robotic mars exploration trajectories using hall ...

AAS 14-364

ROBOTIC MARS EXPLORATION TRAJECTORIES USING HALL THRUSTERS Theresa D. Kowalkowski,* Zachary J. Bailey,† Robert E. Lock‡, Erick J. Sturm§, and Ryan C. Woolley** A variety of Mars exploration architectures for the latter part of this decade and early part of the next are under consideration at NASA, ranging from orbiters to landers to sample return mission scenarios. The use of solar electric propulsion, particularly Hall thrusters, is an attractive option because it can provide increased flexibility to mass growth; alternate launch opportunities; Mars orbit selection, adjustment and rendezvous capabilities; and uncertainty in launch vehicle performance. In this paper, we present Earth-to-Mars and Mars-to-Earth trajectory options using Hall thrusters for potential Mars exploration architectures.

INTRODUCTION Solar-electric propulsion (SEP) missions to Mars have long been desired for their potential cost benefits and mission flexibility but have not had sufficient demonstration and qualification. Previous analyses have illustrated the benefits to cost, risk, and science return of employing a SEP system on missions to Mars.1, 2, 3, 4 In particular, Oh et al showed in Reference 1 that Hall thrusters are particularly well-suited to Mars missions due to their high specific impulse (Isp) compared to chemical engines and higher thrust relative to ion thrusters that enables flight times that are on par with chemical mission architectures. The Dawn mission to the asteroid Vesta and dwarf planet Ceres has established the value and feasibility of using solar-electric propulsion for deep space science missions, and commercial telecommunications satellites have demonstrated large solar power systems and qualified Hall thruster systems well into useful ranges for planetary missions.5 Missions to Mars are generally divided into two categories: orbiters and landers. Orbiters serve several key roles in the overall Mars exploration architecture. Aside from conducting their own scientific investigations to contribute to the greater understanding of Mars and the solar system, orbiters are vital to the telecom infrastructure by providing relay services to landed assets. *

Mission Design Engineer, Jet Propulsion Laboratory, California Institute of Technology, M/S 301-121, 4800 Oak Grove Dr., Pasadena, CA, 91109. † Systems Engineer, Jet Propulsion Laboratory, California Institute of Technology, M/S 321-630, 4800 Oak Grove Dr., Pasadena, CA, 91109. ‡ Systems Engineer, Jet Propulsion Laboratory, California Institute of Technology, M/S 321-690, 4800 Oak Grove Dr., Pasadena, CA, 91109. § Systems Engineer, Jet Propulsion Laboratory, California Institute of Technology, M/S 230-205, 4800 Oak Grove Dr., Pasadena, CA, 91109. ** Mission Design Engineer, Jet Propulsion Laboratory, California Institute of Technology, M/S 301-165, 4800 Oak Grove Dr., Pasadena, CA, 91109.

Copyright 2014 California Institute of Technology. Government sponsorship acknowledged.

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Orbiters also produce high resolution imagery to aid in landing site selection and certification. Furthermore, they can provide a platform for technology demonstrations, such as optical communications. One key element of NASA’s Mars orbiters over the last decade and a half is that they have all used aerobraking to achieve their final science orbits. Mars Global Surveyor, Mars Odyssey, and Mars Reconnaissance Orbiter each propulsively inserted into a large elliptical orbit and then spent several months using the Martian atmosphere to reduce the period and eccentricity of their orbits. Aerobraking saves propellant and propulsion system mass, but the operations required to successfully execute the aerobraking phase, particularly near the end when the orbit period is on the order of a few hours, can be costly and high risk. Orbiter missions that could achieve their final orbits without aerobraking could reduce the operations costs and associated risks of that activity, thereby reducing overall mission cost and risk. Solar-electric propulsion missions to Mars have the potential to eliminate the aerobraking phase, while still providing a large payload mass, by using the SEP system to spiral down from the interplanetary cruise trajectory to the final science orbit. In this scenario, there are no critical orbit insertion events and no complex aerobraking operations. The Dawn mission illustrated the advantage of such an approach when it arrived at Vesta in this manner in July 2011. The gradual approach afforded by SEP could also provide new science opportunities when the spacecraft spends long periods of time in the previously unexplored distant Mars orbit regimes. Dawn also demonstrated the utility of SEP when it departed Vesta in September 2012. Dawn’s ion thrusters gradually increased its orbit around Vesta until it escaped from the giant asteroid entirely. The departure was achieved without any critical events, such as having to fire a main engine at a precise time. Similarly, SEP could be used to depart Mars as part of a sample return architecture where aerobraking is not an option. In this paper, we explore using Hall thrusters for potential Mars missions launching in the timeframe of 2022–2026 with Mars departures in 2026–2028, providing Earth-to-Mars and Marsto-Earth trajectories over a wide range of flight times and solar array power levels. The Earth-toMars (i.e. “outbound”) trajectories provide options for a wide range of orbiters. Paired with the Mars-to-Earth (i.e. “inbound”) trajectories, these round-trip trajectory pairs could form the foundation for Mars sample return missions. APPROACH AND ASSUMPTIONS The goal of this study is to demonstrate the feasibility of using SEP for Mars orbiters and sample return spacecraft. To model the trajectories, we use the Mission Analysis Low Thrust Optimization software, or MALTO.6 MALTO is a preliminary trajectory design tool that models low-thrust trajectory arcs as a series of impulsive maneuvers applied to patched-conic trajectories. Spirals in and out of circular orbits at massive bodies (e.g. Mars) are computed analytically per Melbourne and Sauer.7 In the spiral calculations, the power and number of thrusters are computed at the start of the spiral when spiraling down to a circular orbit and at the end of the spiral when spiraling up from a circular orbit. The power and number of thrusters are held constant throughout spiraling period. The Hall thruster modeled in this study was the BPT-4000 as this thruster has been shown to be a viable long-life option for SEP missions.8, 9, 10 The BPT-4000’s performance (thrust and mass-flow rate) as a function of system input power are given in Table 1.

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Table 1. BPT-4000 Performance Curves11 BPT-4000 High-Thrust Throttle Curves Valid over input power ranges of 0.302 – 4.839 kW Mass Flow [mg/s] = ‐0.011949*P4 + 0.235144*P3 ‐ 1.632373*P2 + 6.847936*P + 0.352444 Thrust [mN] = 0.173870*P4 ‐ 1.150940*P3 ‐ 2.118891*P2 + 77.342132*P ‐ 8.597025 P = System input power in kW

Note that the system input power is defined as the power generated by the solar arrays minus the spacecraft bus power. Also note that these performance curves are based on actual measured thruster performance data and that they do not assume any additional margin. In scenarios involving two thrusters, MALTO applies a simple heuristic to determine how many thrusters are operating at a given time: if there is more power than a single thruster can use, then two thrusters are used with the power divided evenly between them. For example, if the system input power is 5 kW, which is greater than the BPT-4000’s maximum operating power of 4.839 kW, then 2 thrusters are operated at 2.5 kW each. In this analysis, we parametrically vary the solar array power to illustrate the effects of increasing or decreasing the size of the arrays. To make this a valid comparison across launch years, flight times, and number of operating thrusters, many other of the trajectory parameters are kept fixed. These parameters are given in Table 2. Table 2. Trajectory Modeling Assumptions Parameter

Value

Launch Vehicle

Falcon 9 v1.1

Duty Cycle

95%

Spacecraft Bus Power

700 W

Post-Launch Coast

30 days

Pre-Earth-Arrival Coast

30 days

Mars Science Orbit Altitude (circular)

320 km

In formulating mission concepts for Mars orbiters launching in 2022–2026, one important consideration is to keep costs low to fit within the expected NASA budget in the coming years. As a one of the smallest medium-class launch vehicles, with performance in a similar range as the Atlas V 401, the Falcon 9 v1.1 launch vehicle was selected as the baseline launch vehicle for this study. Note that in the trajectory optimization process, the launch mass is a function of the launch hyperbolic excess velocity (V∞) in that it cannot exceed the maximum mass the Falcon 9 can deliver to particular launch energy (C3, defined as V∞2). In the MALTO software, the launch energy is an optimization variable, and the objective function is to maximize the mass at Mars arrival for the Earth-to-Mars trajectories. (Note that the mass at Mars is not technically a “dry mass” value because it is assumed that additional propellant, either chemical or Xenon, is needed for momen-

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tum management and orbit maintenance.) This means that trajectories computed in this study have different launch masses and different launch C3’s even for the same launch year. Using the above standard assumptions, we can vary the solar array power, number of thrusters that can operate simultaneously, and flight time. The solar array power levels assumed in these analyses are the array output at 1 AU. No output degradation is modeled, so for conservatism we report the power as an end-of-life value. MALTO models the available solar array power as a function of solar distance as given in Eq. 1.12

      1  2  23  P rsun rsun  Ppoly  Ppoly rsun   20  2   rsun 1   4 rsun   5 rsun    

(1)

where:

P0

=

Reference power at 1 AU [kW]

rsun

=

Distance from the spacecraft to the Sun [AU]

i

=

Set of 5 constant parameters defining array performance model

Table 3 lists the values of the solar array constants used in this study. Recall that the spacecraft bus power (Table 2) is subtracted off the array output power to yield the system power used in the thruster models (Table 1). Table 3. Solar Array Model Parameters Solar Array Model Parameter

Value

1

1.32077 AU2

2

-0.10848 AU3

3

-0.11665 AU4

4

0.10843 AU-1

5

-0.01279 AU-2

For mission robustness, JPL design practice requires SEP spacecraft to carry at least one fullyredundant thruster flight spare. This means, for example, that spacecraft flying trajectories that only require a single operating thruster would actually need to be equipped with two thrusters. For brevity, however, we will ignore the additional thruster in our case descriptions and will only refer to the number of thrusters that can operate concurrently. In this paper we do not attempt to compare the relative benefits of the mass impacts of adding additional thrusters or solar array power capability, however Bailey et al leverage the results of this study to perform that analysis.13

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It should be noted that the flight time that is varied in this study is actually the time from launch until Mars “arrival,” defined as achieving the same position and velocity as Mars (in the patched-conic model, Mars is considered massless). The spiral time (and required propellant mass) is analytically computed based on the spacecraft mass and solar array power at the start of the spiral per Reference 7. The results in the subsequent sections, however, show the sum of the interplanetary and spiral flight times and refer to it as “total flight time.” EARTH-TO-MARS TRAJECTORIES As mentioned above, the optimization goal in computing SEP trajectories from Earth to Mars is to maximize the delivered mass at Mars. In this analysis, the delivered mass is the launch mass minus the SEP propellant mass required by MALTO to arrive at Mars. No additional propellant mass for attitude control or statistical maneuvers is included. The “final mass” shown in the following plots also subtracts the propellant mass required to spiral down to the science orbit. The two plots at the right show the final mass values (i.e. the mass at the end of the spiral down to the final science orbit) for launches in 2022. The trajectories in Figure 1 use a single Hall thruster and solar array power levels ranging from 4–12 kW. Figure 2 shows the results of using two Hall thrusters in the 10–20 kW range. Trajectory data plots for 2024 and 2026 can be found in the Appendix. In these plots, the interplanetary flight time was

Figure 1. Mass delivered to Mars science orbit vs. total flight time. Launch is in 2022 and a single BPT-4000 thruster is used.

Figure 2. Mass delivered to Mars science orbit vs. total flight time. Launch is in 2022 and two BPT-4000 thrusters are used.

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parametrically varied, and the spiral time of flight was computed with the sum of the two plotted as the “total flight time.” The apparent “kink” in the 14 kW curve in Figure 2 at approximately 570 days total time of flight is due to MALTO’s aforementioned method of determining the number of operating thrusters for the spiral portion of the trajectory. Due to Mars’ elliptical orbit, the heliocentric range at Mars arrival (and the start of the spiral) varies with the arrival date. For the shorter flight times in the 14 kW curve, the Mars arrival dates Figure 3. Plot of a trajectory launching in 2022 using a sinare earlier and closer to aphelion. gle BPT-4000 thruster and an 8 kW solar array. Therefore, the system power available for the Hall thrusters was only sufficient to operate a single thruster. For longer flight times and later arrival dates, the increased solar array output allowed for two operating thrusters. Since the spiral calculation assumes a constant power and number of thrusters for the duration of the spiral, this creates the discontinuity seen in Figure 2. There are several key points about SEP missions to Mars that are illustrated in the preceding figures. The first is the observation that for most cases, final mass increases with flight time. This is important to note because of the flexibility it offers the spacecraft and payload design. If, during the development phase, the spacecraft and/or payload need a greater mass allocation than was originally given, the overall system could accommodate this mass growth without changing the basic system parameters by simply opting for a longer flight time. For example, in the 2022 single-thruster case, an 8 kW system taking ~550 days to reach its science orbit at Mars could provide approximately 900 kg (plotted in Figure 3). An increase of 150 kg could be realized by increasing the flight time by about 50 days without changing the solar array size. In this example, however, approximately 50 kg of additional Xenon is required to execute the longer, more efficient trajectory (see Figure 4). A larger propellant tank might be required to accommodate this increased Xenon mass, but strategies for handling this possibility are discussed in Reference 13. While it may be counterintuitive for a trajectory to deliver more mass while simultaneously requiring more propellant, in SEP trajectories the launch C3 and launch mass are optimized parameters. In our example case above, the 550-day trajectory has a launch mass of ~1400 kg (C3=25 km2/s2) whereas the 600-day case’s launch mass is ~1600 kg (C3=22.4 km2/s2), as shown in Figure 5. Of this 200 kg difference, 50 kg is required as additional propellant and the remaining 150 kg is increased mass at Mars.

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Another key point is that the same mass can be delivered to Mars orbit for different power levels and flight times. Suppose it is determined during development that the solar array output will be less than originally expected. The reduced capacity can be accommodated by adjusting the time of flight. In Figure 1, for example, a 9 kW trajectory with a 600-day flight time delivers 1200 kg to Mars orbit. An 8 kW trajectory could deliver the same mass with a 50day increase in total trip time. This lower power trajectory would require a different launch C3 and profile, so a post-launch change from one trajectory in Figure 1 to another isn’t possible without an increase in propellant usage. Future studies could analyze the impacts of redesigning the cruise trajectory to accommodate a postlaunch discovery of reduced solar array output power.

Figure 4. Propellant (Xenon) mass required to achieve Mars science orbit vs. total flight time. Launch is in 2022 and a single BPT-4000 thruster is used.

There are some other interesting characteristics of SEP trajectories Figure 5. Launch mass vs. total flight time. Launch is in 2022 and a to Mars, particularly single BPT-4000 thruster is used. when examining the launch C3 values for the optimized trajectories in the previous plots. Figure 6a shows the launch mass versus launch C3 for the 2022 single-thruster case. The dark black line in the plot indicates the maximum capability of the Falcon 9 v1.1. The majority of the trajectories fall on that line, as expected, and the lower C3 values correspond to the longer flight times in Figure 1. However, some of the lowerpower, lower-C3 trajectories actually fall below that line. In those cases, it was optimal to launch with less mass than the launch vehicle could provide to the optimized value of launch C3. This is

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because a larger mass would have required more SEP thrust than could be generated with the available power. a)

b)

Figure 6. Launch and final mass vs. launch C 3. Launch is in 2022 and a single BPT-4000 thruster is used. The thick, black line in (a) represents the maximum capability of the Falcon 9 v1.1.

Figure 7. Final mass vs. launch mass. Launch is in 2022 and a single BPT-4000 thruster is used.

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Even more notable than the launch mass is the final mass plotted against launch C 3 (Figure 6b). With the exception of the cases with launch masses below the launch vehicle curve, all of the final mass values for all power levels fall along a single curve. This suggests that mass delivered to Mars orbit is a function of C3 and is independent of solar array power (subject to practical limits on final mass that a given power can achieve). If we plot the final mass versus the launch mass, all the values lie along a single curve that is nearly a straight line (Figure 7). A linear curve fit of the data (R2=0.9993) yields mf=m0*0.74-110 [kg]. This relationship is supported by the data for the 2022 single-thruster case with the assumptions listed in Table 2 only. More analysis would be needed to apply this type of relationship to other launch years, thrusters, and launch vehicles. One significant way the data in Figure 7 can be used is during the preliminary spacecraft design process. If the total spacecraft mass at Mars orbit is known, then the launch mass and by extension the propellant mass can be determined, independent of flight time and solar array power. Different solar array power levels would then drive the time of flight. Maximizing the array size would minimize the flight time while keeping the propellant mass constant. For example, if 1000 kg is needed in Mars orbit, then Figure 7 and the above relationship tell us that the launch mass needs to be 1500 kg, 500 kg of which is Xenon. Figure 1 tells us that flight times for a spacecraft of this size range from 450 days with a 12 kW array to 720 days for a 6 kW array. Furthermore, Figure 6 tells us that the launch C3 is 24 km2/s2. Another benefit of using SEP for missions to Mars is the relatively small difference in performance from one Mars launch opportunity to another. The Earth-Mars synodic period is 26 months, and SEP trajectories generally follow the same pattern as chemical missions in that good launch opportunities present themselves at roughly this same interval. With chemical missions, there can be variations in mass delivered to a 1-sol aerobraking orbit of up to 25% over the 2022– 2026 time period and differences of up to 35% across the seven-opportunity cycle. SEP missions, on the other hand, show greater consistency across launch opportunities. Figure 8 plots the final

Figure 8. Mass delivered to Mars science orbit vs. total flight time. Launches are in 2022, 2024, and 2026, and a single BPT-4000 thruster is used.

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mass for single-thruster cases launching in 2022, 2024, and 2026. While the final masses can vary by 15% across opportunities for a fixed flight time, the same final mass can be achieved with the same power level in different opportunities if flight time is allowed to vary. This is significant because it allows a single spacecraft to be designed for multiple Mars launch opportunities. MARS-TO-EARTH TRAJECTORIES In support of Mars sample return mission analysis, we have also evaluated the return portion of a potential round-trip Mars mission. The trajectory optimization approach is different for these inbound trajectories than it was for the outbound (Earth-to-Mars) ones because we do not have the launch mass (and launch C3) as optimization variables. In this scenario, the spacecraft would use its Hall thruster system to spiral out from Mars orbit and then continue on toward Earth. Without a launch vehicle model to determine the initial mass, we instead assume an arrival mass at Earth and use MALTO to minimize the Mars departure mass. (As with the calculation of the spiral down in the Earth-to-Mars trajectories, the spiral up in the Mars-to-Earth trajectories is not in the optimization cost function. Instead it is calculated after the interplanetary trajectory is optimized.) For this analysis, Earth arrival masses of 500 kg, 1000 kg, and 1500 kg are used to build a database of trajectories that can be interpolated to match with Earth-to-Mars trajectories. In this way, round-trip trajectories can be analyzed as in Reference 13. Chemical Earth-return trajectories from Mars typically have arrival V∞ magnitudes in the range of 2.8 km/s to 5.7 km/s, and a direct entry into Earth’s atmosphere is effectively the only feasible method of returning a sample without incurring large ΔV costs to chemically insert into Earth orbit. In this study, we evaluate two different types of Earth return scenarios: 1) allowing the Earth arrival V∞ to be as high as 4.5 km/s for a direct entry, and 2) enforcing an Earth arrival V∞ maximum of 1.5 km/s for either lower-speed Earth entry or ballistic capture into an Earth “storage” orbit using a series of lunar flybys.14, 15,16 Option 2 is desirable for both types of return scenarios it supports. In the direct entry scenario, the lower arrival V∞ means a lower Earth entry speed, which simplifies the entry vehicle and heat shield design. In the storage orbit case, we could avoid the complications associated with a direct entry and allow the sample to be retrieved at a later date from a very long-term stable orbit. The storage orbit option could enhance contingency planning in the event of planetary protection concerns surrounding the integrity of sample and entry vehicle. Additional potential advantages of using SEP for the return trajectory include the ability to change from the direct entry to the storage orbit option during the Mars-to-Earth cruise as well as the ability to adjust the incoming asymptote for better landing site access and landing ellipse orientation. Future analysis is needed to quantify the extent to which SEP can enable these benefits. For two-thruster Mars-to-Earth trajectories, MALTO’s algorithm for selecting the number of operating thrusters produced inconsistent results in that there were several cases where higher power levels performed more poorly than lower power levels. This occurred because the BPT4000 has a lower specific impulse (Isp) when operated at a lower power, and the return trajectories’ performance is dominated by Isp, whereas the Earth-to-Mars trajectories were driven as much by thrust as Isp because of the need to actually rendezvous with Mars at the end of the trajectory. Referring to the example in the Approach and Assumptions section, if we have 5 kW of available system power, MALTO will model operating two thrusters at 2.5 kW (Isp=1560 s) even though operating a single thruster at maximum power (4.839 kW) is more efficient (Isp=1865 s). In an actual mission, the number of thrusters and operating power of each during each trajectory phase would be more judiciously selected to optimize the trajectory’s performance.

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For analysis purposes, we created a new thruster model that allows the thrust and mass flow rates to be continuous across the total operating range of two thrusters (up to 9.678 kW of operating power). For operating power levels greater than a single thruster’s P max of 4.829 kW, data tables were created for the mass flow rate assuming that one thruster was operating at P max and the second thruster was operating with the remaining power. Curve fits of this data are given in Table 4. Using this new “super thruster” model means that we select a single thruster in MALTO with Pmax=9.678 kW to model our two-thruster cases. While it is understood the super thruster model is less accurate than using the published model in Table 1, the smooth curve avoids the inconsistent results found using the standard two-thruster model in Mars-to-Earth trajectories. For our preliminary design work, this approximation is adequate. Table 4. BPT-4000 Two-Thruster Performance Curves for Mars-to-Earth Trajectories BPT-4000 “Super Thruster” Throttle Curves Valid over input power ranges of 0.302 – 9.678 kW Mass Flow [mg/s] = ‐0.0148673*P4 + 0.287729*P3 ‐ 1.77217*P2 + 6.75915*P + 0.49655 Thrust [mN] = -0.092*P4 + 1.822*P3 ‐ 11.958*P2 + 87.095*P ‐ 10.4 P = System input power in kW

In Figure 9 we plot a trajectory departing Mars in 2026 and arriving at Earth with a 500 kg spacecraft. This trajectory uses an 8 kW array and a single Hall thruster. The point in the lower right of the figure is the beginning of the spiral up from Mars orbit. Note that interplanetary thrusting (indicated by the red arrows) doesn’t begin until more than a month after Mars departure. Figure 10 shows the propellant mass required to depart Mars and arrive at Earth for Mars departures in 2026 with a spacecraft mass at Earth of 500 kg. (The comparable traFigure 9. Plot of a trajectory departing Mars in 2026 using a jectories departing Mars in single BPT-4000 thruster and an 8 kW solar array. 2028 are found in the Appendix.) The propellant mass and flight time include the period of spiraling up from Mars orbit as well as the interplanetary cruise to Earth. In Figure 10a, the maximum arrival V∞ is 4.5 km/s, so these cases are only applicable to direct entries at Earth. Figure 10b plots the propellant mass required for a maximum arrival V ∞ of 1.5 km/s, which applies to direct entries with reduced entry speed or to storage orbit options.

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a)

b)

Figure 10. Xenon mass to spiral out from Mars orbit and cruise to Earth vs. total flight time. Mars departure is in 2026 and the spacecraft mass at Earth is 500 kg. In (a) the maximum Earth arrival V∞ is 4.5 km/s, and in (b) the maximum is 1.5 km/s. One BPT-4000 thruster is used.

One obvious feature of both plots is that the required Xenon mass is fairly flat with decreasing flight times until the knee in the curve is reached. This flatness occurs because for longer interplanetary flight times, MALTO applies little or no thrust for many days after the spiraling is complete. In those cases, the spacecraft would be essentially coasting with Mars until the optimal thrusting geometry is reached. The optimal thrusting geometry occurs at the intersection of Earth’s and Mars’s orbit planes, which is the most efficient place to perform a plane change. For shorter interplanetary flight times, Mars departure (end of spiraling) occurs when the spacecraft has already passed that intersection. Without being able to thrust at the most efficient place for the Mars-to-Earth transfer, the propellant mass costs get very high for those short time of flight cases. Therefore, for Mars-to-Earth trajectories, longer flight times do not necessarily result in trajectories with lower Xenon mass requirements. In Figure 11, the spacecraft mass at Earth is double what it was in Figure 10, 1000 kg versus 500 kg. (Note that the power levels and plot scales are different in the two figures.) For the 1000 a)

b)


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kg spacecraft the Xenon mass required is approximately double what it was for the 500 kg spacecraft at the same power level. Also note in Figure 11 (both (a) and (b)) that the 11 kW and 12 kW curves are nearly on top of each other. This happens because the BPT-4000 would be operating at its maximum power level throughout the trajectory with 11 kW, so the additional solar array power with a 12 kW array is essentially wasted. For the 1500 kg spacecraft, two thrusters were used in the form of the “super thruster” model given in Table 4. In Figure 12, all but the 20 kW system require approximately the same amount of propellant. Higher power systems, however, could make the trip from Mars to Earth in much less time. An examination of the knees in the curves in Figure 12a shows that the 18 kW system could save almost six months of flight time over the 10 kW system, with a similar savings evident in Figure 12b. The reason the propellant masses have very little difference is because for SEP system input power levels between 5 kW and 10 kW the Isp is essentially constant. a)

b)

Figure 12. Xenon mass to spiral out from Mars orbit and cruise to Earth vs. total flight time. Mars departure is in 2026 and the spacecraft mass at Earth is 1500 kg. In (a) the maximum Earth arrival V∞ is 4.5 km/s, and in (b) the maximum Earth arrival V ∞ is 1.5 km/s. The two BPT4000 thrusters were modeled with the “super thruster” curve fits.

ROUND-TRIP LAUNCH PERIOD One additional benefit of using SEP for missions to Mars is the much longer launch periods that the efficient systems could provide. In most conventional missions to Mars, launch periods of 20 or 21 days are desired to provide a high probability of being able to launch. In some opportunities, the launch energy required across those days can vary by 3 km2/s2 or more, and the costs can become very steep if longer launch periods are desired. Using SEP, on the other hand, allows for much longer launch periods with significantly less difference in performance from one day to the next. This feature is evident from the following analysis. To evaluate a launch period using SEP, some basic parameters must be established. First off, the launch mass must be a fixed value because in a real mission the same vehicle would be launched on any given day in the period. This mass dictates an upper bound on the launch C 3 because of the performance limits of the launch vehicle. (Lower values of C 3 are permissible, though.) Additionally, a solar array size and number of simultaneously operating thrusters need to be established. In this study, we are analyzing a full Mars round-trip mission, so we also need to consider any mass changes during the stay at Mars due to station-keeping and momentum management. Furthermore, a minimum stay time at Mars should be established (measured from

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the end of the spiral down to Mars orbit until the start of the spiral up). Table 5 lists the parameters used in this launch period analysis in addition to those given in Table 2. Table 5. Launch Period Modeling Assumptions Parameter

Value

Launch Mass

2465 kg

Maximum Launch C3

11.7 km2/s2

Solar Array Power

11 kW

Number of Thrusters

1

Mass Change (drop) at Mars

180 kg

Minimum Mars Stay Time

300 days

Maximum Earth Arrival V∞

4.5 km/s

The objective function in the launch period analysis was to maximum the mass at Earth return for a series of fixed launch days. Figure 13 plots the final mass and total flight time for potential launch dates spanning a 180-day period. Note that the time of flight curve bounces between two different curves, one around 1810 days for launches in early July and the other around 1860 days in that same timeframe. This occurs because there are two local minima for the Mars-to-Earth portion of the trajectory that deliver nearly the same mass performance, and MALTO doesn’t al-

Figure 13. Round-trip launch period (Earth-Mars-Earth).

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ways converge to the same one. The shorter flight time cases generally have an Earth arrival V ∞ at the upper bound of 4.5 km/s whereas the longer flight times are closer to 4.0 km/s at Earth. Across the entire period of possible launch dates evaluated, the maximum mass at Earth arrival is 1223 kg for launch on 30-Sept-2024. If we take the 21-day period that has the highest minimum mass, we could establish a launch period opening on 17-Sept-2024 and continuing through 7-Oct-2024 (indicated with the red arrow and bar in the figure). The lowest mass over this time period is 1221 kg, which is only 2 kg less than optimal launch date. In terms of Xenon mass, that is less than a 0.2% variation across 21-day the launch period. For a 30-day launch period (indicated with the blue arrow and bar in the figure), the first day would be 9-Sept-2024 and the last would be 8-Oct-2024 with a minimum final mass of 1218 kg. The difference in propellant mass across those 30 trajectories is less than 0.5%. Alternatively, if we know what final mass we need at the end of the mission we can determine the maximum launch period duration. For example, a 1200 kg spacecraft could have a launch period as long as 73 days with only a 2.1% increase in Xenon mass over the optimal launch date. CONCLUSION Solar-electric propulsion missions to Mars using Hall thrusters, and the BPT-4000 in particular, provide a wealth of advantages over traditional chemical missions for both science and relay orbiters as well as sample return orbiters. These types of missions are robust to mass growth during the design phase and also offer a wide range of feasible system parameters to aid in the flexibility of the system design. Furthermore, SEP missions offer the potential for much longer launch periods than with chemical missions to Mars. Mission demonstrations showing the practical advantages of SEP on long term planetary missions and for the applicability of the BPT-4000 have shown the way for low-cost missions to, and from, Mars. ACKNOWLEDGMENTS This work was conducted at the Jet Propulsion Laboratory, California Institute of Technology. Government sponsorship is acknowledged. The authors wish the thank Richard Hofer, Steve Snyder, Austin Nicholas, and Damon Landau for their input, guidance, and suggestions. APPENDIX: ADDITIONAL TRAJECTORY DATA The next two plots show the final mass versus total flight time for Earth-to-Mars trajectories launching in 2024 (Figure 14) and 2026 (Figure 15). The last three plots are for the Mars-toEarth trajectories departing Mars in 2028. Figure 16 plots the Xenon mass required to deliver a 500 kg spacecraft to Mars with a single BPT-4000 thruster. The results in Figure 17 also use a single thruster, but the spacecraft mass at Mars is 1000 kg. The final plot (Figure 18) is for a twothruster system delivering 1500 kg to Earth.

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a)

b)

Figure 14. Mass delivered to Mars science orbit vs. total flight time. Launch is in 2024. In (a) a single BPT-4000 thruster is used, and in (b) two BPT-4000 thrusters are used.

a)

b)

Figure 15. Mass delivered to Mars science orbit vs. total flight time. Launch is in 2026. In (a) a single BPT-4000 thruster is used, and in (b) two BPT-4000 thrusters are used.

a)

b)


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a)

b)


a)

b)

Figure 18. Xenon mass to spiral out from Mars orbit and cruise to Earth vs. total flight time. Mars departure is in 2028 and the spacecraft mass at Earth is 1500 kg. In (a) the maximum Earth arrival V∞ is 4.5 km/s, and in (b) the maximum is 1.5 km/s. The two BPT-4000 thrusters were modeled with the “super thruster” curve fits.

REFERENCES 1

Oh, D., Hofer, R., Katz, I., Sims, J., Warner, N., Randolph, T., Reeve, R., and Moeller, R., “Benefits of using Hall Thrusters for a Mars Sample Return Mission,” IEPC-2009-217, 31st International Electric Propulsion Conference, Sept. 2009. 2

Brophy, J. R. and Rodgers, D. H., "Ion Propulsion for a Mars Sample Return Mission," AIAA Paper 2000-3412, July 2000. 3

Oh, D. Y., Benson, S. W., Witzberger, K., and Cupples, M., "Deep Space Mission Applications for NEXT: NASA's Evolutionary Xenon Thruster," AIAA Paper 2004-3806, July 2004. 4

Donahue, B. B., Green, S. E., Coverstone, V. L., and Woo, B., "Chemical and Solar-Electric-Propulsion Systems Analyses for Mars Sample Return Missions," Journal of Spacecraft and Rockets 43, 1, 170 (2006).

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5

Rayman, M. D., Fraschetti, T. C., Raymond, C. A., and Russell, C. T., “Dawn: A Mission in Development for Exploration of Main Belt Asteroids Vesta and Ceres,” Acta Astronautica, Vol. 58, 2006, pp. 605-616. 6

Sims, J., Finlayson, P., Rinderle, E., Vavrina, M., and Kowalkowski, T., “Implementation of a Low-Thrust Trajectory Optimization Algorithm for Preliminary Design,” AIAA/AAS Astrodynamics Specialist Conference, Paper No. AIAA2006-6746, Aug. 2006. 7

Melbourne, W. G. and Sauer, C. G., “Performance Computations with Pieced Solutions of Planetocentric and Heliocentric Trajectories for Low-Thrust Missions,” Space Programs Summary 37-36, vol. IV, Jet Propulsion Laboratory, Pasadena, California, pp. 14–19, December 31, 1965. 8

Hofer, R. R., Randolph, T. M., Oh, D. Y., Snyder, J. S., and De Grys, K. H., "Evaluation of a 4.5 kW Commercial Hall Thruster System for NASA Science Missions," AIAA Paper 2006-4469, July 2006. 9

Hofer, R. R., Goebel, D. M., Snyder, J. S., and Sandler, I., "BPT-4000 Hall Thruster Extended Power Throttling Range Characterization for NASA Science Missions," Presented at the 31st International Electric Propulsion Conference, IEPC-2009-085, Ann Arbor, MI, Sept. 20-24, 2009. 10

De Grys, K. H., Mathers, A., Welander, B., and Khayms, V., "Demonstration of 10,400 Hours of Operation on 4.5 kW Qualification Model Hall Thruster," AIAA Paper 2010-6698, July 2010. 11

Hofer, R. R., “High-Specific Impulse Operation of the BPT-4000 Hall Thruster for NASA Science Mission,” AIAA Paper 2010-6623, July 2010. 12

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Bailey, Z. J., Sturm, E. J., Kowalkowski, T. D., Lock, R. E., and Woolley, R. C., “Round-Trip Solar Electric Propulsion Missions for Mars Sample Return,” AAS/AIAA Space Flight Mechanics Conference, AAS Paper 14-365, Jan. 2014. 14

Nock, K. T. and Uphoff, C. W., “Satellite Aided Orbit Capture,” AAS/AIAA Astrodynamics Specialist Conference, AAS Paper 79-165, June 1979. 15

Cline, J. K., “Satellite Aided Capture,” Celestial Mechanics, Vol. 19, May 1979, pp. 405–415.

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Landau, D., McElrath, T., Grebow, D., and Strange, N., “Efficient Lunar Gravity Assists for Solar Electric Propulsion Missions,” AAS/AIAA Space Flight Mechanics Conference, AAS Paper 12-165, Jan. 2012.

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