Todd Mosher MicroSat System, Inc 8130 Shaffer Parkway Littleton, CO

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1 An Evolvable Lunar Communication and Navigation Constellation Concept Kathryn Hamera Colorado Center for Astrodynamics Research 429 UCB Boulder, CO Todd Mosher MicroSat System, Inc 8130 Shaffer Parkway Littleton, CO Mark Gefreh Colorado School of Mines 1500 Illinois Street Golden, CO Robert Paul, Leon Slavkin, Joseph Trojan 12 University of Colorado - Boulder 429 UCB Boulder, CO Robert.paul@colorado.edu, slavkin@colorado.edu, Joseph.Trojan@colorado.edu Abstract NASA s Global Exploration Strategy and proposed lunar architecture present a roadmap for future U.S. missions. The exploration plan begins with robotic precursor missions, followed by short human sorties, eventually progressing to a permanent base on the lunar surface. NASA s Lunar Architecture Team concluded that this permanent base would be located near the lunar South Pole. The location of an outpost at the lunar South limits direct communication links with the Earth. A lunar relay element will be necessary to provide critical communication and navigation support for the upcoming missions. This paper presents a highly evolvable, low-cost lunar relay constellation concept using small satellites in Halo orbits about the Earth-Moon libration points L 1 and L 2. The initial constellation is designed to provide coverage of the Lunar South Pole in support of the inaugural robotic missions and is easily expanded to provide global coverage. Two satellites in an L 2 Halo orbit provide continuous South Pole coverage for the initial constellation. A final constellation providing nearly continuous global coverage can be achieved by the addition of two spacecraft in a Halo orbit /08/$ IEEE 2 IEEEAC paper #1491, Version 4, Updated November 8, 2007 about L 1. A basic set of requirements and desired capabilities for the constellation is developed, based on NASA reports and Constellation C3I compatibility. A preliminary spacecraft bus and subsystems design is presented along with expected performance. TABLE OF CONTENTS 1. INTRODUCTION CONSTELLATION DESIGN HALO ORBIT DESIGN SPACECRAFT DESIGN CONCLUSION...16 ACKNOWLEDGEMENTS...16 REFERENCES...17 BIOGRAPHY INTRODUCTION On January 14, 2004, President George W. Bush delivered to NASA a new Vision for Space Exploration with the 1

2 fundamental goal to advance U.S. scientific, security, and economic interests through a robust space exploration program [1]. In order to bring the vision to reality, NASA will conduct the following activities related to the lunar environment: Undertake lunar exploration activities to enable sustained human and robotic exploration of Mars and more distant destinations of the solar system; Initiate a series of robotic missions to the Moon to prepare for and support future human exploration activities; Conduct the first extended human expedition to the lunar surface as early as 2015, but no later than 2020; Use lunar exploration activities to further science, and to develop and test new approaches, technologies, and systems to support sustained human space exploration to Mars and other destinations. In December of 2006, NASA unveiled the initial elements of the proposed U.S. lunar architecture. One of the key elements is the buildup of a lunar outpost, starting around NASA s Lunar Architecture Team concluded that the most advantageous location for the lunar outpost is the South Pole. Robotic precursor missions will be designed to support the human exploration phase. These missions will include landing site reconnaissance, technology risk reduction, and natural resource assessment. The major technical challenge for operating at the South Pole is that the Earth is not usually visible for direct radio communications. Therefore, in their Lunar Exploration Objectives, NASA stated that it is necessary to implement early communications capabilities, including telemetry, tracking, and control (TT&C) and mission data transmission to meet early lunar robotic needs. NASA further stated that early communication systems could be used to test technology for subsequent systems to meet human mission needs. The Space Communication Architecture Working Group (SCAWG) produced a report detailing recommendations for NASA s communication and navigation architecture [2]. The report recommends that early communication and navigation (comm/nav) systems support robotic activities at the South Pole and that the final comm/nav system should provide global coverage of the entire lunar surface to support human exploration. To buildup a global coverage constellation from an initial South Pole constellation, NASA s Exploration Roadmap can be summarized in three phases: Phase A - Robotic Precursor, Phase B - Early Human Exploration, and Phase C - Lunar Base. Table 1 presents key communication and navigation requirements for the three phases and the approximate dates when each phase should be operational. The spacecraft design presented in this paper focuses on meeting the communication and navigation requirements for Phase A. The orbit for the constellation was designed for the coverage requirements in Phase A while considering the capability and ease of expanding to a constellation that would meet the requirements for global coverage in Phase C. Table 1 - NASA Lunar Exploration Phases Phase A Phase B Phase C Intermediate phase in support of human exploration missions Initial phase in support of robotics missions Final phase in support of a permanent lunar base Completed By Continuous and Coverage redundant South Continuous South pole coverage, Pole coverage increased overall Global coverage surface coverage Navigation Accuracy (3D 100 m 20 m 10 m 1! Position) Aggregate Return Link Requirements 1 Mbps total 10 Mbps Goal 100 Mbps total 300 Mbps Goal 1 Gbps total 10 Gbps Goal Link Type RF (S and Ka-band) RF (Optical?) RF (Optical?) 2. CONSTELLATION DESIGN Several architecture options were considered for the lunar navigation and communication (nav/com) constellation. The SCAWG report identified 50 specific cases [2] representing eight classes of lunar relay orbits to provide coverage of the South polar cap, an area defined as the region between 80 and 90 South latitude. Of the list of 50 cases, seven options were further evaluated by the SCAWG team and weighted based on a figure of merit (FOM). The SCAWG report recommended that a constellation of two satellites in an elliptical frozen orbit should be used for the initial constellation due to its high FOM score. Several academic publications [3][4][5][6] contend that libration point orbits, particularly halo orbits, provide many advantageous qualities for lunar nav/com relays. The halo orbits described by Grebow et al. [3] as possible candidates for relays were not examined thoroughly by the SCAWG committee. Thus, this paper examines two possible orbits for the initial constellation design: A lunar halo orbit about L 2 and an elliptical Frozen orbit. L 2 Lunar Halo Orbit The first option analyzed to provide communication and navigation support for the lunar South Pole was a constellation of two spacecraft in a halo orbit about the 2

3 second Earth-Moon Lagrange point, L 2. The Lagrange points, or libration points, are a set of five equilibrium points that exist for each three-body system. A three-body system is one where the gravity of two large bodies, (such as the sun, a planet or a moon) influences the dynamics of the third smaller body, such as a spacecraft. The locations of the lunar libration points are shown in Figure 1. rotating) frame, which is centered on the barycenter. The units are given in kilometers and km/s for the inertial Moon centered frame and non-dimensional units for the synodic frame. Table 2 - Halo orbit initial conditions. Coordinate System Inertial Moon Centered Spacecraft 1 Spacecraft 2 Synodic Inertial Moon Centered Synodic x y z vx vy vz Figure 2 illustrates the geometry of the halo orbit. Figure 2(a) present a three-dimensional view and Figure 2(b) shows the X-Z view. The origin of the plot is the barycenter. In this coordinate system, the Earth would be located slightly to the left of the origin on the x-axis. Figure 1 - Locations of the lunar librations points. The libration points are fixed in a system that rotates at the same rate as the Moon and Earth rotate around the center of mass of the system, also known as the barycenter. There are families of orbits that exist around the libration points. One type of orbit family contains orbits known as halo orbits. Robert Farquhar coined the term halo orbit because the orbit appears to form a halo around the Moon when viewed from the Earth [5]. There are an infinite number of halo orbits about the libration points. Certain halo orbits at L 2 have a unique advantage in that they are always in view of the Earth and can be oriented such that they provide excellent South Pole coverage. The halo orbit selected for the initial analysis has a period of 7.5 days and a Jacobi constant, C = Halo orbits are not governed under two-body dynamics, and thus do not have a defining set of orbital elements, such as the Keplerian orbital elements. The Jacobi Constant is one parameter that can be used to classify halo orbits. The spacecraft spends approximately 95% of its orbital period in view of the South Pole. This translates into 7.12 days of continuous South Pole view for each spacecraft. An initial constellation of two spacecraft in this orbit phased one-half a period apart will provide 100% continuous South Pole coverage and 90% two-fold coverage. In addition, the Earth is visible to each spacecraft at all times. The initial conditions for the orbit listed in Table 2 are similar to the halo orbits described by Grebow et. al [3]. The initial conditions are given in two coordinate systems: an inertial Moon centered frame, and the synodic (or Figure 2 - The Halo orbit constellation: (a) 3D view, (b) X-Z View. The cost of establishing a constellation at L 2 can be greatly reduced using a Ballistic Lunar Transfer (BLT) [7] [8] [9]. The launch vehicle will propel the spacecraft toward a Sun- Earth libration point. At this million-kilometer distance, the spacecraft does not have enough energy to escape the Earth. However, the spacecraft will be significantly influenced by the gravitational effects of the Sun. Due to the combined effects of the gravity of the Earth, Moon, and Sun, the spacecraft will fall back towards the Moon and ballistically enter into a lunar halo orbit with no orbit insertion maneuver. This elimination of the orbit insertion maneuver decreases both the cost and risk of the mission. 3

4 standard notions of orbits dominated by non-spherical gravity effects do not properly characterize the motion [14]. Frozen orbits take into account the perturbative effects of the Earth s gravity and as a result, require little orbit stationkeeping. The orbital parameters selected were taken from Ely and Lieb, and can be found in Table 3. The superscript (op) denotes that the orbital elements are reconciled in a frame at the Moon with the z-axis parallel to the normal of Earth s apparent orbit around the Moon. Figure 3 - Ballistic Lunar Transfer in the rotating frame. Figure 3 presents an example BLT. The transfer takes approximately three to four months, but by removing the need for an orbit insertion maneuver, payloads up to 35% larger may be sent to the Moon. Using a BLT, it is possible to send spacecraft to the Moon for as low as 3.2 km/s, an energy that can be provided entirely by the launch vehicle. This is less energy than is needed to send a satellite to a Geostationary orbit. Upon arrival at the Moon, the spacecraft use low-energy transfer to achieve proper orbit phasing with ΔVs as low as 2 m/s. In addition, there are multiple families of BLTs. If the specified launch date is missed, a mission designer can analyze a BLT map [7] and subsequently locate a slightly different trajectory that will reach the same orbit. Many BLT maps show that a launch may occur any day of the year, although this will affect the transfer time. The halo orbit constellation is easily expandable to provide global coverage of the lunar surface. As shown in Figure 1, the first lunar libration point, L 1, is located between the Earth and the Moon. A constellation consisting of two spacecraft at L 1 and two spacecraft at L 2 will provide global coverage, with only a few small mid-latitude regions unable to communicate with the constellation for brief periods of time. An additional spacecraft in either the L 1 or L 2 halo orbit could rectify this problem. Furthermore, it is possible to transfer from one halo orbit to another for a very low ΔV using low-energy transfers. Research has shown it is possible to transfer between libration point orbits for as little as 10 m/s [10] [11] [12]. This greatly reduces the ΔV budget. Frozen Orbit The second option analyzed for South Pole coverage was a constellation of three satellites equally phased on an inclined elliptical frozen orbit. The orbit is termed frozen because, on average, the eccentricity and argument of periapsis of such orbits remains stationary [13]. Higher altitude lunar orbits (500 20,000 km) are heavily influenced by Earth perturbations and as a result, the Table 3 - Frozen orbit initial conditions. Parameter Orbit 1 Orbit 2 Orbit 3 a km km km e (op) i ! (op) " (op) M Figure 4 presents two views of the constellation of frozen orbiters. The spacecraft are represented by the red dots and the size of the Moon is to scale to the orbit. One spacecraft spends approximately 70% of its orbital period, or 8.5 hours in view of the lunar South Pole region. The three orbiters provide 100% continuous, two-fold South Pole coverage. Figure 4 The Frozen orbit constellation: (a) 3D view, (b) YZ view. The method to establish the frozen orbit constellation would employ a traditional Apollo-like trajectory. This trajectory would take approximately 4.5 days at an approximate ΔV cost of 3.13 km/s from a 185 km Low-Earth-Orbit (LEO) onto a trans-lunar trajectory, and an additional 330 m/s for orbit insertion around the Moon. Upon arrival to the frozen orbit, it is not a trivial matter to achieve proper spacecraft phasing. Assuming all of the spacecraft are on the nominal frozen orbit, two of the spacecraft will require approximately 500 m/s of ΔV for phasing. There are ways to combine the orbit insertion and phasing maneuvers that may decrease the ΔV budget. However, this is a complex optimization problem and is beyond the scope of this study. 4

5 A constellation of frozen orbits can be designed to provide global coverage of the lunar surface. Ely and Lieb developed a constellation of six spacecraft equally phased in two orbital planes that provide 99.99% global coverage over a ten-year period. However, this constellation is a nearly circular orbit with a completely different set of orbital elements than the constellation optimized for South Pole coverage. The spacecraft would have to carry a great deal of fuel to reconfigure to the new orbits, or an entirely new set of spacecraft would be required to establish the new constellation. Orbit Trade Study A trade study was conducted to determine the best option for the South Pole coverage constellation. Table 4 presents the key numerical characteristics of each orbit. Table 4 - Numerical comparison of key orbit characteristics. Orbit Characteristic Frozen L 2 Insertion cost per satellite (m/s) Orbit changing costs ~ ΔV (m/s) Min # of sats for Global Coverage 6 4 Station-keeping cost (m/s/year) 5 5 Sun exposure 95% 99% South Pole coverage (per satellite) 72% 95% Earth access (% of orbital period) 95% 100% Orbit period (days) Navigation accuracy 3σ (m) Max time in eclipse (min) Max distance to Lunar surface (km) The chart is colored to show the Excellent (green), Moderate (yellow) and Poor (red) qualities of each orbit. Table 4 shows that there are many excellent qualities of the L 2 option: The low orbit insertion and orbit changing costs, continuous Earth access, a lower number of spacecraft necessary for near global coverage, and higher navigation accuracy. The Frozen orbit option is advantageous in that the distance it travels from the lunar surface is almost an order of magnitude less than the L 2 option. Figure of Merit A Figure of Merit (FOM), with similar parameters used in the SCAWG report, was created to analyze the options and to help quantify the importance of the numerical characteristics presented in Table 4. The following parameters were included in the FOM: Visibility, Orbit Stability, Failure Tolerance, Navigational Utility, Mission Evolvability, Link Capacity, and User Burden. Visibility: Assets anywhere on the polar cap must have at least one visible relay back to the Earth at all times with a 10 minimum elevation angle (to overcome topographical interference). Both options selected meet this criterion. Therefore, the visibility FOM was quantified by the twofold coverage percentage and the percentage of the orbit period that one spacecraft is visible to the polar cap. Orbit Stability: This value measured the effort required to maintain the satellite in the nominal orbit. The FOM was quantified based on the ΔV required for station-keeping over a one year period. Orbit insertion and end of line maneuvers were not included. The station-keeping values were based on numerical results presented in literature. Failure Tolerance: This FOM is the percent of South Pole visibility in any given 24 hour period with one satellite failure in the worst-case scenario. Navigational Utility: This is quantified by the ability of the constellation to support navigation for lunar assets. The value was quantified by the 3-D position accuracy and the amount of tracking time from Earth-based assets required to converge on a solution. For example, if Constellation A can provide 25-meter accuracy with only 4 hours of tracking data, it will have a higher score than Constellation B, which can provide 25-meter accuracy with 10 hours of tracking data. Mission Evolvability: This quantifies the ability to easily modify the constellation by inserting additional satellites to increase coverage areas and lunar exploration capabilities. This FOM considers the minimum number of satellites necessary to provide global coverage and the ΔV costs associated with changing orbits to reconfigure the constellation. Link Capacity: This FOM is an assessment of possible data rate, data volume, and real-time latency based on communication distances and required spacecraft size. It is quantified through maximum distance from the polar cap, Earth visibility for uplink and downlink, and the percentage of the orbital period in exposed to the Sun. User Burden: This is a measure of the effort required by users to use the communication services provided based on user antenna size, broadcast power, and complexity of user's communication subsystem. This also considers the ease of tracking (i.e. how quickly must it track spacecraft in the constellation). To create the FOM, specific weightings were assigned to each of the parameters discussed above. The weighing values and parameter breakdown by percentages are presented in Table 5. The overall FOM scores for each orbit option are presented in Table 6. The color of each box represents if the score is Excellent (green), Moderate (yellow) or Poor (red). Table 6 shows that the L 2 option has greater visibility, higher navigation utility, and has a much greater evolvability capacity than the Frozen orbit option. In addition, the L 2 orbit has an FOM score 10 points higher 5

6 than the Frozen orbit. Thus, the L 2 halo orbit was selected for the initial constellation design. Table 5 Figure of Merit Parameter Quantification and parameter breakdown. Parameter FOM Weight Parameter Breakdown South Pole coverage per satellite (% of 60% Visibility 25.33% orbital period) 40% Two-fold coverage (% of orbital period) Stability 12.00% 100% Station-keeping budget (m/s/year) Final constellation two-fold coverage 30% Failure with one spacecraft lost 14.67% Tolerance Initial constellation coverage with one 70% spacecraft lost Evolvability 14.67% 60% Minimum satellite for global coverage 40% Orbit changing cost (m/s) 50% Maximum distance from Lunar assets Link 16.00% 40% Earth access (% of orbital period) Capacity 10% Sun exposure (% of orbital period) User burden 6.67% 50% Ease of tracking Navigation Utility 50% Antenna size needed 10.67% 100% Navigation accuracy (3D 1σ positioning) Table 6 Figure of Merit scores. FOMs Weight Value Frozen L 2 Visibility 25.33% Orbit Stability 12.00% Failure Tolerance 14.67% Evolvability 14.67% Link Capacity 16.00% User Burden 6.67% Navigation Utility 10.67% TOTAL % HALO ORBIT DESIGN The following sections detail the design of the halo orbits, the lunar coverage characteristics, and the performance of the constellation for Phases A, B, and C. A brief discussion on the creation of halo orbits precedes the discussion on orbit performance. The Circular Restricted Three Body Problem The motion of a spacecraft about one of the lunar libration points must account for the gravitational forces of both the Earth and the Moon. The equations of the Circular Restricted Three Body Problem (CRTBP) are used to model the motion of the spacecraft in this project. This model assumes that the mass of the third body - the spacecraft - is negligible in comparison to the two more massive bodies, defined as the primary and the secondary (the Earth and Moon in this case). It can further be assumed that the two primaries are now subjected to the Keplerian laws that govern two-body motion. In addition, it is assumed that the two primaries rotate in circular orbits about the center of mass of the system, known as the barycenter. It is then possible to model the motion of the spacecraft in a frame of reference that rotates about the barycenter at the same rotation rate as the two primaries. This is known as a synodic reference frame. A full derivation of the equations of motion for the CRTPB may be found in Szebehely [15]. The halo orbits analyzed in this project were generated in the CRTBP using the Single Shooting method developed by Howell [16]. The basic algorithm uses symmetry about the x z plane to locate periodic orbits and can be summarized as follows: An initial state in the x z plane with no velocity in the x and z directions is integrated forward in time until it pierces the x z plane. If the crossing with the x z plane is perpendicular, then the orbit is periodic. If not, the initial conditions are modified. This process is iterated until a periodic orbit is found. A detailed derivation of the Single Shooting algorithm may be found in Howell. Halo orbits generated in the CRTBP were later converted into the JPL ephemeris approximation of the Solar System, which models the motion of a massless object in the presence of the planets and moons in the real solar system. The motion of the planets and moons are approximated by the most accurate ephemeris constructed by the Jet Propulsion Laboratory to date. The JPL Ephemeris model used in this project is the JPL Planetary and Lunar Ephemerides, DE405/LE405, which was constructed in by Standish in 1998 [17]. The model uses the International Celestial Reference Frame as its coordinate system and includes the ephemerides of the positions and velocities of the Sun, the four terrestrial planets, the four gas-giant planets, the Pluto/Charon system, and the Moon. Once the halo orbit was modeled in the JPL ephemeris, AGI s Satellite Tool Kit (STK) was used for further detailed analysis. The ephemeris files for the halo orbits were imported into STK and complete reports were generated for lunar coverage, Earth access times, eclipse conditions, and cross-link access. Phase A The constellation for Phase A will consist of two spacecraft, equally phased on a Southern L 2 halo orbit with a period of 7.5 days, Jacobi Constant = , and initial conditions given in Table 2. The two spacecraft will provide 100% continuous, 90% two-fold coverage. Each spacecraft has 100% access to the Earth. Figure 5 shows an STK screen shot of the lunar coverage during Phase A. A facility was created at the Lunar South Pole, near the Aitken Basin. STK clearly illustrates when each spacecraft has access to the facility by the red lines in Figure 5. The shaded portions of the Moon represent coverage: green areas represent twofold coverage while the yellow represents one-fold coverage. The plot is centered on the far side of the Moon. It can be seen that the initial constellation provides excellent far side and South Pole coverage. 6

7 STK also generated an eclipse report for three years of operations. The analysis showed that the maximum umbra eclipse duration was 1.68 hours and the orbit received cumulative sunlight 99.9% of the time. The maximum coverage gap (maximum time for one-fold coverage of the South-Pole) is slightly over three hours. STK analysis showed that if one spacecraft fails, the remaining spacecraft would have 95% access to the South Pole facility and would be in view of the South Pole for 7.12 days. Figure 7 and Figure 8 show sample coverage during Phase B with the shaded portion representing the number of satellites covering the base at the South Pole. The graphs are color coded as follows: yellow one-fold coverage; green two-fold coverage; blue three-fold coverage; purple four-fold coverage. Figure 7 illustrates that the Phase B constellation provides four-fold coverage of the South Pole during certain times while Figure 8 shows near global coverage during a different time. Figure 5 - STK screen shot of Phase A coverage. Figure 7 - STK screen shot of Phase B coverage: Fourfold coverage of the South Pole. Phase B The Constellation for Phase B will consist of the four total satellites with an operational date of Two spacecraft will be located in the initial Phase A L2 Halo orbit. The two other spacecraft will reside in a new L2 Halo orbit with a Jacobi Constant of and a period of days. The geometry of the orbits for the Phase B constellation can be seen in Figure 6. Figure 8 - STK screen shot of Phase B coverage: Near global coverage of the lunar surface. The new L2 halo orbit selected for Phase B was designed to have the same Jacobi Constant as the initial orbit used in Phase A. Low energy transfers exist between halo orbits, although it is not always a trivial matter to locate them. By ensuring the two orbits have the same Jacobi Constant, a constraint is placed on the system, so that low energy transfers may be more easily found between the two orbits [10] [11]. Using low energy transfers, the spacecraft will be able to transfer between the two orbits for ΔVs on the order of 5-10 m/s. In the event of a spacecraft failure, it would be possible to inexpensively reconfigure the constellation to optimize coverage with the remaining spacecraft via lowenergy transfers. Figure 6 - Phase B orbit configuration. The constellation provides continuous, redundant South Pole coverage and increased lunar far-side coverage. Additionally, the constellation will be in view of portions of the near-side; supplementing the coverage provided by the DSN. Phase C The constellation for Phase C consists of four satellites that will be operational by Two spacecraft will be in the larger of the L2 halo orbit from Phase B. The other two 7

8 spacecraft will be located in a halo orbit about the EarthMoon L1 point. The L1 orbit has a Jacobi Constant of and a period of 11.8 days. As seen from Figure 1, a spacecraft in a halo orbit about L1 would provide coverage of the near side of the Moon and have 100% access to the Earth. Figure 9 presents four views of the Phase C orbit configuration. be achieved by using three spacecraft in the L1 halo orbit and three spacecraft in the Phase B L2 halo orbit. Orbit Maintenance Halo orbits are inherently unstable. Over time, small perturbations will exponentially grow, causing the spacecraft to drift from the nominal orbit. To account for the instabilities of the orbit, station-keeping maneuvers must be performed. The stability index of an orbit, ν, can be correlated to the station-keeping cost. The stability index is calculated by the following: 1$ 1 ' " = & #max + ) 2% #max ( (1) where λmax is the maximum eigenvalue of the monodromy matrix [3]. A stability index of 1 indicates a stable orbit whereas a! stability index greater than one implies instability. In general, a higher stability index corresponds to higher station-keeping costs. The orbit selected for Phase A coverage has a stability index of 1, which points to a low station-keeping cost. Although a full station-keeping analysis was not completed due to the complexity of optimizing the problem, a budget can be estimated based on current academic publications. Grebow et al calculated approximately a 5-m/s/year ΔV budget for seven and eight day halo orbits [3]. It is reasonable to assume that a 7.5-day halo orbit will have a similar budget. This is a conservative budget, as the results were not optimized. It is also expected that the ΔV budget will be smaller due to the use of LiAISON navigation, which will be discussed in an upcoming section of this paper. Using LiAISON navigation, Hill et al calculated a ΔV budget of 16.2 cm/s/year, although they surmised the budget would be roughly 1 m/s/year accounting for burn losses and error in maneuver execution [4]. Figure 9 - Phase C orbit configuration. The four spacecraft will provide nearly 100% continuous global coverage. There are a few small coverage gaps in the mid-latitude regions. A sample coverage plot generated in STK can be seen in Figure 10. The color-shading scheme used in Figure 7 was used in Figure 10 as well. Figure 10 illustrates that the constellation provides periods of threefold coverage of the South Pole. The coverage gap can be seen in the upper center of the plot; however, this is only for a brief period of time. Launch Vehicle A trade study was conducted to evaluate available launch vehicles for the constellation. The options analyzed included the Minotaur 4, Taurus 3110, Falcon 9, Delta II, Delta IV-Medium, Athena 3 and the Atlas II. The trade study compared the launch cost for the entire Phase A constellation, reliability, shroud volume, and mass margin. The SpaceX Falcon 9 with the 3.6meter fairing was selected as the best option for this mission. The advertised cost of $35 million was attractive, as was the large shroud fairing in which the entire Phase A constellation could be housed with ample room for a piggyback load, if applicable. The Falcon 9 is currently in production with the demonstration launch scheduled in late The Minotaur 4 was selected as a backup vehicle in the event the Falcon 9 cannot be used. However, the Minotaur 4 would require two launches to establish the initial constellation. Figure 10 - STK screen shot of Phase C coverage. The L1 orbit for Phase C was designed to have the same Jacobi constant as the orbits in Phases A and B. Again, this is done to allow mission designers to more easily locate low-energy transfers. Thus, the spacecraft would have the capability to transfer between any of the three halo orbits for minimal ΔV. The constellation is highly reconfigurable. If, for example, during Phase C, increased South Pole coverage becomes necessary, a spacecraft could transfer from the L1 halo orbit to the Phase A L2 halo orbit for a ΔV as low as 5 m/s. In addition, 100% continuous global coverage could 8

9 Spacecraft Overview 4. SPACECRAFT DESIGN A spacecraft was designed to meet the requirements for Phase A highlighted in Table 1. The spacecraft will consist of three antennas, solar arrays, and the bus, shown in Figure 11. The three antennas allow for simultaneous link with the Earth, Moon, and the other satellites of the constellation. The large antenna is a 1.6-meter diameter parabolic dish. The dish is fixed to the bus and used for the communication link between the spacecraft and the Moon. The two smaller parabolic antennas have a diameter of 0.8-meter and are used for communication between the Earth and establishing the cross link with the rest of the constellation. Although a smaller dish could be used for establishing a link to the Earth, the dishes are identical to allow for mission flexibility. The mass from the individual subsystems is the sum of the components needed. A mass contingency of 30% of the dry mass is the recommended minimum standard contingency advocated by ANSI and AIAA for a class 1 spacecraft between 50 to 500 kg preparing for the conceptual design review [18]. Stowed Satellite Configuration The available volume within the launch vehicle fairing was a driving factor for the stowed satellite configuration. The 3.6-meter fairing of the Falcon 9 has a dynamic envelope of 3.2-meters. This diameter limited the upper end of the spacecraft design. The primary antenna to the Moon was the driving factor in the spacecraft size. After the size of the main dish was determined, the spacecraft was small enough to place the two spacecraft side by side in the payload fairing. Other configurations were considered, however, this configuration minimized the moment loading on both the spacecraft. In order to prevent the antennas from colliding with each other as a result of the random vibration during launch, an angle of 15 was placed in the launch vehicle adapter to provide the necessary separation. This is illustrated in Figure 12(b). Figure 11 - Conceptual drawing of the satellite. A design for the following spacecraft subsystems was completed: Attitude Determination and Control (ADCS), Command and Data Handling (CDH), Communication (Comm), Power, Propulsion, Structures, and Thermal. The subsystem designs will be discussed in forthcoming sections of this paper. Table 7 summarizes the mass budget for a satellite. Table 7 - Mass budget for the satellite. Component Mass (kg) % Dry Weight % Wet Weight ADCS % 6.0% CDH % 4.9% Comm % 13.3% Power % 13.0% Propulsion % 3.3% Structure % 19.8% Thermal % 2.0% Subsystem Total % 62.4% Contingency % 26.7% Propellant % Dry Mass Wet Mass Figure 12 - Satellites in the full Falcon 9 launch fairing (a) and a close up view (b). A satellite in the launch configuration is shown in Figure 13. The solar arrays are folded next to the body and will be restrained by a releases mechanism. The antenna boom arms will also be secured to the main bus structure. Figure 13 - Stowed spacecraft configuration. 9

10 Figure 14 - Exploded view of the bus. An exploded view of the satellite bus is shown in Figure 14. The primary placement consideration for the components was keeping the communication hardware in the same section of the spacecraft. This minimizes line losses associated with the signal within the hardware. Another significant consideration is the placement of the reaction wheels. The three reaction wheels need to be orthogonal. Each of these was placed parallel with one of the coordinate axis of the spacecraft. The fourth reaction wheel is placed equiangular with respect to the other three reaction wheels for redundancy. The rest of the hardware was placed in such a way to control the center of mass of the satellite. parameters that influenced the communication design included, but were not limited to: user burden, rain attenuation, receiver temperature, data rates, frequency, antenna type, antenna size, transmitted power, and communication subsystem mass. NASA s SCAWG report states that each satellite s communication (comm) subsystem should be equipped with onboard network routing that meets the requirements of the C3I Interoperability Specification to provide networking techniques that facilitate seamless transition between network elements, reduce equipment requirements, and improve resource efficiency. C3I, an Internet Protocol (IP) based network architecture, differs from current NASA systems since it incorporates open standards and establishes interfaces amongst different space-based and ground elements. The C3I network is a virtual system that incorporates routing, store-and-forward, and ad-hoc links that together create a flexible and robust architecture. Integration of the C3I system elements are realized in a layered architecture that facilitates low impact upgrades. Structures The structure for the spacecraft is based on the MicroSat Systems Inc (MSI) 400 kg composite bus structure. MSI has already qualified their bus for spaceflight. The bus structure meets all of the NASA material properties and outgasing requirements. The bus has spaceflight heritage in the TacSat 2 satellite and the performance is known. Communication Subsystem The SCAWG report recommends the Ka-band for all links and the S-band for all links except the crosslink. However, the design incorporates S-band capability on the crosslink antenna to preserve symmetry, redundancy, and adaptability for the system under changing needs. The Ka-band is primarily allocated for mission data and the S-band for Tracking, Telemetry, and Command, (TTC). The Ka-band offers a significant increase in data rate over X and S-bands and will transmit TTC within the data stream for a nominal cost. This dual band approach offers maximum flexibility for users. The communication architecture is shown in Figure 15. The communication subsystem, the primary payload for each spacecraft, was a principal driver of the spacecraft mass and size. The selection of the halo orbit drove the mass of the spacecraft because it established a link distance between the spacecraft and lunar South Pole an order of magnitude greater than the frozen orbit. Despite this, a communication link was established to support robotic video for two lunar assets at 1.5 Mbps. The satellite communication system was based on a Communication Satellite Multiplex design typical for GEO communication satellites. The design permits signals to be stored and forwarded or up/down converted. Frequency selection and data handling were based on recommendations by the SCAWG report, the Command, Control, Communication, and Information (C3I) initiative [19], and the Consultative Committee for Space Data Systems (CCSDS) [20]. Other 10

11 in Figure 16. The plot shows the values obtained for the parabolic dishes. The empirical formula provided by Brown does not offer much information below a 0.4 m dish. However, the dish diameter was increased from the minimum value of 0.4 meters to 0.8 meters to provide geometric spacecraft symmetry and an alternative crosslink dish. Figure 15 - Communication Architecture for Phase A. Mission data will be transmitted at a rate of 1.5 Mbps to accommodate video transmission. With two spacecraft in view of the Lunar South Pole, a 3.0 Mbps data rate to Earth is possible. Data compression is beyond the scope of this report; however, future design phases may use it to provide a significant increase in rate for some types of data like video and photos. The link design maintains a 3dB link margin for all legs. The L 2 Halo orbit provides each spacecraft with a continuous view of the Earth. The Earth Ground Stations were assumed to be the Deep Space Network (DSN) 34-m dish system. The navigation solution for the spacecraft is computed onboard each spacecraft with an initial calibration with respect to ground stations. Once the calibration is performed, the spacecraft will require the ground stations for transmission and/or receipt of mission data, and TTC only. Tracking is not necessary due to the implementation of Liaison navigation, a technique that will be discussed in the navigation section of this paper. The crosslink is nearly continuous providing a signal used primarily for Doppler range and range-rate computations, and time updates of navigation solutions to and from each spacecraft. However, the link is designed to provide the same data rate as the Earth link if needed. For the Lunar Relay element, the user burden was assumed to be a 25 cm parabolic dish with a no more than 100 W available for the uplink, a value suggested by Noreen [21]. The antenna diameters were selected based on empirical formulas and the desire to preserve symmetry in the spacecraft. Brown [22] presents an empirical formula based on flight heritage to compute the antenna mass as a function of parabolic antenna diameter and the comm subsystem mass fraction as a function of transmitted power. The combined mass of the antenna and comm subsystem power system was plotted against the antenna diameter and shown Figure 16 - Communication subsystem mass as a variation of antenna diameter. In the K a -band rain attenuation can result in a 37 db loss in many regions on the Earth. Guaranteeing a link for this condition significantly increases the size of the spacecraft due to either an increase in antenna diameter or transmitted power to maintain the link in rain conditions. Rain attenuation is an issue regardless of the orbit selected for the lunar relay due to the distance between the Earth and the Moon. Rather than sizing the spacecraft to make a continuous link regardless of weather conditions, this spacecraft will accept temporary outages due to weather and will store-and-forward data as required. Three summary link budgets are presented in Table 8, Table 9, and Table 10. Attitude Determination and Control Subsystem The primary control mechanism onboard the spacecraft will be reaction wheels due to their 3-axis capabilities, accuracy and reasonable agility. The spacecraft will also make use of a system containing sun sensors, star trackers, and inertial measurement units. Sun sensors will be used in the spacecraft for coarse attitude determination, specifically during sun acquisition and any other time when the spacecraft needs to know its attitude to no less than 1 degree. Star trackers will be used to provide fine attitude determination whenever the spacecraft is pointing one of the antenna arrays. Star trackers will also provide position data to be used by the Guidance Navigation and Control (GNC) subsystem. Inertial measurement units (IMUs), which contain both accelerometers and gyroscopes, are used to provide relative motion data. 11

12 Table 8 - Ka-band crosslink and S-band safe mode link budget. LL 2, ES, and LS denote the Halo Orbit, Earth Surface, and Lunar Surface, respectively. DATA TYPE Bit Rate Units Sat/Sat Link Safe Mode Mission Data 1.5 Mbps Ka-Band ( 0.8m Parabolic Dish ) S-Band ( Omni Antenna ) Tracking, Telemetry Command (TTC) 8.0 kbps Crosslink to Crosslink from Uplink Downlink Command (CMD) 4.0 kbps TTC & Data TTC & Data Safe Mode Safe Mode PARAMETER Symbol Units LL 2 - LL 2 LL 2 - LL 2 ES - LL 2 LL 2 - ES Link Distance - km Frequency f GHz Transmitter Power P W < 0.05 Carrier-to-Noise C/N o db-hz Data Rate + Overhead R Mbps 4.31 Mbps 143 bps 143 bps Margin - db Table 9 - Lunar Vicinity link budget in Ka- and S-band. DATA TYPE Bit Rate Units Lunar Vicinity Link Lunar Vicinity Link Mission Data 1.5 Mbps Ka-Band ( 1.6m Parabolic Dish ) S-Band ( 1.6m Parabolic Dish ) TTC 8.0 kbps Uplink Downlink Uplink Downlink Safe Mode 0.1 kbps Data Data TTC TTC PARAMETER Symbol Units LS - LL 2 LL 2 - LS LS - LL 2 LL 2 - LS Link Distance - km Frequency f GHz Transmitter Power P W Carrier-to-Noise C/N o db-hz Data Rate + Overhead R Mbps 4.29 Mbps 34.3 kbps 34.3 kbps Margin - db Table 10 - Trunk line budget to and from halo spacecraft in Ka- and S-band. DATA TYPE Bit Rate Units DSN Earth/Lunar Link DSN Earth/Lunar Link Mission Data 1.5 Mbps Ka-Band ( 0.8m Parabolic Dish ) S-Band ( 0.8m Parabolic Dish ) TTC 8.0 kbps Uplink Downlink Uplink Downlink CMD 4.0 kbps TTC & Data TTC & Data CMD TLM PARAMETER Symbol Units ES - LL 2 LL 2 - ES ES - LL 2 LL 2 - ES Link Distance - km Frequency f GHz Transmitter Power P W Carrier-to-Noise C/N o db-hz Data Rate + Overhead R Mbps 4.31 Mbps 11.4 kbps 22.9 kbps Margin - db

13 Guidance, Navigation and Control Classically, the DSN has been used to provide navigation support for deep space missions. To alleviate the high cost of using the DSN, a new technique, known as Linked Autonomous Interplanetary Satellite Orbit Navigation (LiAISON, or Liaison Navigation [23] [24]) may be used. Liaison Navigation utilizes the asymmetrical geometry of halo orbits in conjunction with scalar satellite-to-satellite tracking (SSST) data, such as crosslink range, to simultaneously estimate the relative and absolute positions and velocities of both spacecraft. In conic orbits, SSST alone is insufficient to autonomously determine the absolute orientation for two spacecraft in near Earth or Lunar orbits. This is due to the fact that SSST only provides information on the size, shape, and relative orientation of the two orbits. Keplerian orbits of a given size, shape and relative orientation can have any absolute orientation about the primary body. However, lunar halo orbits are very strongly influenced by two primary bodies, the Earth and the Moon. The gravitational force field in the three-body problem is asymmetrical; thus a halo orbit with a given size and shape can only have a single orientation with respect to the Earth and Moon. Therefore, a spacecraft in a halo orbit can track another spacecraft using crosslink range measurements and determine the absolute positions and velocities of both spacecraft simultaneously without Earth-based tracking or mathematical constraints. Only one spacecraft is constrained to be in a halo orbit; the other may be in another halo orbit, a lunar orbit, or in transit somewhere in the Earth-Moon system [23] [24]. Liaison navigation simulations have shown excellent accuracy results for lunar halo orbits in the CRTBP as well as in the Earth-Moon system using the DE403 planetary ephemeris, solar gravity, solar radiation pressure (SRP) and the LP100K lunar gravity field in an Extended Kalman Filter [25]. The position errors for halo orbiters are on the order of 100 m RSS. However, if a halo orbit is tracking a low lunar orbiter, the position errors for the low lunar orbiter are on the order of 10 m. Liaison will provide more accurate navigation solutions than the DSN alone. Additionally, it will significantly reduce the system s reliance on the DSN, reducing overall cost of the mission and the amount of Earth downlink time necessary for navigation solutions. This allows increased time for mission specific tasks. The DSN will be used to back up the GNC system. The DSN will determine the satellites position during the ballistic lunar transfer and will then be used to back up and verify Liaison methods once the spacecraft have been inserted into the orbit. Star trackers will also be used in conjunction with these position determination systems to provide intermediate data pertaining to the relative motion of the spacecraft allowing for more accurate predicted position. Thermal Three thermal modes were considered for analysis: Relay, Standby, and Eclipse. The Relay and Standby modes were considered to be equilibrium analysis. To get a realistic understanding of the impact of eclipse on the satellite, a transient analysis was performed to determine the minimum temperature of the bus. The temperature of the solar array was also calculated. The distances and constants used in the thermal analysis are shown in Table 11 and Table 12. Table 11 - Distances used in Thermal analysis. Distance Max Distance from Earth to Sat Ave Distance from Earth to Sat Min Distance from Earth to Sat Max Distance from Moon to Sat Ave Distance from Moon to Sat Min Distance from Moon to Sat Table 12 - Constants used in Thermal analysis. Value km km km km km 6143 km Constant Value Max Solar Flux 1418 W/m 2 Solar Constant W/m 2 Min Solar Flux 1326 W/m 2 Max IR Lunar Flux 1268 W/m 2 Min IR Lunar Flux 5.2 W/m 2 Earth Blackbody Tempearture K Moon Black Body Temperature K Earth Albedo Constant 0.34 Lunar Albedo Constant 0.07 The Relay Thermal State is the highest temperature state. The analysis was performed using an energy balance of a control volume defined by the surface of the bus, which, for simplicity, was assumed to be a sphere with the same surface area as the actual bus. There are five irradiations present in the relay thermal state: irradiation generated by the Sun, irradiation based on the blackbody radiation of both the Earth and Moon, and the albedo of the sunlight reflected off both the Earth and Moon. Each incoming irradiation was calculated with the constants that gave a worst-case scenario for temperature. This occurs when the satellite has its closest lunar approach and when it is on the Sun side of the Earth where all five irradiations will be present. The energy leaving the control volume is limited to radiation into deep space at 0K. 13

14 The Standby Thermal State was calculated in a similar fashion to the relay thermal state to give a nominal minimum temperature. The incoming irradiation will be limited based on position of all of the bodies with respect to the satellite. For minimum non-eclipse temperature conditions, the satellite will be at maximum distance from the Moon and on the opposite side of the Earth as the sun. In this scenario there will be no irradiation due to albedo. The Eclipse Thermal State was determined based on an STK eclipse analysis for the nominal halo orbit. The STK simulation showed only seven eclipses over a one-year period with average eclipse time of 1.12 hours and a maximum duration of 1.43 hours. The STK simulation was extended to three years and eclipse analysis showed a maximum eclipse duration of 1.68 hours. Over a given one-year period, the spacecraft will spends less than 10 hours in eclipse, corresponding to over 99.9% Sun exposure. Eclipse conditions occur as the spacecraft passes through the lunar shadow. Eclipses do not occur every orbit because Sun s position changes relative to the Earth-Moon system. The Eclipse Thermal state required a transient thermal analysis to determine a reasonable temperature limit for all of the components, as an equilibrium analysis would place the bus to near cryogenic temperatures. The transient analysis assumed a lump capacitance of the spacecraft over the duration of the longest eclipse. Incoming irradiation included albedo from the Earth, but no direct solar irradiation. The analysis was based on a time dependant energy balance given by the differential equation E in" E out+ E Generated = m # c p # dt dt, where E in, E out, and E Generated are the energy flow rates, m is the mass of the spacecraft and c is the lump heat capacity of the spacecraft. Due to the fact that radiation dominates the energy transfers, direct integration was not possible. Instead, an iterative method was used based on the equation T n +1 = "t # (E in+ E Generated $% #& bus # A surf # T 4 n ) + T n. m # c p Table 13 presents the results of the thermal analysis. The analysis shows that active thermal control will only be needed during eclipse periods. Heaters will be used for components whose operating temperatures drop below the minimum operating temperatures during eclipse. In addition to active thermal control, passive control will be used in the form of Multi-Layer Insulation (MLI) and a surface coating of black paint. The amount of MLI needed will depend on the capabilities of the heaters. p Table 13 - Critical thermal state temperatures for the bus and solar array. Relay Temperature Standby Temperature Eclipse Temperature Propulsion Bus Solar Array K C K C Several Trajectory Correction Maneuvers (TCM s) will be performed during the lunar transfer trajectory in order to account for any launch vehicle trajectory insertion errors. Due to the dynamics of the BLT, the spacecraft should theoretically enter into the halo orbit with no insertion maneuvers required, particularly if the TCMs are effective. There are two options for phasing the spacecraft. The spacecraft could perform small maneuvers while in transit to the halo orbit, or the spacecraft could use low-energy transfers once at the halo orbit to achieve proper phasing. For a conservative estimate, a total of 25 m/s ΔV is budgeted for the phasing and insertion maneuvers. This value is significantly smaller then a typical lunar mission. Once on orbit the spacecraft will perform station-keeping maneuvers once every two days of approximately 3-5 cm/s. This translates into a conservative estimate of 10 m/s ΔV necessary for one year, and a total of 50 m/s ΔV budgeted over the mission life. The actual ΔV budget may as low as 2-5 m/s/year due to the relative stability of the selected halo orbit [3] and the use of Liaison navigation, which has the potential to significantly lower the stationkeeping budget [4]. Momentum-dumping maneuver will be performed once every orbit period to de-saturate the reaction wheels. This maneuver will be performed during the brief period when the spacecraft is out of view of the South Pole since the power requirements on the spacecraft are smallest during this time. Finally 25 m/s ΔV is budgeted for orbit repositioning in case the coverage needs on the lunar surface change over the mission lifetime. This value is significantly smaller than typical repositioning maneuvers due to the unique characteristics of a halo orbit. A summary of the ΔV budget is shown in Table 14. The Isp values used were 220s for orbit insertion and phasing and 160s for orbit repositioning and orbit maintenance. As shown in Table 14, the total ΔV budget is only 100 m/s. A preliminary analysis showed that to perform the same tasks - orbit insertion, maintenance, and orbit 14

15 repositioning - a Frozen orbit would require a ΔV budget of approximately 1350 m/s. Therefore, the use of the halo orbit represents a significant cost and mass savings to the constellation. Table 14 - ΔV Budget. Manuever Propellant Mass (kg) Orbit Insertion/phasing Orbit Maintenance (5yr) Orbit Repositioning Momentum Dumping Subtotal Margin (20%) 7.00 Residual (3%) 1.26 TOTAL components via the loads control board. Excess power is stored in the Lithium-Ion battery for use during eclipses. Power is also fed back to the drive electronics and actuator motors so the solar arrays remain continuously pointed at the sun. Power will be generated via Ultra Triple-Junction Gallium Arsenide/Germanium solar cells. These cells were chosen because they are the most efficient solar cell currently in production and are approved for space applications. With the solar array properties given in Table 15, the solar array area was computed to be 3.66 m 2. This value corresponds to the worst-case power requirements for the spacecraft and for the majority of the mission, excess power will be dissipated through the power distribution unit. Table 15 - Solar array characteristics. A trade study was conducted to determine the type of propulsion system. Currently available space propulsion systems can be categorized as cold gas, chemical, or electric. More exotic systems are in development, but are beyond the scope for this mission. A bipropellant system offers better performance then a monopropellant system but is significantly more complicated since both fuel and oxidizer are needed in separate tanks. Having a monopropellant system allows for a simpler system design which eliminates risk and saves cost. The disadvantage comes from the need for more fuel, but, given the low ΔV requirements for this mission, the fuel saving of a bipropellant system would only be 13.4 kg. This value represents about 3% of the total wet mass of the spacecraft, yet would cost two to three times more dry mass. Thus a Hydrazine monopropellant system with nitrogen as the pressurant was selected for the spacecraft design. Due to the volume constraints of the bus, the propellant will be held in two spherical titanium tanks that will feed into a single propellant line to the thrusters through a system of valves and line filters. The entire system will need to be maintained above 3 ºC throughout mission life to ensure that the hydrazine does not freeze inside the pipes. Pressure sensors, temperature sensors, and tank and line heaters are provided to ensure proper operation throughout the mission. Six one Newton thrusters will be used for de-saturation maneuvers for the three-axis wheel configuration. These thrusters will be positioned in groups of two, one, two, and one on opposing corners of the spacecraft in order to provide a moment balance during burns. One main 22N thruster will be used for all ΔV maneuvers. Power The electrical power system (EPS) has four main components: the power source, storage, regulation, and distribution units. The system generates power from the solar arrays, which feeds power into the charge control unit. The power is then distributed to all necessary Solar Cell efficiency 28.60% Inherent Degradation 77% Cell degradation / year 2% Mission Life 5 years Average S/C Power Required 536 W Power solar array must produce 677 W Beginning of Life Power production 276 W/m 2 End of Life Power production 185 W/m 2 Total Required Solar Array Area 3.66 m 2 The energy storage system will provide the spacecraft with the required power during launch and commissioning, and will store energy for survival during eclipses and solar array malfunctions. Lithium Ion batteries were chosen for this mission because they have a high specific energy and voltage, which minimizes the mass of the system. Eight cells in series will supply the bus with 28V and the 39 Amp-hour capacity will allow for 4.53 hours of survival time in the event of a solar panel malfunction. The battery life is sufficient for normal mission operations, as the expected peak eclipse time is only 1.68 hours. During relay mode the power draw on the spacecraft is dominated by the communications system. For the other power modes the power requirements are significantly smaller. During standby and safe modes, the communication power requirements are significantly smaller since minimal data is transmitted during these times. For orbit adjustments and de-saturation modes, the majority of the power draw comes from the ADCS and propulsion subsystems since the reaction wheels and thrusters are in use during these times. These two modes are not common and only occur five times every 7.5-day orbit period. Eclipse mode is the least common and only occurs seven times a year. It is very similar to safe mode but has the highest thermal requirements of all the modes. 15

16 Cost The Small Satellite Cost Model (SSCM) was used to estimate spacecraft unit costs. Space Mission Analysis and Design [26] analysis was used to estimate operations costs for five years. Information available from SpaceX cited the cost of the Falcon 9 as $35 million in January 2007 US dollars. The cost analysis result is shown in Table 16. An early goal of this study was develop a mission that fit within a budget similar to the one currently allocated by NASA for a Small Explorer (SMEX) mission of $100M, but not including the cost of launch. The study reached this goal and considers the results conservative given that in separate analysis, the SSCM model has been shown to overestimate the cost of an MSI bus significantly. The total mission cost including launch is also significantly lower than what many have projected an initial lunar comm/nav constellation would cost. spacecraft in halo orbit than for a spacecraft in a lunar orbit. However, this research has shown this is not a limiting factor to the spacecraft design. The links can be established with a 3dB margin and a user burden of a 25 cm parabolic dish on the lunar surface. The spacecraft design shown is in the preliminary phases. Future work will be required to optimize the spacecraft. Additionally, this research assumed communication requirements in RF based on the recommendations from the SCAWG report. Future work may also be directed to different forms of communication, such as optical navigation, which also has been investigated for launch comm/nav architectures. This study, and other research on halo orbits for lunar comm/nav relays shows enough promise that the initial SCAWG decision to focus on elliptical frozen orbits should be reviewed. Ultimately, a halo orbit architecture may prove to be superior. Table 16 - Mission cost summary. Source Cost (FY07$M) First Unit Cost 56.7 Second Unit Cost 30.3 Operations Cost (5 yr) 8.5 Mission Cost 95.5 Launch Vehicle Cost 35 Total Cost ACKNOWLEDGEMENTS This project was funded by the NASA s Exploration Systems Mission Directorate (ESMD) program to the Colorado Space Grant Consortium. The majority of the research was conducted at MicroSat Systems, Inc and we are in debt for the expertise and knowledge we gained from the employees of MSI. Additionally, we also wish to thank Jeffrey Parker, Keric Hill, and George Born at the Colorado Center for Astrodynamics Research who provided information on Ballistic Lunar Transfers and Liaison navigation. 5. CONCLUSION It has been shown that small satellites can be used in halo orbits to provide communication and navigation support to NASA assets in the lunar environment. A low-cost mission was designed with a constellation that not only provides excellent lunar South Pole coverage, but also has the capacity to expand to a constellation that provides global coverage. There are several advantages to a mission that uses halo orbits. The unique geometry of halo orbits allows for the use of Liaison navigation, which provides lunar orbital accuracies on the order of 10 m and eliminates the need for Earth-based tracking. No costly orbit insertion maneuver is required, as the spacecraft will arrive ballistically onto the nominal orbit using a BLT. The spacecraft is in an orbit with a period of 7.5 days rather than in an orbit with a near half-day period. This means that assets on the lunar surface require less slewing to track the spacecraft. To meet coverage goals for both South Pole and global lunar coverage, fewer spacecraft are required which reduces the overall mission cost and the number of launches required. Finally, the constellation is easily adaptable and expandable through the use of low-energy transfers. The link distances from the constellation to the lunar surface are greater for a 16

17 REFERENCES [1] Vision for Space Exploration. National Aeronautics and Space Administration. February [2] Space Communication Architecture Working Group: NASA Space Communication and Navigation Architecture Recommendations for Final Report, May 15, [3] Grebow, D., M. Ozimek, K. Howell, and D. Folta, Multi-Body Orbit Architectures for Lunar South Pole Coverage, AAS , AAS/AIAA Space Flight Mechanics Conference, Tampa, Florida, January 22-26, [4] Hill, K., J. Parker, G. H. Born, and N. Demandante, A Lunar L2 Navigation, Communication, and Gravity Mission, AIAA , AIAA/AAS Astrodynamics Specialist Conference, Keystone, CO, Aug , [5] Farquhar, R.W. The Control and Use of Libration- Point Satellites, NASA Technical Report TR R-346, [6] Farquhar, R. W. and A. A. Kamel, Quasi-periodic Orbits About the Translunar Libration Point, Celestial Mechanics, Volume 7, 1973, pp [7] Parker, J. S., Low-Energy Ballistic Lunar Transfers, Ph.D. thesis, University of Colorado Boulder, May [8] Parker, J. and M. Lo, Shoot the Moon 3D, AAS , AAS/AIAA Astrodynamics Specialist Conference, Lake Tahoe, California, August 7-11, 2005 [9] Parker, J., Families of Low-Energy Lunar Halo Transfers, AAS , AAS/AIAA Space Flight Mechanics Conference, Tampa, Florida, January 22-26, [10] Lo, M.W. and Parker, J.S., "Chaining Simple Periodic Three-Body Orbits," AIAA/AAS Astrodynamics Specialist Conference, Paper No. AIAA , Lake Tahoe, CA, August 7-11, [11] Parker, J. and K. E. Hamera, Chaining Periodic Three Body Orbits, Forthcoming, [12] Gómez, G, A. Jorba, J. Masdemont, S. Simó. Study of the Transfer between Halo Orbits. Acta Astronaut. Vol [13] Elipe, A, and M. Lara. Frozen Orbits about the Moon. Journal of Guidance, Control, and Dynamics, Vol 26. No. 2, March-April, 2003 [14] Ely and Lieb Constellation of Elliptical Inclined Lunar Orbits Providing Polar and Global Coverage. AAS/AIAA Astrodynamics Specialist Conference, Lake Tahoe, CA. August 7-11, 2005 [15] Szebehely, V., Theory of Orbits: The Restricted Problem of Three Bodies, Academic Press, New York, [16] Howell, K., Three-Dimensional, Periodic, Halo Orbits, Celestial Mechanics, Volume 32(53), [17] Standish, E. M., JPL Planetary and Lunar Ephemerides, DE405/LE405, Technical Report IOM 312.F , Jet Propulsion Laboratory, August [18] Guide for Estimating and Budgeting Weight and Power Contingencies for Spacecraft Systems (AIAA-G ), Sponsor: American Institute of Aeronautics and Astronautics, [19] Constellation Program Command, Control, Communication and Information (C3I) Interoperability Standards Book, Volume 1: Interoperability Specifications [20] The Consultative Committee for Space Data Systems website; [21] Noreen, G. K., Integrated Network Architecture for Sustained Human and Robotic Exploration, IEEE, [22] Brown, C. D., Element of Spacecraft Design, American Institute of Aeronautics and Astronautics Inc, Virginia, [23] Hill, K. and G. Born, Autonomous Interplanetary Orbit Determination Using Satellite-to-Satellite Tracking, Journal of Guidance, Control, and Dynamics, Volume 30(3), 2007 [24] Hill, K. A., G. H. Born, and M. W. Lo, Linked, Autonomous, Interplanetary Satellite Orbit Navigation (LiAISON) in Lunar Halo Orbits, AAS , AAS/AIAA Astrodynamics Specialist Conference, Lake Tahoe, CA, Aug. 7-11, [27] Hill, K. A., Autnomous Navigation in Libration Point Orbits, Ph.D. thesis, University of Colorado Boulder, May [26] Wertz, J. R., and W. J. Larson, eds. Space Mission Analysis and Design. 3rd ed. El Segundo, CA: Space Technology Library,

18 BIOGRAPHY Kathryn Hamera is a PhD student at the University of Colorado at Boulder. She has a BS in Aerospace Engineering from the University of Missouri Rolla as well as a MS in Aerospace Engineering from the University of Colorado at Boulder where she has served a TA and was a co-instructor for an Interplanetary Mission Design Class. She is a recipient of a National Science Foundation Graduate Student Research Fellowship. Her research interests include phasing spacecraft on halo orbits, low energy libration point transfers, and mission design. She recently served as the program manager for the Colorado Space Grant ESMD that completed a Lunar Navigation and Communication constellation design. Todd Mosher is currently the Director of Advanced Systems at Microsat Systems Inc. Dr. Mosher joined MSI after serving as Senior Manager of Advanced Exploration Systems for Lockheed Martin Space Systems Company, where he was a part of the group that was awarded the Orion Crew Exploration Vehicle from NASA. Prior to working at Lockheed Martin, Dr. Mosher was an assistant professor at Utah State University (USU) where he was the Director of the Center for Advanced Satellite Manufacturing. Dr. Mosher earned his Ph.D. in aerospace engineering from the University of Colorado, has two master s degrees in aerospace engineering and systems engineering from the University of Colorado and the University of Alabama in Huntsville respectively, and received his bachelor s degree in aerospace engineering from San Diego State University. He is also a faculty member and graduate of the International Space University. Mark Gefreh is currently a first year graduate student at the Colorado School of Mines studying mechanical engineering. Mr. Gefreh earned his bachelor s degree of Engineering Physics from the Colorado School of Mines in He became involved with an undergraduate group building a working prototype of a lunar excavator as his senior design project. Feeling the design was marketable; the team became one of ten semifinalists in the Lunar Ventures, a national business plan competition. Over the next year, the team plans to modify the design in order to enter the Regolith Challenge, one of NASA s Centennial Challenge competitions. During the summer of 2007, Mr. Gefreh was one of five students chosen to design an inexpensive lunar navigation and communication satellite. The study was the result of a partnership between the Colorado Space Grant and Microsat Systems. Robert Paul is a Graduate student at the University of Colorado at Boulder. He has a BS in Aerospace Engineering from the Embry-Riddle Aeronautical University Prescott and is completing an MS in Aerospace Engineering from the University of Colorado at Boulder. He is presently a TA and his research interests include filter optimization and adaptive orbit determination. He recently served as a team member for the Colorado Space Grant ESMD project that completed a Lunar Navigation and Communication constellation design. Leon Slavkin is currently an MS/BS student at the University of Colorado at Boulder, studying Aerospace engineering. His fields of study include Astrodynamics, Propulsion and Spacecraft design. He hopes to pursue a career as a Systems engineer, designing human spacecraft for the next generation of space exploration. Born in the former Soviet Union, he moved to Colorado at an early age and has lived in the United States a majority of his life. His education provided a strong background in Mathematics, and he has participated and won several math competitions, including the American Mathematics Competition. His most recent activities include participating on a Mars rover research project through the Colorado Spacegrant, designing and building a Hybrid rocket as a senior design project, and performing a Lunar Nav/Comm study sponsored by NASA at MicroSat Systems in the summer of Joseph Trojan is currently a senior in Aerospace Engineering at the University of Colorado at Boulder. After graduation with a Bachelor s degree, he plans to pursue a Master s Degree in Astrodynamics and Satellite Navigation at CU. Joseph is currently working on a project with the Colorado Space Grant to develop an altitude reducing drag device for the DANDE satellite. 18