geosynchronous orbit having a semi-major axis and a predetermined orbital plane. The apparatus includes a propulsion thruster oriented on the spacecraft to generate a thrust having a predetermined force on the spacecraft. The apparatus further includes a controller for controlling the timing of firing the propulsion thruster.

The controller includes means for firing the propulsion thruster at apogees of intermediate orbits to successively increase the perigees thereof until the semi-major axis of an intermediate orbit is substantially equal to the semi-major axis of the geosynchronous orbit, thereby defining an initial transfer orbit for the spacecraft. The controller also includes a means for thereafter continuously firing the propulsion thruster to translate the orbit of the spacecraft from the initial transfer orbit to the geosynchronous orbit while maintaining the substantial equality of the geosynchronous semi-major axis and the transfer orbit semi-major axis.

The various advantages of the present invention will become apparent to one skilled in the art by reading the following specification and by reference to the following drawing in which:

FIG. 1 illustrates a typical injection sequence for launching a spacecraft from ground zero to an injection orbit;

FIG. 2 is a perspective partial exploded view of a launch vehicle and satellite;

FIG. 3 schematically depicts a spacecraft as shown in FIG. 2 having mounted thereon electric propulsion thrusters for effecting translation of the spacecraft to geosynchronous orbit and for performing stationkeeping functions;

FIG. 4 illustrates generally the controller portion of the spacecraft for operating the electric propulsion thrusters for translation to geosynchronous orbit;

FIG. 5 depicts the spacecraft at injection orbit around the Earth and a final geosynchronous orbit;

FIG. 6 depicts the spacecraft at a supersynchronous orbit during an apogee burn to raise perigee;

FIG. 7 depicts the angle of inclination between the geosynchronous orbit and an orbit followed by the spacecraft;

FIG. 8 depicts the spacecraft in a series of intermediate orbits about a central body during a continuous thruster firing sequence;

FIG. 9 depicts the spacecraft having reached geosynchronous orbit;

FIG. 10 is a flow diagram of a sequence implemented by the controller for firing the electric propulsion thrusters to reach geosynchronous orbit; and

FIG. 11 is a graph of the transfer orbit duration (TOD) of a spacecraft to geosynchronous orbit versus the beginning of life (BOL) weight of the spacecraft delivered to geosynchronous orbit for various transfer orbit propulsion systems.

The following description of the preferred embodiments is merely exemplary in nature and not intended to limit the invention or its application or uses. In this specification, note that elements having similar structures or functions will be referred to using like reference numerals.

Referring to FIG. 1, a spacecraft 10 launched from a position on the earth 12 follows a path predetermined in accordance with parameters of the launch vehicle and settles into an elliptical orbit defined as the injection orbit 16. The optimal transfer orbit trajectory mechanism and apparatus determines how to translate the spacecraft 10 from the injection orbit 16 to a geosynchronous orbit 18. During the launch sequence, the spacecraft 10 separates from first, intermediate, and final stages as schematically shown at reference numeral 20 before reaching injection orbit 16. The number of stages from which spacecraft 10 separates during launch to injection orbit 16 depends upon the parameters, capabilities, and particular application for the launch vehicle. Such parameters, capabilities, and applications vary widely, but are well known to persons skilled in the art.

Referring to FIG. 2, the spacecraft 10 is shown with other component parts which comprise launch vehicle 22. Launch vehicle 22 shown in FIG. 2 is commonly referred to as a DELTA 7925 launch vehicle and is merely exemplary of one of a number of launch vehicles known to persons skilled in the art. The component parts of launch vehicle 22 include thrust augmentation solids 24, first stage oxidizer tank 26, center body 28, and fuel tank 30, all of which comprise the first stage of launch vehicle 22. Interstage 32 links fuel tank 30 to second stage 34 and also provides additional propulsion. Second stage 34 includes truss 36 for supporting guidance electronics 38. Guidance electronics 38 attaches to spin table 40 which in turn attaches to third stage motor 42 via clamp bands 44. Third stage motor 42 attaches to spacecraft 10 via attached fitting 46. During launch, fairings 48 provide protection for second stage 34, third stage motor 42, spacecraft 10 and the various associated components therewith. After launch vehicle separation 20 of FIG. 1, only spacecraft 10 continues to injection orbit 16.

In operation, launch vehicle 22 is supported on a launch pad (not shown) on the earth 12 and loaded with the appropriate fuels in preparation for lift-off. At lift-off, first stage components 24-30 operate as described above and provide initial thrust to propel launch vehicle 22 off of the launch pad. At a predetermined time in the launch sequence the first stage will detach, at which time interstage 32 activates to provide thrust. Similarly, interstage 32, second stage 34, and third stage 42 will sequentially provide thrust, then detach from the remainder of launch vehicle 22. Also at a predetermined time, the fairings 48 will separate and be jettisoned exposing second stage 34, third stage 42, and spacecraft 10. Eventually, after all components have separated from launch vehicle 22, only spacecraft 10 remains and continues to injection orbit 16. Note that the above described launch vehicle 22 and launch sequence are merely exemplary, and it will be recognized by one skilled in the art that the invention described herein is equally applicable to any of a number of various launch vehicles and launch sequences.

Referring to FIG. 3, a thruster positioning diagram of spacecraft 10 is shown. Spacecraft 10 may be one of any of a number of shapes and sizes known in the art, which typically depends upon the particular application for which the spacecraft is to be used. Spacecraft 10 has a center of mass 52 through which pass three axes, a Z axis 54, an X axis 58, and a Y axis 60. The Z axis 54, X axis 58, and Y axis 60 are shown extending in a positive direction in accordance with arrows 56, 60, and 62, respectively. Spacecraft 50 includes electric propulsion thrusters 50 arranged so that when activated, spacecraft 10 experiences a force in the positive direction of Z axis 54. Electric propulsion thrusters 50 may optionally be canted so the thrust vector of any particular electric propulsion thruster 50 is slightly off parallel from the positive Z axis in order to provide redundant directional thrust for use as a backup, secondary attitude control system. However, the resultant thrust vector when all electric propulsion thrusters 50 fire preferably parallels positive Z axis 54. Additional electric propulsion thrusters 63 primarily provide thrust for performing attitude control and stationkeeping of spacecraft 10. Typically, electric propulsion thrusters 63 are smaller and provide less thrust than electric propulsion thrusters 50 because they only need exert relatively small forces to carry out relatively minor spacecraft positioning adjustments. Propulsion thrusters 63 are shown mounted on the same panel as propulsion thrusters 50, and are canted so that individually they exert resultant thrust inwardly towards center of mass 52. Electric propulsion thrusters 50 and 63 are preferably either xenon-ion-propulsion-thrusters (XIPS) or arcjet propulsion thrusters.

Although propulsion thrusters 50 and 63 preferably electric propulsion thrusters, and are referred to accordingly throughout this specification, will be understood by persons skilled in the art that propulsion thrusters 50 or 63 may be replaced chemical propulsion thrusters. As noted above, electric propulsion thrusters provide much lower thrust than chemical propulsion thrusters, but deplete significantly less mass the amount of thrust delivered.

Referring to FIG. 4, controller selectively activates electric propulsion thrusters 50 in accordance with a predetermined fire control routine. Controller may optionally control the firing of electric thrusters 63 to provide attitude control. In operation, controller receives input information from sensor block 65 and determines if electric propulsion thrusters 50 should be activated. Sensor block 65 provides input data such as attitude, orientation, and position with respect to earth 12. Controller evaluates such information and generates appropriate control signals in response to the received information. Controller may also optionally control other spacecraft functions and operate as an integrated spacecraft controller. Furthermore, controller may provide other than simply firing sequences for transfer orbit propulsion thrusters 50. For example, controller may effect communication between spacecraft 10 control systems, may communicate with ground or space based receivers-transmitters, or may control other instrumentation as required by the particular application.

FIGS. 5-9 depict a transfer orbit trajectory sequence of spacecraft 10 from injection orbit 16 to geosynchronous orbit 18. As noted above, like reference numerals will be used to describe similar elements to those already previously described. Referring to FIG. 5, spacecraft 10 is shown in injection orbit 16 orbiting around a central body such as the earth 12. Geosynchronous orbit 18 is also depicted in FIG. 5. Injection orbit 16 is an elliptical orbit having an apogee 66 and a perigee 68 which are defined as the highest and lowest points, respectively, of the elliptical orbit with respect to earth 12. It will be recognized by one skilled in the art that injection orbit 16 is attained in accordance with a number of predetermined application parameters. Specifically, the speed of spacecraft 10 at perigee 68 and the height of perigee 68 define the height of apogee 66 and the eccentricity of the elliptical injection orbit 16.

Referring to FIG. 6, spacecraft 10 is shown in proximity to apogee 66 of an intermediate orbit 74 having an elliptical shape. When spacecraft 10 is oriented in a predetermined attitude and direction using any of a number of methods known to one skilled in the art, controller 64 activates electric propulsion thrusters 50 causing a change in velocity vector, .DELTA.V, and raising perigee to a new perigee 72 of a new intermediate elliptical orbit 74. The desired change in velocity vector, .DELTA.V, substantially points orthogonally to a line between apogee and perigee in the direction that spacecraft 10 travels when at apogee 66. Firing propulsion thrusters 50 of spacecraft 10 during consecutive passes around apogee 66 raises the perigee 72 of each successive intermediate orbit 74. Intermediate orbit 74 has the same apogee 66, but has an increased perigee 72 and decreased eccentricity. Note again that intermediate orbit 74 of FIG. 6 represents a number of intermediate orbits resulting from successive firings of electric propulsion thrusters 50 at apogee 66 to exert a change in velocity, .DELTA.V, resulting in successive intermediate orbits 74 having successively increasing perigees 72 and decreasing eccentricity. In addition to raising perigee 72, firing the electric thrusters 50 around apogee 66 also results in an increase in the semi-major axis, defined as the average of the apogee and perigee, of the orbit of spacecraft 10. The semi-major axis is raised to be substantially equivalent to the semi-major axis of geosynchronous orbit 18, which in accordance with the laws of physics, necessarily implies that the orbital periods of both the geosynchronous orbit 18 (24 hours by definition) and transfer orbit 74 are substantially equivalent as well.

Firing thrusters electric thrusters 50 at apogee 66 after the spacecraft has been placed in the desired burn attitude has two effects. First, as described above, firing electrical propulsion thrusters 50 at apogee 66 raises perigee 72. Second, referring to FIG. 7, firing electric propulsion thrusters 50 at apogee 66 also enables adjustment of the angle of inclination 73 of the orbital plane 75 of injection orbit 16 with respect to the geosynchronous plane 77. Because the angle of inclination 73 of injection orbit 16 can be no lower in degrees than the latitude from which spacecraft 10 was launched, adjustment may be necessary. In order to adjust the angle of inclination 73 (to the geosynchronous plane 77, for example), it is necessary to incline spacecraft 10 to an attitude so that Z axis 56 does not parallel the plane defined by transfer orbit 74 and points in the direction of geosynchronous plane 77. When this occurs, the angle of inclination 73 of the orbital plane 75 of intermediate orbit 74 changes as electric propulsion thrusters 50 fire. As described above with respect to intermediate orbit 74, there are a number of successive intermediate orbital planes 75a-b and angles of inclinations 73a-b through which spacecraft 10 translates while the angle of inclination 73 is reduced so that orbital plane 75 and geosynchronous plane 77 substantially coincide.

Firing at such a supersynchronous orbit yields the added benefit that the supersynchronicity of the orbit provides a longer burn for raising perigee 72 and decreasing the angle of inclination 73 than for a less supersynchronous orbit. For example, in a subsynchronous orbit, a perigee raising burn may last six out of 10 hours versus nineteen out of 22 hours for a supersynchronous orbit. Accordingly, the time of the burn for rasing perigee 72 lasts longer and raises perigee 72 faster.

Referring to FIG. 7, during the above described process of raising perigee 72, the angle of inclination 73 between the plane 75 defined by the orbit followed by the spacecraft (orbit 74 in FIG. 6) and the geosynchronous plane 77 is adjusted. Spacecraft 10 follows orbit 74, and while the direction of thrust primarily points in the direction of the change in velocity .DELTA.V lying within orbital plane 75, it is also directed out of parallel from orbital plane 75 to sufficiently decrease the angle of inclination 73. Ideally the rate of change of the angle of inclination 73 and of the increase of perigee 72 is such that the angle of inclination 73 reaches zero degrees and perigee 72 reaches the semi-major axis of the geosynchronous orbit 16 at substantially the same time. As described further herein below, when the angle of inclination 73 approaches zero degrees, the attitude of the spacecraft is reoriented so that the change in velocity .DELTA.V is substantially parallel to the orbital plane 75 which will then be substantially coincident with geosynchronous plane 77.

In FIG. 8, after perigee 72 of transfer orbit 74 has been raised to the predetermined level 78a or orbit 76a, spacecraft 10 oriented so that when controller 64 activates propulsion thrusters 50 a thrust in the direction of the desired .DELTA.V as shown in FIG. 8 results along the positive Z axis 54. Spacecraft 10 remains in this predetermined orientation while orbiting around the earth 12, and also remains in a substantially fixed attitude so that the positive Z-axis and .DELTA.V are substantially parallel to orbital plane 76a. Controller 64 fires electric propulsion thrusters 50 around the entirety of intermediate orbits 76a, 76b, and 76c. This continuous firing has two effects on transfer orbits 76a-c. First, each succeeding transfer orbit 76a to 76b and 76b to 76c has a progressively higher perigee 78a-c and a progressively lower apogee 66a-c. Second, at the same time, the eccentricity of the successive orbital ellipses 78a-d decreases as spacecraft 10 approaches the eccentricity of geosynchronous orbit 18. Once in geosynchronous orbit 18 as shown in FIG. 9, the spacecraft 10 may be reoriented into an operational orientation. For example, as shown in FIG. 9, spacecraft 10 is positioned with the positive Z axis 54 oriented towards the earth 12.

Referring to FIG. 10, a flow chart depicting the steps carried out by controller 64 for translating spacecraft 10 from injection orbit 16 to geosynchronous orbit 18 is shown and will be referred to generally as flow chart 80. At block 82, the launch vehicle 22 of FIG. 2 injects spacecraft 10 into a supersynchronous orbit 16 as depicted in FIG. 5. At block 84, the spacecraft 10 is reoriented to the desired burn attitude so that when electric propulsion thrusters 50 are activated, the resulting .DELTA.V points in the desired direction. This reorientation maneuver is typically performed using attitude control propulsion thrusters 63. Control then passes to block 86 where the electric propulsion thrusters 50 are fired during consecutive passes around apogee 66 of transfer orbit 74 of FIG. 6. In block 86, firing propulsion thrusters 50 raises perigee 72 and may also adjust the angle of inclination 73. Once the orbital plane is properly adjusted as described with respect to FIGS. 6 and 7, the spacecraft is reoriented (if necessary) at block 88 so that Z axis 54 lies parallel to orbital plane 74 and is parallel to .DELTA.V of FIGS. 6.

After reorienting spacecraft 10 to an in-plane attitude, at block 90 controller initiates continuous firing of electric propulsion thrusters 50 as spacecraft 10 orbits around earth 12. Such firing is depicted in FIG. 8, where spacecraft 10 is shown at a number of locations 10, 10' and 10" following intermediate orbits 76a, 76b, and 76c, respectively. This continuous firing results in a continuous raising of perigee 78a-c and a continuous lowering of apogee while maintaining a nearly constant semi-major axis for each of intermediate orbits 76a-d which remains substantially equal to the semi-major axis of geosynchronous orbit 18. Controller maintains continuous activation of electric thrusters 50 until spacecraft 10 has translated to geosynchronous orbit 18. At block 92, controller 64 tests whether geosynchronous orbit has been achieved. Once spacecraft 10 achieves geosynchronous orbit, block 92 passes control to block 94 where controller 64 discontinues firing of electric propulsion thrusters 50. Thereafter, electric propulsion thrusters 50 may be fired as necessary for stationkeeping and other maneuvers.

As noted above with respect to FIG. 3, electric propulsion thrusters 50 and 63 described herein may be embodied as, but need not be limited to, either XIPS or arcjet electric propulsion systems. Alternatively, as also noted above, electric propulsion thrusters 50 and 63 may be embodied as a hybrid or complete chemical propulsion system. Referring to FIG. 11, a graph depicts selected performance characteristics of the XIPS and arcjet implementations of electric propulsion thrusters 50 and 62 as well as a hybrid of the XIPS and a chemical propulsion system. In the graph, the ordinate, depicts the transfer orbit duration (TOD) in days and the abscissa depicts beginning of life weight (BOL) in kilograms. As can be seen from the graph of FIG. 11, while the chemical propulsion system has a very short transfer orbit duration, a great expense is incurred in terms of the beginning of life weight. This implies that a spacecraft can be put into geosynchronous orbit rather quickly using chemical propulsion thrusters and chemical transfer orbit strategies, but with much less pay load and stationkeeping fuel. On the other hand, the XIPS and arcjet thrusters demonstrate that while the transfer orbit duration is substantially greater than for chemical propulsion thrusters, a much greater beginning of life weight is achieved. This translates into substantially more instrumentation and fuel, which may ultimately increase the life expectancy of the spacecraft 50% or greater. Alternatively, for the same spacecraft mass, a launch vehicle having less capability, and a lower cost, can inject the spacecraft.

Also shown in FIG. 11 is a plot for a hybrid chemical and XIPS system. This system combines features of both chemical and electric propulsion thrusters to both decrease the transfer orbit duration and increase the beginning of life weight. Along this plot, as the TOD increases, a higher proportion of electrical propulsion translates the spacecraft to geosynchronous orbit. As the TOD decreases, a lower proportion of electrical propulsion translates the spacecraft to geosynchronous orbit. It can be seen from this plot that beginning of life weight can be significantly increased by use of the hybrid system.

A significant advantage realized by the method and apparatus described herein is that an equivalent beginning of life weight can be delivered to geosynchronous orbit 18 using much smaller and less expensive launch vehicles. For example, a spacecraft having a beginning of life weight which typically requires launch by an ATLAS or ARIANE 4L booster could be delivered by the much less expensive Delta II booster. By the same token, greater payloads can be delivered by identical launch vehicles if electric propulsion engines translate the spacecraft to geosynchronous orbit. The increased payload can be translated into spacecraft lifetime because electric propulsion requires much less mass for stationkeeping, approximately 6 kilograms per year, compared to chemical propulsion systems, approximately 27 kilograms per year. Further, the time required to achieve geosynchronous orbit has been optimized while utilizing a smaller launch vehicle for the same payload.

Although the invention has been described with particular reference to certain preferred embodiments thereof, variations and modifications can be effected within the spirit and scope of the following claims.