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monitoring, quasi-satellite orbits on EML1, EML2, EML4, EML5 and the Mars-Phobos reconnaissance. With the continuous advancement in technologies it is ...

AAS 16-493

COMMERCIAL CUBESAT TECHNOLOGY TO ENHANCE SCIENCE: COMMUNICATIONS, SPACE DEBRIS IDENTIFICATION AND MOON SURFACE RECONNAISSANCE USING LAGRANGIAN CYCLERS Pedro J. Llanos∗, Abdiel Santos† This paper deals with novel cycler trajectories for cubesats that will depart from low-Earth orbit (LEO) to help determine the resources needed for interplanetary travel and infrastructure required for space colonization on the Moon. Our cubesats will depart from a 400-km parking orbit aboard the International Space Station (ISS) to provide significant opportunities to enhance communication and navigation strategies while improving space exploration capabilities. Different cycler orbits connecting the Lagrange points in the Earth-Moon system are explored, which will enable us to improve our communications and navigation from Earth via low ∆V connection nodes often referred to as the Interplanetary Superhighway.

INTRODUCTION Increasing interest in space exploration past low-Earth orbit has stimulated novel mission concepts such as asteroid mining, deep space stations, and further solar system exploration. Within these mission concepts, many challenges exist because of the large use of resources needed for interplanetary travel and infrastructure required for space colonization. A novel phenomena known as the Interplanetary Superhighway (IPS) uses the Lagrange points as stepping stones due to the low energy trajectories and inherent low ∆V required. These Lagrange points act like natural seeds (similar to the DNA of human body) and generate different types of orbits such as halo orbits, Trojan orbits, tadpole orbits, horseshoe orbits and quasi-periodic orbits.1 Some of these families of periodic orbits (halo orbits) can be connected using the invariant manifolds associated to these halo orbits. Furthermore, homoclinic and heteroclinic connections1 between these periodic orbits is feasible but also between the triangular points in both the Sun-Earth system and the Earth and Moon system. By placing spacecraft at certain Lagrange points, extremely efficient orbital maneuvers can be used to send spacecraft to other planetary Lagrange points at low cost of fuel, therefore permitting more payload capability to be launched into space at the expense of longer duration missions. Several missions have undergone similar natural dynamics and have proven to be successful. Both the NASA’s Genesis2, 3 mission (2001) and the ESA’s SMART-1 mission (2003) utilized the invariant manifolds to place the spacecraft in the Sun-Earth L1. The NASA’s ARTEMIS mission (2007) connects both L1 and L2 points in the Earth-Moon system. On February 15th of 2015, SpaceX launched a space weather satellite on Falcon 9. The Deep Space Climate Observatory (DSCOVR) satellite was also placed at the Lagrange point L1 in the Sun-Earth system. In addition, NASA is currently working on a cubesat concept, MARS Cube One (MARCO) that would be sent on an interplanetary mission to Mars. Recently, NASA’s Launch Services Program (LSP) has awarded Venture Class Launch Services (VCLS) contracts to three commercial companies: $5.5M to Firefly Space SyStems Inc., $6.9M Rocket Lab USA ∗ Assistant

Professor, Commercial Space Operations, Applied Aviation Sciences, Embry-Riddle Aeronautical University, Daytona Beach, Florida, 32114, Member AIAA. † Undergraduate Aerospace engineering student, Embry-Riddle Aeronautical University, Daytona Beach, Florida, 32114

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Inc., and $4.7M to Virgin Galactic. These contracts will involve small satellites such as microsats (10 -100 kg) and nanosats (1 - 10 kg) or cubesats. Since 2013, there has been a continued and emergent growth of commercial cubesats4 launched by many commercial partners (see Figure 1). It is envisioned about 200 cubesats launched by the end of 2015 and about 2,500 cubesats by the year 2020. On September 20th 2015, the Chinese vehicle Long March 6 launched 20 micro satellites from the Taiyuan satellite launch center in China.

Figure 1. cubesats launches since 2000 to present time of 2015.

Using this IPS model, we can generate novel cycler orbits that would require very little control for stationkeeping and therefore fuel to operate small spacecraft. Our cubesat is expected to depart from the International Space Station at an altitude of 400 km parking orbit. This would provide significant opportunities for satellite departure from the ISS, as well as advanced communication and navigation applications, robotics, and advanced exploration capabilities. Different cycler orbits will be explored within the Earth-Moon system and will enable us to improve our communications and navigation at Earth in a safe, efficient, reliable, and more autonomous way through the Interplanetary Transport Network5 or IPS. MODEL AND METHODOLOGY We used the circular restricted three-body problem (CRTBP) in the trajectory analysis for this study.1 The Sun is the primary body, the Earth is the secondary body, and the spacecraft is the third body or infinitesimal mass in this system. To simplify the analysis, we used the normalized and non-dimensionalized convention so that the mass of the secondary body is 0 < µ < 1 and the mass of the primary body is 1-µ. The distance between the primary and secondary bodies is normalized to one with the primary body located on the x-axis at -µ and the secondary body at 1-µ. The x-axis is directed from the primary body to the secondary body. The y-axis is 90◦ from the x-axis in the primary plane of motion. Finally, the z-axis completes the right-handed system, defining the out-of-plane direction. For this work, µ = 3.040423389123456E-6 for the Earth-Moon barycenter model based on the combined mass of the Earth and Moon, MEM baryc , using JPL DE405 constants. Finally, time corresponds to the angle between the x-axis of the rotating frame and the x-axis of the inertial frame so that the period of the rotating frame becomes 2π. Using this convention, the motion of the infinitesimal mass in

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Figure 2. Left: Low energy trajectories connecting the Sun-Earth-EL1 and EarthMoon LL1 halo orbits (black) through where a small body (eg. NEA, cubesat) can be brought back into orbit (black) around the Lunar L1. Right: Low energies (heteroclinic) trajectories connecting the Earth-Moon-LL1 and the Earth-Moon-LL2.

the rotating frame can be described by the governing equations of motion: x+µ x−1+µ x ¨ − 2y˙ = x − (1 − µ) 3 − µ r1 r23   1−µ µ y¨ + 2x˙ = 1 − − 3 y 3 r1 r2   1−µ µ z¨ = − + 3 z r13 r2

(1)

where r1 and r2 are the distances from the spacecraft to the Sun and Earth, respectively. p r1 = (x + µ)2 + y 2 + z 2 p r2 = (x − 1 + µ)2 + y 2 + z 2 and µ=

MEM baryc MEM baryc + Ms

where Ms denotes the mass of the Sun. In Figure 2, we show feasible trajectories using the unstable manifold that connects a halo orbit in the Sun-Earth L1 with a halo orbit in the Earth-Moon L1 along the stable manifold. Then, the satellite can be transported from this new LL1 halo orbit along the unstable manifold to a new LL2 halo orbit along the stable manifold. This generic example shows how a small body such as a Near Earth Asteroid (NEA) or a cubesat could be navigated via these manifolds given the propulsion technology exists. CUBESAT TECHNOLOGY Cubesats are proving to be more and more prominent in the current market of space science and technology and the utilization for cubesats continues to increase. Currently, cubesats are mostly implemented for LEO missions. However, there is a large capability for using cubeSat technology for deep space missions and space weather monitoring.

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Among a slew of cubesats being developed by many different universities, Embry-Riddle Aeronautical University has been designing concepts for two cubesats since 2013. Application for Resident Space Object Automated Proximity Analysis and IMAging (ARAPAIMA)6 is the first of these cubesats that has been granted a slot in the NASA Educational Launch of Nanosatellites (ELaNa) program and is currently working through the University NanoSatellite Program sponsored by the Air Force Research Laboratory (AFRL). This satellite is a new class of inspector satellites able to digitally image and map a Resident Space Object (RSO) without previous knowledge of such an object. The potential for this mission could be expanded for: (1) space debris monitoring; and space weather observations and communications from (2) a Quasi-Satellite Orbit (QSO)1 in the Earth-Moon system and (3) Earth-Moon five libration points and the two Sun-Earth libration points closest to Earth, granted such optical technology exits. The second cubesat is the PIRARUCU or Mars Moon Prospector Mission designed to explore Phobos and will be competing in the recent Revolutionary Airspace Systems Concepts-Academic Linkage (RASC-AL) competition. It is a 12U satellite∗ (see Table 1) with detachable 1U daughters that will make a sample return from the surface of Phobos. With utilization of the IPS manifolds and libration point navigation, attainability of mission objectives would increase the feasibility for larger sample return and less ∆V at the expense of longer mission travel. Table 1. Characteristics of a 12U-cubesat cubesat (D=10 cm, L=10 cm)

Parameter

Tank Pressure Tank Temperature Area Fuel Density Number of Tanks Propellant Tank Volume (single) Total Volume (2U) Fuel Mass (2U) cubesat Dry Mass

101, 000 N/m2 293 K 2(12 × 6 × 10 cm × 10 cm) = 1.44 m2 1,000 kg/m3 (H2 0) 2 8U πD3 /6 + πD2 L/4 = 1, 309 cm3 2, 618 cm3 2.618 kg 2 × 8.3467 = 16.69 kg

As cubesats continue to evolve technological opportunities continue to arise. In this paper, we have decided to investigate the possibilities and capabilities that these cubesats have to offer through the selection of several mission scenarios. These scenarios include imaging asteroids, space debris imaging and monitoring, weather monitoring, quasi-satellite orbits on EML1, EML2, EML4, EML5 and the Mars-Phobos reconnaissance. With the continuous advancement in technologies it is possible to develop a general guideline for these missions with a significant usage of the IPS and by exploiting novel Quasi-Satellite Orbits (QSOs). For the scenarios viewed in following sections, possible propulsion capabilities will be based of upcoming Commercially Off The Shelf (COTS) technology. Tethers Unlimited7 is developing green propellant, highthrust propulsion for orbit-agile cubesats which are based off electrolysis of water, separating liquid state water into Liquid Oxygen and Hydrogen for combustion. The HYDROS thruster propulsion system is currently at Technology Readiness Level (TRL)-5 and is expected to have flight models available in 2016. These cubesats are upgradable and scalable performance for this unit which could provide ∆V of greater than 2 km/s. By using multiple units on a cubesat with the scalable HYDROS, insertion maneuver capabilities will increase to perform transfers from LEO (including ISS) to EML1, and EML2. This configuration is more suitable for bigger unit cubesats such as a 24U or 27U cubesat. Once stationed at the Libration Points, stationkeeping maneuvers will be provided by the PowerCube.7 ∗ Feasible

configuration of a 12U cubesat for our mission parameters

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This module gives power, propulsion and attitude control that will maintain the cubesat orbiting the desired location. The propulsion system of this PowerCube provides up to 6 m/s per orbit. Tethers Unlimited is currently developing another propulsion system,7 known as the MicroPET or µPET. Using the Earth magnetic field the system is capable of providing a propellantless propulsion capability that will raise the orbit of satellites from ISS to about 700 km, which is the altitude where certain sensors are being considered to be placed for space debris monitoring that we will be discussing in the latest section of the paper. NOVEL QUASI-SATELLITE ORBITS FOR SCIENCE-COMMUNICATION This section will be devoted to analyze innovative quasi-satellite orbits and novel transfer orbits between different libration points in the CRTBP of the Earth-Moon system. In this part, we will show prospective trajectories with Matlab and STK that will take the cubesat from the EML1 to the EML2 in the Earth-Moon system. Quasi-satellite orbit connecting EML1 and EML2 4

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Closest Approach to the Moon (km)

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Figure 3. a: Quasi-satellite orbit around the Moon in the Earth-Moon rotating system. The x, y and z axis are expressed in Lunar Distance (LD) or 384,400 km. b: Close approach of cubesat when orbiting the Moon via the QSO. Figure 3(a) illustrates a QSO (in blue) centered around the Moon (in grey) in the Earth-Moon rotating system. The trajectory has been integrated using the CRTBP over the time span of about 68.25 days after leaving a halo orbit with an amplitude of 24,371 km in the EML1. Over this time, the cubesat will appear to orbit the Moon in the rotating frame during eight revolutions. Each revolution implies a different close approach with respect to the Moon. The cubesat spends about one month (revolutions second to sixth) with closest approaches between 20,000 km and 30,000 km. After seven revolutions, the cubesat starts making as close approaches to the Moon as 3,169 km as displayed in Figure 3(b). The cubesat trajectory has excursions in the XZ and YZ planes of about 6,500 km, therefore being able to monitor all regions of the Moon including the poles while serving as a communication relay satellite. The intend of this example is to show that the trajectory of the cubesat can perform several revolutions around the Moon and not being captured at EML2. However, our next example displayed in Figure 4 will connect EML1 and EML2. These close approaches can make the cubesat to be ejected out of the Earth-Moon system or can make the cubesat to orbit the Earth as we will show in other examples. In these next examples, the cubesat will have close approaches to the Moon so that it can monitor different landing sites for future Moon missions.

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STK scenario: Transfer from EML2 to EML1 To prove feasibility transfer and orbit keeping capabilities between Libration Points, we used the the Systems Tool Kit (STK) to analyze different scenarios.

Figure 4. 3D representation of stationkeeping and transfer orbits from EML2 to EML1 performed through STK. Figure 4 shows both stationkeeping and orbit transfers. Minor stationkeeping at EML2 shows a low ∆V of no more than 50 m/s which is feasible in accordance with the cubesat Technology section.

(a)

(b)

(c)

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Figure 5. a: Close up of cubesat departing ISS. b: cubesat leaving Earth c: Simulated transfer maneuver from ISS orbit to EML1 in the Earth-Moon rotating frame. d: Close up of EML1 insertion. This cubesat performs six orbits about EML2 during a span of 2 months and 11 days. The cubesat loops

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around the Moon once before it is injected into the EML1 where it performs two loops. The cubesat will need station-keeping maneuvers if desired to be in both the EML1 and EML2. Figure 4 displays a direct transfer which requires a ∆V of approximately 350 m/s. This maneuver has a transfer time of close to 17 days. Though this ∆V is high for current cubesat technology, there is future prospect for cubesats to perform such maneuvers.7 Cubesat ejection from ISS occurs at approximately 400 km and an orbital transfer for EML1 insertion shown in Figure 5. The ∆V required for the insertion was 3.073 km/s (needs further optimization). In this particular example, the cubesat is depicted in Figure 5(a) trailing the ISS for about 250 m. Figure 5(b) displays the cubesat leaving the ISS along the magenta trajectory. Figure 5(c) illustrates the entire transfer arc (magenta) from the ISS to the EML1 and Figure 5(d) shows a close up of Figure 5(c) of the cubesat around EML1. STK scenario: Reaching Moon’s Orbit Several NASA missions are scheduled to be launched within the next two or three years. Going back to 1959, Pioneer 4 launched a 6.1 kg launch mass which for today’s standards is the equivalent of a 6U satellite or large cubesat.

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(b) Translunar Injection DV Effect on Altitude around the Moon

CubeSat Fuel Expenditure in function of Altitude around the Moon

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18 Mdry=17 kg

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Figure 6. a: Trajectory from Earth at 300 km to an near polar orbit around the Moon. b. Trajectory as seen from the Moon’s fixed frame. c: Cubesat fuel expenditure in function of the altitude around the Moon. d: Fuel expenditure change in function of the altitude around the Moon due to errors in the translunar injection maneuver.

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One of the current technology demonstration missions is the Lunar Flash Light, which consists on a 6U satellite (10 × 20 × 30) cm that will attempt to search for volatiles in the surface of the Moon. This mission will be the first mission to use green propulsion and the first one to use lasers to look for water ice as part of NASA’s Strategic Knowledge Gaps (SKGs). Another concept mission is the Lunar Polar Hydrogen Mapper or LunarH-Map (also a 6U cubesat) that will measure the surface reflection and composition of shaded crater in the polar regions from an altitude of 5-12 km. Both cubesats are planed to be launched onboard the Space Launch System (SLS) Earth-Moon-1 flight on the summer of 2018. As an example, a translunar injection maneuver of 3.125547 km/s will bring a nano satellite of 22 kg to an altitude of 10.089 km around the Moon. The insertion maneuver around the Moon requires 14.396 kg of propellant. Equipping cubesats with propulsion capability will allow performing small correction maneuvers to correct for translunar injection errors that may occur during the launch phase (see Figure 6(d)). Moreover, equipped cubesats will increase maneuverability to avoid collisions with other objects in space while alleviating with some of the space traffic management issues.11

Quasi-satellite orbits around the Earth The Earth-Moon system has been studied extensively, yet some of the orbits that we have investigated are novel solutions to the CRTBP. Our study shows that quasi-periodic orbits can be used as paths for cubesats for long periods of time. The two orbits displayed in Figure 7(a) and Figure 7(b) have been integrated over time span of 100π in nondimensional units or about 1,365 days. During this time the cubesat stays in the vicinity of the Earth and would not require to execute any station-keeping maneuvers and be able to perform science. 3D Quasi−Satellite Orbit in Earth−Moon System

3D Quasi−Satellite Orbit in Earth−Moon System

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Figure 7. a: Quasi-satellite orbit around the Earth (blue sphere) in the Earth-Moon rotating system. b: Quasi-satellite orbit around the Earth in the Earth-Moon system. The x, y and z axis are expressed in Lunar Distance (LD) or 384,400 km.

Figure 7(a) illustrates a quasi-periodic orbit with excursions in the z-direction of about 224,297 km while the cubesat travels about 200,000 km (about half the distance from Earth to the Moon) in the x-direction. On the other hand, the orbit depicted in Figure 7(b) has excursions of 119,433 km in the z-direction and travels as far as 220,569 km in the x-direction from the Earth. The cubesat moves within a tori as close as 160,000 km and as far as 609,000 km from the Earth. The tori has an average width of about 700,000 km and 630,000 km in the x- and y-directions, respectively.

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Quasi-satellite orbits around the Moon Some of these orbits display a natural stability in their dynamics, that is, the cubesat will be able to autonomously navigate without using any propellant for long periods of time (see Figure 8(a) and Figure 8(b)). 3D Quasi−Satellite Orbit in Earth−Moon System

3D Quasi−Satellite Paraboloid Orbit in Earth−Moon System

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Figure 8. a: Quasi-satellite orbit around the Moon (grey sphere) in the Earth-Moon rotating system. b: Paraboloid quasi-satellite orbit around the Moon in the EarthMoon system. The x, y and z axis are expressed in Lunar Distance (LD) or 384,400 km. Both Figure 8(a) and Figure 8(b) show the integrated trajectory of two different QSOs around the Moon over the time span of 1,365 days. The first QSO is similar to a Lissajous orbit (therefore it will be referred as QSO-Lissajous) and the second QSO is like a paraboloid (referred as QSO-paraboloid). Closest Approach of 3D QSO−Paraboloid to the Moon

3D Quasi−Satellite Paraboloid Orbit in Earth−Moon System

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Figure 9. a: Paraboloid quasi-satellite orbit around the Moon (grey sphere) in the Earth-Moon rotating system. b: Closest approach of the paraboloid QSO around the Moon in the Earth-Moon system. The x, y and z axis are expressed in Lunar Distance (LD) or 384,400 km. The cubesat travels around the first QSO-Lissajous with z-excursions of about 30,000 km in both the XZ and YZ planes. The excursions of the cubesat via the QSO-paraboloid are about 36,000 km (distance of a GEO satellite from the center of the Earth) in the XZ and YZ planes. Figure 8(b) displays an interesting behavior as depicted by the shape of a paraboloid of the QSO (in purple). One single revolution is equal to

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about 22.75 days as shown by the black trajectory in Figure 8(b). In Figure 8(b), we have also depicted the shape of a paraboloid (in green) for comparison purposes with our QSO-paraboloid. The plotted function of the paraboloid is z > αx2 + βy 2 + γ where α = β = 0.119 and γ = −0.0612. After doing a mesh-grid in Matlab, the last thing we did is to translate the paraboloid so it is centered at 0.91 < x(LD) < 1.06, −0.055 < y(LD) < 0.055 and −0.036 < z(LD) < 0.095 in the x, y and z directions, respectively. The XY projection of the QSO-paraboloid is displayed in Figure 9(a) and the range of the cubesat to the surface of the Moon is depicted in Figure 9(b). As mentioned before, this QSO is very stable in the CRTBP and the minimum distance is always greater than 5,000 km over the integrated time span of 1,365 days. The black thick line indicates a single revolution of about 22.75 days and the small grey sphere represents the Moon.

5:3 resonant Quasi-Satellite Orbit in the vicinity of the Moon Recent investigation of QSO indicate that these are also possible in the Earth-Moon system. In previous works,1 we found 1:1 QSO in the Sun-Earth and Mars-Phobos systems. 3D Quasi−Satellite Orbit in Earth−Moon System

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Figure 10. a: 3D QSO around the Moon (grey sphere) in the Earth-Moon rotating system. b: XY projection of the QSO.

In this present work where we have studied other QSO in the Earth-Moon system, we found that 5:3 resonant QSOs are present as displayed in Figure 10(a). This means, that the cubesat (trajectory in red) revolves around the Moon (grey sphere) three times in the same time that the Moon revolves (grey path) around the Earth (blue sphere) in five revolutions. We have also depicted a GTO circle (in blue) around the Earth for comparison purposes. The cubesat performs each revolution in about 1.2π or 1.2π/(2π)×27.33 days = 16.398 days. Therefore, the cubesat takes 5 × 16.398 = 81.99 days to go around the Moon. Also, the Moon goes around the Earth in about 27.33 days so it takes 3 × 27.33 days = 81.99 days to go around the Earth. The 5:3 QSO completes 83.4 revolutions around the Moon so that 1.2π × 83.4 = 100π which is the integration time used in our simulation. The maximum excursions of this 5:3 QSO are near 27,000 km in the Z-direction when looking at both the XZ and YZ planes. This orbit shows a very stable natural behavior over the integrated time span of 1,365 days which can be utilized to place a cubesat. The cubesat may not need to perform any station-keeping maneuvers.

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Quasi-satellite orbits in the vicinity of the Earth and the Moon The EML1 is a portal gate through which a satellite can be channeled as we shown in our example in Figure 11(a) and Figure 11(b). The EML1 portal gate is a halo orbit of 17,144 km in amplitude in the y-direction and 5,512 km in the z-direction. 3D Quasi−Satellite Orbit in Earth−Moon System

QSO with T=1365 days

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Figure 11. a: 3D quas-satellite orbit in the Earth-Moon rotating system. b: XY projection of the orbit. The x, y and z axis are expressed in Lunar Distance (LD) or 384,400 km. By varying the amplitude of the halo orbit, we can obtain longer or shorter excursions out of the plane and or closer or further passages to the Moon and back to the Earth. In this case, the excursions are of the order of about 7,688 km covering most latitude regions of Earth. Since the EML1 halo orbit is unstable, the cubesat can go through this portal gate freely back and forth until it gets a close approach, where the cubesat would get a gravity assist by the Moon and get ejected of the Earth-Moon system or can impact the Moon via a ballistic trajectory. In our example illustrated in Figure 11(a) and Figure 11(b), the cubesat drifts towards the Earth spending about 180 days before returning to the EML1 where it stays for about a month. then it returns to the vicinity

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of the Earth where it spends about 315 days. The cubesat is channeled through the EML1 portal gate a second time but this time, it stays for about 60 days around the Moon. The cubesat has regular excursions in the z-direction in the vicinity of the Moon of about 3,000 km (first passage) and 5,000 km (second passage) and will be able to cover most of the Moon’s surface for scientific purposes. After this second approach (subsequent close approaches) to the Moon, the cubesat leaves the vicinity of the Moon through the EML1 portal gate towards the Earth and stays in the vicinity of the Earth for the remainder time of the 2.15 years. The total integrated simulation time is 1,365 days. The Moon is noted by a grey sphere, the Earth is represented by a blue sphere and the Geosynchronous Transfer Orbit (GTO) is illustrated as a blue circle for comparison purposes. Quasi-satellite orbits in the vicinity of the EML4 and EML5 Orbits around the triangular points in the Earth-Moon system8 can be very attractive since these equilateral Lagrange points show strong stability behavior for long periods of time. Several families of QSOs are illustrated in Figure 12(a) and Figure 12(b). 3D Quasi−Periodic Orbits in the Earth−Moon System

3D Quasi−Periodic Orbits in the Earth−Moon System

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Figure 12. a: 3D QSO around the Lagrange points L4 and L5 in the Earth-Moon rotating system. b: XY projection of different QSO (black, green and magenta). The x, y and z axis are expressed in Lunar Distance (LD) or 384,400 km. In Figure 13(a) and Figure 13(b), we displayed the 3D and 2D plots a long tadpole-like trajectory of 250 Moon periods around the Earth-Moon L5 point (indicated by the red star) for an initial velocity vector of (22.4 m/s; 60.1 m/s). The uncovered banana-shape-like area of the spacecraft in the middle of the tadpole orbit represents a forbidden region through which the spacecraft never travels. That is, the spacecraft approaches this region and touches the zero-velocity surface. If we take the end points of this trajectory and reverse the velocities, the resultant trajectory would yield a trajectory that spirals inward to L5 in the Earth-Moon system. This means, that we could place a satellite on favorable, resonant orbits that could be retained for many years around the triangular points. This orbit has long and short-periods as shown by the big and small loops, respectively. The tadpole orbit has excursions of about 47,000 km in the z-direction. Because the tadpole orbit shows strong stability properties, the cubesat would not require any station-keeping maneuvers while orbiting EML5. Some of these orbits around the EML4 and EML5 can be connected via heteroclinic connections as displayed in Figure 14(a) and Figure 14(b). This heteroclinic connection has excursions of about 57,000 km and 42,000 km in the positive z-direction and in the negative z-direction, respectively.

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Long Orbit 250 Moon Periods around L5 Earth−Moon

Long Orbit 250 Moon Periods around L5 Earth−Moon 0.8 0.6 0.4

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Figure 13. a: 3D QSO around the Moon (grey sphere) in the Earth-Moon rotating system. b: XY projection of the QSO. The x, y and z axis are expressed in Lunar Distance (LD) or 384,400 km.

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Figure 14. a: 3D orbit connecting both EML4 and EML5 in the Earth-Moon rotating system. b: XY projection of the orbit. The x, y and z axis are expressed in Lunar Distance (LD) or 384,400 km.

New commercial private stake holders are emerging with novel approaches to provide both suborbital and orbital services to space in Europe. PDL Space is a Spanish company based in Alicante in process of designing two brand-new reusable rockets known as ARION 1 and ARION 2. ARION 1 is a reusable and single stage launch vehicle that will be able to send up 100 kg of scientific and technological payloads to about 250 km in altitude. ARION 2 will be able to launch 150 kg of payload to about 400-km orbit or 80 kg to a Sun Synchronous orbit (SSO). ARION2 could bring up to 5 kg of payload to an orbit around the Moon. ARION 1 first suborbital test flight is scheduled for 2018 while ARION 2 orbital mission to the Moon is scheduled for 2023. ARION 1 could also be used to send technological payloads that will help monitoring space debris objects contaminating some of the main space debris bands (eg. inclinations of 7◦ , 25◦ and 28.5◦ ) as shown in Figure 15.

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SPACE DEBRIS MONITORING The Debris Resistive/Acoustic Grid Orbital Navy Sensor (DRAGONS) is one of the latest NASA’s technologies9 that is intended to detect and characterize sub-millimiter micrometeoroid and orbital debris (MMOD) impacts on the International Space Station (ISS).

Figure 15. Debris bands located at Low Earth Orbit. Adapted from reference.10 After this technology is demonstrated, the ultimate goal is to deploy DRAGONS of a large area of about > 1 m2 to LEO (700 - 1,000 km) altitude to better understand the orbital debris environment of 0.5 to 1 mm size objects. We can design orbits for space debris monitoring. About two thirds of the space debris is located in LEO in ten different bands as depicted in Figure 15. Many of these objects are located at different inclinations (7◦ , 25◦ , 28.5◦ , 39.5◦ , 51.6◦ , 62.5◦ , 65◦ , 74◦ , 82◦ and 98◦ , as indicated by the orange vertical boxes between 100 km and 600 km. While most of these objects are located in high inclination orbits, there are also other objects located in between these bands (grey area). Cubesat technology could be used onboard of suborbital flight vehicles such as the Lynx-Mark III which has a dorsal pod (see Figure 16(a)) from where a nanosat of about 20 kg (a 12U cubesat is under 17 kg as shown in Table 1) could be deployed into LEO∗ . The Embry-Riddle Aeronautical University is actively involved into the design of cubesat technology and it also has a Suborbital Space Flight Simulator laboratory for training and operation purposes. This simulator can provide different suborbital trajectory profiles (up to 340,000 ft or 104 km) that can be used to better analyze the science (eg. study the noctilucent clouds in the mesosphere, cubesat deployment for space debris identification, etc.). The cubesat could be deployed with a dual stage rocket from the XCOR’s Lynx Mark III dorsal pod (see Figure 16(a)) when reaching apogee at about 100 km (see Figure 16(b)) and then it can be boosted towards higher altitudes (eg. 200 km) from where space debris could be monitored, and the noctilucent clouds could be further monitored and studied from these higher altitudes.11 The first two flight profiles displayed in Figure 16(b) are displayed in magenta and green and were obtained using an exponential atmospheric model and the ARDC atmospheric model from 1956 for the atmospheric ∗ XCOR

Lynx Mark III can carry a large dorsal pod with a payload of about 15 kg to a 400-km orbit with 28.5 degrees of inclination

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Figure 16. a: Cubesat will be deployed from the XCOR’s Lynx Mark III dorsal pod. b: Simulated ascent trajectories for the Lynx space vehicle.

density, respectively. As we can see, both models provide very similar flight profiles. The vehicle goes through the mesosphere region in about fifteen seconds on the ascent leg and it would take another fifteen seconds on the way down through the mesosphere. The total time of the vehicle going at about 75◦ pitch angle through the mesosphere would be about thirty seconds . This is a short amount of time to obtain samples of the microstructures of the mesosphere that may provide critical information pertinent to the Earth’s climate. The simulated trajectory of the Lynx reaches about 15 km during the first 100 seconds and about 67 km after 180 seconds after the main engine cut off (MECO) for the different ascent flight profiles depicted in Figure 16(b). After MECO, the vehicle follows a ballistic trajectory until it reaches apogee of about 100 km at about 260 seconds (4 minutes and 20 seconds). The other two flight profiles displayed in Figure 16(b) depict two trajectories where the time spent in the mesosphere is about one minute (blue trajectory) and ninety seconds (brown trajectory). While the vehicle is flying longer along the horizontal direction, it will be able to obtain further samples of the mesosphere for longer times, therefore maximizing the time of science. These trajectories will be further analyzed in a future

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paper when considering further flight parameters that may affect flight operations. The next set of plots shown in Figures 17(a), 17(b), 17(c) and 17(d) are contour maps of the density of space debris at polar orbits. The contour maps were obtained for the right ascension of the ascending node and the argument of periapsis. From orbital mechanics, we know that both the right ascension of the ascending nodes and the argument of periapsis are influenced by the oblateness of the Earth (J2 effect) and the gravitational force of the Sun and the Moon. The rotation of apsides is caused by a greater than normal acceleration near the equator and subsequent overshoot at periapsis, which is very typical in elliptical orbits. Map Density of Space Debris

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Figure 17. Map density of space debris in polar orbits. a: RAAN contours in function of inclination and periapsis altitude near the ISS. b: Argument of periapsis contours in function of inclination and periapsis altitude near the ISS. c: RAAN contours in function of inclination and periapsis altitude where DRAGONS could be deployed. d: Argument of periapsis contours in function of inclination and periapsis altitude where DRAGONS could be deployed.

Figure 17(a) displays a contour map of the right ascension of the ascending nodes (RAAN) of space debris located between inclinations ranging from 97◦ to 101◦ and periapsis altitudes ranging from 390 km and 490 km which is the approximate altitude of the ISS. Figure 17(b) displays a contour map of the argument of periapsis of space debris located between inclinations ranging from 97◦ to 101◦ and periapsis altitudes ranging from 400 km and 600 km. Figure 17(c) displays a contour map of the RAAN of space debris located between inclinations ranging from 96◦ to 99.5◦ and periapsis altitudes ranging from 680 km and 820

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km, which is the altitude where the DRAGONS spacecraft can be deployed to further characterize MMOD impact on the ISS. Figure 17(d) displays a contour map of the argument of periapsis of space debris located between inclinations ranging from 97◦ to 101◦ and periapsis altitudes ranging from 680 km and 820 km. SUMMARY Embry-Riddle Aeronautical University has been actively involved in developing cubesat technology, yet these small satellites have never flown into space. NASA is currently deploying small satellites from the NanoRacks aboard of the ISS as other entities have done already. This project will involve faculty and students at Embry-Riddle in Daytona Beach Campus and work together with government centers to be part of future exploration using cubesat technology while maintaining and extending the communications services with the ISS and other Earth mission satellites via these cyclers in the Earth-Moon system. The Lagrange points (especially L1 and L2) are especial locations since we can place fuel depots in orbits around these points allowing astronauts to have constant access to almost any region on the Moon where resources can be found. Cyclers of low energy to the L2 Lagrange point from the ISS will be further investigated to help alleviate some of the main constraints in space travel, such as propellant usage. In the near future, we will not be building these cubesats on Earth but on the ISS as well as other tools and devices via 3D printing technology. International space stations and their cooperation will be a key to leverage the transport of equipment and these cyclers could be used to transition the in-space-built infrastructures to different parts between the Earth and Moon or any of the Lagrange points. This research will help understand different aspects of the trajectory mission design and cubesat technology capabilities to send different cubesat configurations to the Moon by different commercial stake holders. Cubesat missions to the Moon will be used as precursors missions to reach further destinations such as Mars, Phobos and Deimos. Cubesats will be not only future assets for improving space debris ephemeris but also will serve as cubesat beacons that can improve the communications within the National Airspace System (NAS). These emerging technologies will be able to help GPS and Automatic Dependent Surveillance-Broadcast (ADS-B) systems to alleviate some of today’s aviation challenges. REFERENCES [1] P. J. Llanos, G. R. Hintz, M. W. Lo, and J. K. Miller, “Heteroclinic, Homoclinic Connections between the Sun-Earth Triangular Points and Quasi-Satellite Orbits for Solar Observations,” Vol. AAS/AIAA Astrodynamics Mechanics Meeting, AAS-13-786, 2013. [2] M. W. Lo, “The interplanetary superhighway and the Origins Program,” Vol. IEEE Aerospace Conference Big Sky, MT, USA, 2002. [3] J. E. Marsden and S. D. Ross, “New Methods in Celestial Mechanics and Mission Design,” Vol. 43,1, 2006, pp. 43–73. [4] “https://sites.google.com/a/slu.edu/swartwout/home/cubesat-database,” accessed on October 17, 2015. [5] S. Ross, “The Interplanetary Transport Network,” Vol. Sigma Xi, The Scientific Research Society, 2006. [6] K. harris, M. McGarvey, H. Y. Chang, M. Ryle, T. R. II, B. Udrea, and M. Nayak, “Application for RSO Automated Proximity Analysis and IMAging (ARAPAIMA): Development of a Nanosat-based Space Situational Awareness Mission,” Vol. 27th Annual AIAA/USU Conference on Small Satellites, SSC13-WK-6, 2013. [7] I. Tether Unlimited, “Transformative Technologies for Space, Sea, Earth, and Air,” Vol. www.tethers.com, accessed on July 1, 2015. [8] P. J. Llanos, “Trajectory Mission Design and Navigation for a Space Weather Forecast,” Ph.D Thesis, University of Southern California, 2012. [9] N. O. D. P. Office, “Orbital Debris Quarterly News,” Vol. 16, Issue 3, National Aeronautics and Space Administration, July 2012. [10] J. B. Bacon, “Sizing of ’Mother Ship and Catcher’ Mission for LEO Small Debris and for GEO Large Object Capture,” Vol. NASA Johnson Space Center/OM3, 2009. [11] P. J. Llanos and R. Triplett, “Integrating ERAU’s Suborbital Space Flight Simulator -ADS Data into NextGen TestBed Simulations,” Vol. Space Traffic Management, STM-15-1107, 2015.

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