CUTIE: A cubesats tether-inserted mission for moon exploration

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CUTIE: A cubesats tether-inserted mission for moon exploration C. Bettaninia,b,∗, E.C. Lorenzinia,b, G. Colombattia, A. Aboudana, M. Massironia,c a b c

Center for Studies and Activities for Space (CISAS) – University of Padova, Padua, Italy Department of Industrial Engineering - University of Padova, Padua, Italy Department of Geosciences, University of Padova, Padua, Italy

A R T I C LE I N FO

A B S T R A C T

Keywords: Dual cubesat mission Librating passive tether Fast propellant-less orbit insertion Spacecraft dynamics Moon science

This paper presents the concept of a dual cubesat mission designed for Moon exploration that enables scientific measurements that are not accessible by high orbital or landed missions thanks to the use of a long passive tether for orbital insertion. Due to the intrinsic characteristic of the Moon environment, low altitude orbiting spacecrafts are in fact requested for mapping key parameters such as plasma, volatiles and magnetic field. Inserting a satellite in such low trajectories from an orbiter has usually a high cost of propellant to achieve the orbit change or requires a long time to finalize the maneuver with electrical propulsive systems. Limitations are even higher for cubesats that have very limited capacity for orbital adjustment, so they cannot perform substantial orbital changes by using classical propulsive techniques. The use of a long passive tether to exchange momentum between two cubesats can eliminate such drawbacks and provide fast, far-reaching and accurate orbital changes with almost no propellant being consumed. A mission scenario is presented with the two mated cubesats released by an orbiter in circular Moon orbit at 500 km altitude. Thanks to the momentum exchanges provided by the swinging tether the upper cubesat will be left in a 520 × 737 km orbit and the lower cubesat into a 460 × 26 km orbit with a low periselenium that provides an ideal altitude for close observation of the lunar surface and monitoring of characteristic parameters of the Moon environment. With a high-inclination orbit, the low-altitude orbital passes will map the entire Moon surface in around 14 days. The upper cubesat will be transferred on a highly predictable and low-perturbation orbit and equipped with laser corner reflectors and a radio link band transponder to allow tracking both from laser stations on Earth (Matera, Italy ASI geodesy station) and from the Lunar Orbiter via radio link. The integrated analysis with radio signals between Cubesats can also be used to improve orbit determination and study perturbation effects on orbital dynamics.

1. Introduction Recent advancements in micro satellite technology are paving a new era for space missions extending the potential of small satellite mission to a wide range of applications for space and planetary exploration; on board electronics and subsystem miniaturization along with the recent innovations in remote sensing technology have enabled cubesat-based missions to provide scientific returns at an extremely reduced cost. The result is a fast-growing interest in their use in dedicated scientific mission as demonstrated by the latest involvements of main space agencies in the definition of future missions envisioning application of multiple CubeSat for Earth and Moon exploration (as NASA CubeSat Launch Initiative contest and ESA Sysnova Invitation to Tender for Moon exploration.) In fact, Moon exploration has lately regained interest in the scientific community, following analysis of data from missions LADEE

∗

(Lunar Atmosphere and Dust Detector Explorer), LRO (Lunar Reconnaissance Orbiter), SELENA (Kaguya) and ARTEMIS (Acceleration, Reconnection, Turbulence and Electrodynamics of Moon's Interaction with the Sun), which has shown a much more dynamic lunar environment than was originally thought. This discovery along with the possibility of future human missions to the Moon set by new space policies by space agencies drive the need of scientific investigations in proximity of the lunar surface. Due to the intrinsic characteristic of the Moon environment, low altitude orbiting spacecraft are requested for mapping key parameters as plasma, volatiles and magnetic field, enabling measurements that are not now accessible by high orbital or landed missions. As an example, Moon mini-magneto spheres, formed by the interaction of the solar wind with intense localized magnetic fields within the lunar crust, can be detected only below 40 km altitude, while understanding of the type, mass and distribution of lunar polar volatiles can be achieved only

Corresponding author. Center for Studies and Activities for Space (CISAS) – University of Padova, Padua, Italy. E-mail address: [email protected] (C. Bettanini).

https://doi.org/10.1016/j.actaastro.2018.09.005 Received 3 May 2018; Received in revised form 27 August 2018; Accepted 2 September 2018 0094-5765/ © 2018 Published by Elsevier Ltd on behalf of IAA.

Please cite this article as: Bettanini, C., Acta Astronautica, https://doi.org/10.1016/j.actaastro.2018.09.005

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on impact and throwing large clouds of lunar dust into space. The lack of atmosphere means these particles follow pure ballistic trajectories and unless ejected at greater than orbital velocity of 1.6 km/s, over time, they will travel through space and land back on the Moon. This “churning” of the surface by micrometeorite impact permits us to sample distant areas on the Moon from a single place (although determining the point of origin of such a sample is virtually impossible). The dust thrown through space is in flight, hence a transient phenomenon, but debris is hitting the Moon constantly and thus, the ejecta thrown up from these impacts is constant. In principle, the Moon should be surrounded by a “cloud” of dust ejecta, thrown out into space by the constant “rain” of micrometeorites. Lunar dust “clouds” are not suspended, but are in constant ballistic motion, some particles ascending and some descending, depending upon their crater of origin. But collectively, these particles make up a dust exosphere that varies in density and position with time. New studies indicate that the Moon possesses a permanent dust cloud [8], generated by impact and constantly filling the space surrounding it. Dust exospheres have been clearly observed and measured around the icy moons of Jupiter and Saturn, but the history of observations of the lunar dust cloud is murkier. We first had an inkling that dust might exist in the space above the lunar surface during the Surveyor missions (the series of unmanned soft landers flown in the 1960s, designed to pave the way for the Apollo astronauts). Surveyor found that the Moon's surface is composed of very fine dust yet is cohesive enough to bear the weight of both a heavily laden astronaut and a loaded Lunar Module. Now, published results from the Lunar Atmosphere and Dust Environment Explorer (LADEE) mission indicates that the Moon is surrounded by a cloud of dust, just as the satellites of Jupiter, and at about the same density. From their data, it was also found that the density of the dust notably spikes during known annual meteor showers. These showers occur when the Earth and Moon fly through the orbital paths of short period comets (icy bodies that shed debris as they get close to the Sun). This debris orbits the same path around the Sun as the comet nucleus and thus forms “corridors” of dust in space. As the Earth-Moon system passes through the corridors, the dust hits both bodies, forming a spectacular “shower” of high velocity meteors on Earth, where they burn up in the dense atmosphere, but hit the unprotected lunar surface at high speed. These lunar impacts kick up ejecta, adding to the dust cloud that surrounds the Moon. A dust detector able to measure mass and speed of dust particles will be able to characterise and monitor the variation of the dust cloud with time. Analysis of the dust grains lofted near the lunar surface (< 10 km) show that there are lofted dust grains in the region of the terminator. In fact, the LEAM (Lunar Ejecta and Meteorites) experiment shows a peak in the presence of dust while passing through the terminator (i.e. from the Apollo 17 mission) [6]. The causes of this phenomenon were not attributed to hyper velocity impacts by cosmic dust but was instead considered due to lower velocity impacts attributed to the transport of electrostatically charged lunar dust. The dust impacts were observed to peak around the terminator regions, the boundaries between the dayside and the night side. Recent measurements by the Lunar Atmosphere and Dust Environment Explorer (LADEE) mission [9] found a persistent cloud of dust around the Moon that was thicker at the sunrise terminator. High-velocity cometary dust particles were suggested as the source of this dust cloud.

passing through tenuous atmosphere of moving dust particles near the crust. Furthermore, low altitude observations may strongly support the search of traces of water remains on the Moon (either on the surface or embedded within the crust) and the analysis of lava tubes and subsoil cavities with the use of remote sensors such as SAR (Synthetic Aperture Radar). 1.1. Analysis of magnetosphere and SWIRL The origin of lunar magnetism is a long-debated issue in lunar science. The first spacecraft to leave the Earth and pass by the Moon, Luna1 in 1959, carried a magnetometer. Luna-1 did not measure any global magnetic field, but in the subsequent decades, scientists surprisingly found magnetized portions of the lunar crust (up to 100 km in length), as well as magnetized samples returned by the Apollo program [1]. From that time onward, there is a general agreement that an old lunar dynamo was required to magnetize most, if not all these materials [2]. However, our knowledge is still lacking important information such as the dynamo typology, its power source, its duration, and what it implies in terms of Moon geological history. Important magnetic “anomalies” have been identified on the moon crust, and several hypotheses have been formulated to explain them. They can either be due to the configuration of the magnetic field of an ancient lunar dynamo, or be magnetized remnants related to plasmas formation during meteoroid and cometary impacts [3]. Discriminating among these hypotheses would help to define the global picture of the planetary magnetism observed in our solar system. In the framework of magnetic anomalies investigations, the “swirls” (e.g. Reiner Gamma in Ocean Oceanus Procellarum or Ingenii and Hopmann areas in the South Pole Aitken basin) occupy a prominent part. Among all the lunar landscapes and surface features, these albedo markings are peculiar having variegated boundaries (either diffuse or sharp) with meandering shapes unrelated to topography. Swirls range from large clusters of many complex loops and ribbons to single isolated features; the length of the single swirl are typically of tens kilometers, but can be grouped into clusters covering areas of hundreds of kilometers [4]. The leading explanation for this bright terrain is that solar wind protons, normally a darkening agent, are being deflected by the magnetic field, keeping the underlying surface bright [5]. If true, these features are natural laboratories for studying space weathering effects. However, as any enigmatic features on planetary science also swirls have multiple explanations, one of them is that fine dust, which is widely believed to be lifted above the lunar surface after every terminator crossing, may be accumulating in these regions due to solar wind interactions with the magnetic field [6]. Finally, the most recent explanation is that they can be residuals of highly energetic cometary impacts, resulting in scouring of the surface by large amounts of vapor, dust and ice particles coming from the inner coma [7]. Up to date very poor spatial resolution of swirls and associated with only high altitudes lunar spacecraft is available. Multiple measurements at lower altitudes and even at the surface would provide information about the coherence of the surface and subsurface magnetizations, addressing whether they formed in a uniform field, as expected from a dynamo or are due to variable abundances of different materials in the lunar crust. A simultaneous measurement of any lofted dust would help quantify the loftening process, any possible correlation with the formation of these local anomalies and the extent of the local mini-magnetospheres.

1.3. Subsurface investigations and lava tube research Thanks to the GRAIL mission for gravitational analysis of the Moon and to SELENA (Kaguya) radar sounding surveys, subsurface layers, including potential buried empty lava tubes, have been detected [10,11]. Lava tubes have been identified as future possible locations for human settlements, since these sites are protected from cosmic radiation, micrometeorite impacts and the lunar harsh environment.

1.2. Analysis of moon dust Since the Moon has no atmosphere and hence, no hydrosphere, there is nothing to slow down or stop material – usually traveling at cosmic (extremely high) velocities – from striking the surface. Meteoroids hit the lunar surface at about 20 km/s, vaporizing particles 2

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2.1. Orbital insertion: librating tether-mediated injection

Furthermore, living parameters could be maintained at lower energy cost providing stable environment for long-term/permanent lunar habitation [12]. Lunar lava tubes also offer the unique advantage to analyse a portion of the Moon that is still unexplored and untouched up to now; information on the lunar geological history and subsurface environment could be inferred [13]. All these potential observable scenarios must cope with limiting factors related to a standard cubesat operation: a commissioning orbit not designed for scientific analysis operation, since cubesats are usually launched as piggy back for bigger satellites and have very limited capacity for orbital adjustments with consequent impossibility to perform substantial orbital changes by using classical propulsive techniques or requiring a long time to finalize maneuver with electrical propulsive systems.

Cubesats have very limited capacity for orbital adjustments and consequently cannot perform substantial orbital changes by using classical propulsive techniques. However, a long tether can be used to exchange momentum between the two cubesats and deliver them on the desired orbits starting from a circular orbit with almost no propellant being consumed. The two multi-unit cubesats will start in a mated configuration on a frequently used 500-km circular orbit and at a given time will be separated by deploying the tether connecting them. The technique adopted is similar to that used for the successful tethered missions SEDS-1 (Small Expendable Deployer System) [14] that used a 20-km-long tether (NASA, 1993) and YES-2 [15] with a 32-km-long tether (ESA, 2007). Both those missions used a spooling (non-reeling) tether deployer to realize a librating-type deployment. In our case, the higher cubesat will be inserted into a higher eccentric orbit (520 × 737 km), while the lower one is inserted in a lower (26 × 460 km) eccentric orbit to collect data near the moon's surface. Upon orbital delivery, the tether can be severed at both ends or severed at LOC end and reeled back in HOC to avoid in both cases additional disturbances of the orbit. The proposed mission requires different designs for the two orbiting cubesats. The lower cubesat will be a spinner to cope with the severe thermal environment near the Moon's surface and avoid the need for active thermal control. The higher cubesat will be stabilized in a controlled attitude to provide the desired initial separation attitude and facilitate laser tracking from Earth of the on-board corner cube laser reflectors. The type of deployment in which the system is left oscillating with a large-amplitude libration in the orbital plane (in-plane) is an effective technique for exchanging momentum between the two cubesats. As the tether exits the deployer, the Coriolis force drives the lower cubesat ahead of the circular orbit followed by the system center of mass (where the mated system started) while the opposite occurs for the upper cubesat. The result is a large (i.e., 40°–50°) libration amplitude of the tethered system that is instrumental for momentum exchange and orbital injection. In order to obtain the maximum separation between the delivery orbits the tether must be cut when the tethered system crosses the LV in a retrograde libration [16]. The model adopted for simulating the deployment dynamics is a 2D, straight, rigid tether (i.e., a dumbbell model) with different masses attached to the end of the tether. All perturbation effects such as the non-sphericity of the primary attractor and the presence of solar pressure are intentionally ignored in deployment equatons, being their contribution negligible in the extremely limited duration of the insertion maneuver (around 7000 s) starting from a 500 km altitude orbit. Perturbations have however been taken into account in the orbital dynamics of LOC and HOC satellites after tether cut to properly analyse orbital evolution. The mass distribution of the deploying system is represented in the equations of motion (1) of the system by the equivalent mass m = m1m2/(m1+m2) with m1 and m2 the masses of the two cubesats, as follows [17].

2. CUTIE mission CUTIE proposes a Moon mission with a fast, propellant-less, low mass orbit insertion strategy delivering a cubesat in a precise low altitude orbit, where all above mentioned scientific analyses may be performed. The proposed science and the associated orbital configuration require an architecture with two cubesats which exchange momentum by a passive tether. After being released by the orbiter in a mated configuration the system will separate during the tether swing motion, delivering a low periselenium orbiting CubeSat (LOC: Low Orbiting CubeSat) and a higher orbiting CubeSat (HOC: High Orbit Cubesat). The low periselenium will allow close observation of the lunar surface and monitoring of characteristic parameters. With a high-inclination orbit, the low-altitude orbital passes will map the entire Moon surface in 14 days. The upper cubesat at higher altitude will be on a highly predictable and low-perturbation orbit and will be equipped with laser corner reflectors and a radio link band transponder that can be tracked both from laser stations on Earth (Matera, Italy ASI geodesy station) and from the Lunar Orbiter via radio link. Three main mission phases are therefore foreseen 1. Orbital Insertion phase: in this phase satellites are unmated in the common 500 km altitude circular orbit deploying the passive tether and activating a controlled librational motion; orbital insertion is performed by cutting the tether in a retrograde swing at crossing the local vertical (LV), releasing a Low Orbiting CubeSat and a High Orbiting CubeSat. In the current baseline orbit insertion is achieved in a little less than 2 h after satellite separation. 2. Science phase: in this phase both satellites (now untethered) perform science operation. Foreseen operation window is around 100 days. 3. Termination phase: Low orbit Cubesat (LOC) reaches its termination orbit using a termination impulse at absidal point. Satellite conducts investigations while in a “decreasing” orbit to the surface of the Moon. Mainly in this last part of the mission the LOC satellite will be able to navigate at altitudes below 20 km over the mare regions and perform high frequency measurements of lunar magnetic anomalies and collect dust particles.

PHASE

Orbital insertion

Science ops

LOC Termination

Duration

∼2 h

∼100 days

16 days

l˙ θ¨ + 2 (n + θ˙ ) + 3n2 sin θ cos θ = 0 l

(1.1)

F −T 2 l¨ − lθ˙ − 3n2l cos2 θ − 2nlθ˙ = T m

(1.2)

In equation (1), l = l1 + l2 is the tip-to-tip tether length, l1 and l2 are the respective distances of the upper and lower cubesats from the system center of mass (CM), where the origin of the LV-LH reference frame, moving at constant orbital rate n, is located, θ is the tether inplane angle measured from LV, T is the tether tension, and FT is the thrust of the in-line (i.e., thrusting along the tether line) cold-gas thrusters. The 2-D model is appropriate to describe the deployment

To address overall mission feasibility Low orbit Cubesat (LOC) and High Orbit Cubesat (HOC) orbital evolution before and after tethermediated injection has been simulated in order to characterise the mission scenario and allow optimization of satellite operation timelines. 3

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the upper and lower satellite, respectively, having assumed a mass ratio m1/m2 = 2:1. The horizontal velocity components at release for the two satellites are: δy˙10 = θ˙ r l10 and δy˙20 = θ˙ r l20 . After calling δx = δx10 + δx20, l 0 = l10 + l20 and considering that from the first integral of equation (1.1) for l = l0 and l 0˙ = 0 we can obtain the angular velocity at the crossing of LV as a function of the maximum in-plane tether libration amplitude at end of deployment θmax as follows [20]:

dynamics of a tethered system whenever the initial conditions do not have large out-of-plane components [19]. Deployment is started with an ejection ΔV = 1 m/s, provided by separation springs placed between the two cubesats, at an initial inplane angle θe = 35° with respect to LV and no out-of-plane component. The separation acceleration of the two cubesats is further supplied by a pair of cold-gas, in-line thrusters (i.e. aligned with tether line) with a thrust of 0.2 N operating for 120 s. The separation total impulse FxΔt can be allocated in a different way than the one utilized here between the initial ΔV and the impulse supplied by the thrusters. A higher ejection ΔV will save propellant consumption, but it will require stronger separation springs. After the thruster's cut-off, the tether tension is controlled by a brake system at a steady value well above the expected friction forces of the spooling deployer that are expected to be in the 5–10 mN range [21], followed by a ramping down of the controlled tension to bring the deployment to an almost smooth stop before the tether runs out. Once the system has reached full deployment, the simulation model switches to an elastic tether model, with one longitudinal stretch mode and a constant unstretched tether length. Considering l = l0 + δl, where l0 is the unstretched tether length and δl is the elastic stretch of the tether and assuming δl/l0 « 1, the elaboration of equation (1) drives to the following:

δl˙ θ¨ + 2 (n + θ˙ ) + 3n2 sin θ cos θ = 0 l0

(2.1)

2 δl¨ + ω2δl + 2ζωδl˙ = l 0 θ˙ + 3n2l 0 cos2 θ + 2nl 0 θ˙

(2.2)

θ˙0 =

By using the first of equation (3) and equation (4) for computing the angular velocity at crossing LV, the separation distance δx after nt = π phase angle from release between the orbits of the two cubesats after tether cut is as follows:

δx = 7l 0 +

sin nt δx˙ 0 n

δy = 6(sin nt − nt ) δx 0 + δy0 +

+

2 (1 n

2 (cos n

4 3 nl 0 sin θmax = l 0 (7 + n

48 sin θmax )

(5)

The overall separation must be attributed for 1/3 to the upper satellite and for 2/3 to the lower satellite assuming a mass ratio of 2:1 between the cubesats. In the following we show results applicable to our case with a deployment that achieved a max amplitude θmax = 44° to deliver the two cubesats on the desired orbits. Fig. 1 shows the trajectories in the LV-LH frame centered at the CM of the mated system with deployment starting at t = 0. Libration amplitude shall not exceed a maximum value to avoid that the tether becomes slack, limiting the efficiency of momentum exchange. Neglecting tether elastic elongation (since δl/l0 « 1) and starting from a circular orbit, tether tension can be described by analytical equations as function of libration angle as in Ref. [19]. Modeling the flying system as a “dumbbell” allows in fact simple calculation of gravitational and centrifugal forces at both ends where cubesats are located. Tension in the tether is generated by the vector unbalance of these force couples, since end masses are forced to travel in their mean orbital motion at the angular velocity of the center of

In equation (2) δl¨ and δl˙ are strech acceleration and velocity, ω is the angular frequency of the stretch mode and ζ the damping ratio of the tether material [18]. Reference values of the parameters adopted for the specific CUTIE simulation are: l0 = 60.2 km, ω = 0.08 rad/s, ζ = 0.1, and a realistic final velocity error at reaching the final tether length of < 1 m/s. The final state of the tether backward swing is reached at the crossing of the LV with lo = 60.2 km, l 0˙ = 0 , θ0 = 0, θ˙0 = 0.046 deg / s at the release time t = 7030 s (where the subscript 0 identifies the release conditions). At this point the tether is cut and the two cubesats are released on their respective orbits. Given the release conditions indicated above, the points of release will be respectively the perigee of the upper cubesat and the apogee of the lower cubesat. The orbits of the two cubesats can be readily computed either by using non-linear orbital equations for each satellite or alternatively the Clohessy-Wiltshire (CW) solution of the linearized equations of the dynamics relative to the circular orbit of the CM. The use of the CW solution is justified by the fact that the post release orbits have small eccentricities. We will follow the linearized approach that leads to a very compact formula for computing the separation between the cubesats after 180° orbital phase from release. The Hill-Clohessy-Wiltshire equations have an analytical solution that is written in the following for the 2-D case in the x-y orbital plane with x = LV and y = LV:

δx = (4 − 3 cos nt ) δx 0 +

(4)

3 nsinθmax

− cos nt ) δy˙0

nt − 1) δx˙ 0 +

(

4 n

)

sin nt − 3t δy˙0 (3)

The δx and δy in equation (3) are the radial and horizontal components of the separation distance of the generic satellite from the orbiting reference frame placed at the system CM. We only need to use the first one of equation (3), applied separately to the two cubesats, to compute the radial separation between them and the CM at nt = π rad. After dissipating the small elastic motion – an event that occurs within 600 s from reaching the final tether length at t = 6000 s – the relative radial motion is practically zero. The non-null initial conditions at release are δx10 = (1/3)l0 and δx20 = (2/3)l0 for

Fig. 1. Trajectories of the two cubesats during deployment and tether swing (FD = flight direction). 4

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gravity (for CUTIE mass geometry, the Center of Gravity (CG) is approximately at a distance of 2/3 of total length from LOC and may considered coincident with the center of mass (CM)). The upper mass is therefore experiencing a centrifugal force higher than gravitational force, while the lower mass shows higher gravitational force than centrifugal generating tension in the connecting tether. The problem may be analysed starting from the dumbbell gravity aligned vertical stable condition and afterwards extended to any libration angle configuration. In the gravity aligned configuration the magnitudes of centrifugal and gravitational forces on each end mass can be expressed respectively as

Fgi = mi

μ ri2

(6.1)

Fci = mi ri n2

Fig. 3. Tether length vs. time.

(6.2)

where μ is the gravitational term in Moon two body dynamics, n is the orbital rate of the center of gravity, mi is the end mass value and ri its distance from the center of Moon. Considering as in equations (1.1) and (1.2) the distance along the tether of end mass mi from Center of Mass (CM) as li and therefore being ri = rCM + li, it is possible to calculate the force unbalance, also called gravity gradient force, at each end as

Fgg = 3mi li n2 = T

to simplify control issues, the negative tension zone has been avoided in CUTIE design limiting maximum libration angle by mass design. The final tether length is reached at t = 6000 s from the start of deployment while the LV is crossed in a backward swing at t = 7030 s when the tether must be cut to deliver the two satellites on orbits of altitudes 520 × 737 km and 460 × 26 km, respectively, for the upper and lower cubesat (see Fig. 3). In the present conceptual design, we consider cutting the tether at both ends. Following this strategy, the tether will be left in a roughly circular orbit at 500 km and it will not interfere with the two cubesats. The tether will recoil after the cuts and will end up partially curled-up and with a limited lifetime due to the degradation of the tether material exposed to the space environment. The technique proposed for tether deployment and the innovative orbital injection strategy was experimented successfully in the flight of SEDS-1 [20] that injected the lower-satellite into an atmospheric reentry orbit by using a 20-km tether attached to the second stage of a Delta-II rocket placed in LEO. In case of SEDS-1 the orbit of the released satellite was very accurate and visual imaging was taken of the reentering and burning satellite (that was not designed to survive reentry) from a ground station equipped with a small telescope located in view of the expected reentry trajectory on the West coast of Mexico [14]. A length of about 60 km might seem rather long for a tether but considering the small forces at play in a cubesat mission a 0.1-mmdiameter Dyneema™ is sufficient for the requested maneuver. Samples of the tether mentioned above are available commercially with a breaking strength of 9 N that is much greater than the forces at play. As a matter of fact, the gravity gradient force acting on the 60-km tether is 0.2 N and other transient forces during deployment (e.g., at separation and at end of deployment) are estimated to be well below 1 N in this cubesat tethered system. Furthermore, tether occupies a volume of only 9.8 × 9.8 × 9.8 cm3, assuming a realistic packing ratio of 50%, and has a mass equal to 0.45 kg. Again, taking parameters from previous flights [19], the volume of a spooling deployer hosting a tether of 940 cm3 can be accommodated in a volume less than a 2U-cubesat. The characteristics of the deployment separation system and the deployer internal friction are important issues [19]. Following the experience of previous missions and considering the low masses of cubesats, a robust technique for deploying them can utilize a simple spring system to provide the initial ejection ΔV combined with a cold gas system that provides a roughly 0.2 N thrust along the tether for about 120 s to reach an early relative separation velocity along the tether line of 10 m/s as indicated in Fig. 4. The cold-gas system will be a blow-down system with a latching valve that needs neither thrust modulation nor accurate thrust level nor attitude control of the cubesats. In fact, the desired 0.2 N tether tension, controlled by the tether brake, will maintain on average the thrust aligned with the tether line. The estimated mass consumed for providing the required total impulse with gaseous Nitrogen is ∼50 g.

(7)

In the gravity aligned vertical stable condition Fgg is obviously also the value of tether tension. Such expression may be extended to the not vertical configuration, in case of in-plane dynamics only, considering the following expression [14].

Fgg (θ) = T (θ) = 3mi li n2Y (θ)

(8)

Where Y(ϑ) is the function expressing the dependence of non-dimensional tension (tension divided by 3mi li n2 ) on the libration angle; the function can be calculated starting from in plane libration equations [14] as

Y (θ) = cos 2 (θ) + F (θ) ±

4 F (θ) 3

F (θ) = sin2 (θmax ) − sin2 (θ)

(9.1) (9.2)

Equations (9.1) and (9.2) show that tether non-dimensional tension tension depends not only on the libration angle but also on the maximum achieved value. Fig. 2 shows a parametric plot of the values of the tether non-dimensional tension versus libration angle depending on maximum libration oscillation amplitude It is evident from the plot that libration oscillations with amplitudes below 65° are characterized by having always positive tether non-dimensional tension tension while oscillations with higher amplitude show an angular range where negative tension is present and consequently tether goes slack. Although tether slackness may be limited using tension control laws in the deployment system and performing libration damping strategies,

Fig. 2. Tether non-dimensional tension vs. libration angle. 5

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are as follows:

• LOC: T ≈ 2.2 h (before the Termination phase) • HOC: T ≈ 2.9 h (the HOC satellite period is almost constant for the entire duration of the mission)

During the Science phase the relative distance between the two satellites ranges from 300 to 3000 km allowing interlink communication for around 40% of the LOC orbit period. Visibility from Matera (40°40′N 16°36′E) ground station of the HOC satellite during the mission is between 7 and 14 h per day, allowing precise and continuous tracking of the HOC satellite from Earth ground station. Deployment of LOC from HOC can be performed in a visibility window for monitoring satellite flight dynamics before and after separation, in the view of reducing uncertainty in the determination of orbital position and velocity prior and post separation.

Fig. 4. Tether deploy velocity vs. time.

The combination of the spring and gas system is a safe and effective solution for tether deployment that overcomes the internal deployer friction and the relevant system parameters can be adapted to different deployer designs. The Moon orbital environment is characterized by an almost absence of orbital debris (OD) and the presence of micrometeoroids (MM). By adopting the Grün model [21] of the interplanetary MM flux and the experimentally validated damage model of hypervelocity impacts on cylindrical tethers [22], with an impact crater/hole 3 times bigger than the impactor diameter, we can estimate the survival probability of the tether. In our case, the tether is only utilized for the orbital injection of the two cubesats and, consequently, its exposure to the space environment is only ∼7000 s. Following the assumptions above and assuming a length that increases from zero to 60 km, the estimated survival probability of the above-mentioned tether is about 94%. There is no need in our case to use a fail-safe tether design (which would increase the required storage volume and complicate the deployer design) because of the short exposure time of the tether.

2.3. Termination phase After science phase the LOC can be eventually commanded into its termination orbit (an eccentric 460 m × 5 km orbit) applying an extremely limited ΔV (i.e., less than 10 m/s ΔV at apoapsis) compatible with the use of commercial micro propulsion system. Nominal operation and termination orbits have been simulated using a 4 order LP-165 lunar model (periapsis altitude shows low sensitivity to higher degrees gravitational model) with third body Earth perturbation. Fig. 5 shows an example of the evolution of the periapsis science phase orbits, while Fig. 6 shows the periapsis evolution before Moon impact after LOC has been maneuvered to termination. 3. Preliminary design of HOC and LOC A preliminary flight configuration has been identified for LOC and HOC satellites: HOC satellite being a 6U satellite and the LOC a 4U satellite with a 2:1 mass ratio between HOC and LOC. A 3D impression of HOC and LOC satellite configuration is provided in Fig. 7 and Fig. 8). LOC will be able to map both the latitudinal and time variation of the Moon magnetic field and monitor exosphere dust and grain distribution; the continuous scan of the exosphere will provide information on the distribution of the solar wind and meteoritic sources. LOC will perform high frequency measurements (both in the space and time domain) of lunar magnetic anomalies at low altitudes. It will map the magnetic fields along its pericenter arcs at altitudes well below 50 km, during the first part of the mission. Afterwards higher frequency measurement will be performed while the LOC satellite decreases its pericenter altitude from 26 km down to the surface, enabling to collect data at extremely low altitudes and create a complete figure of the

2.2. Science phase Orbits for LOC and HOC after libration insertion will have the parameters listed in the following Table 1. Were rp and ra are periselene and aposelene radii, a and b are the orbit axes, e is the eccentricity, h is the angular momentum, ε is the specific energy, vp and va are the velocity at periselene and aposelene and T is the period. The periods of the orbits of LOC and HOC satellites Table 1 LOC and HOC orbital parameters after tether insertion. rp, LOC

1763 km

ra, LOC aLOC eLOC bLOC hLOC εLOC vp, LOC

2197 km 1980 km 0.11 1968 km 3097 km2/s −1.24 km2/s2 1.76 km/s

va, LOC TLOC rp, HOC

1.41 km/s 7905 s 2257 km

ra, HOC aHOC eHOC bHOC hHOC εHOC vp, HOC

2474 km 2366 km 0.05 2363 km 3402 km2/s −1.04 km2/s2 1.51 km/s

va, HOC THOC

1.37 km/s 10326 s

Fig. 5. Science phase: periapsis evolution for LOC. 6

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data will be treated with very efficient compression algorithms and sent to the HOC satellite before being downloaded back to Earth via the Lunar Orbiter. Simultaneous images from HOC satellite will help the knowledge of the context where the lava tubes and subsurface structure are identified. Scientific payload characteristics have consequently been identified comprising a magnetic instrument based on two tri-axial AMR sensors or equivalent Miniaturized Flux Gate (MFG) sensor, a dust collector derived from a miniaturization of GIADA (Grain Impact Analyser and Dust Accumulator) instrument and a MiniSAR payload based on CORISTA heritage on space-based radars and antennas. The mini-SAR sub-surface radar sounder will be able to detect and map the presence and size of buried empty lava tubes under the lunar surface. Both for the LOC and HOC instrument will have a dedicated Central Electronic Unit (CEU) will be realized based on the expertise developed in the design of completely autonomous sensor suites for space mission as in the one flown on ESA Exomars 2016 mission [23]. While the LOC will be a spinner to cope with the severe thermal environment without the need for active thermal control, the HOC cubesat will be stabilized in the early phases to provide desired initial separation attitude and facilitate laser tracking from Earth of the onboard corner cube reflectors. Arrays of retroreflectors currently present on the lunar surface are still able to provide a useful return signal to telescopes of 1.5 m of opening (the LLR stations of Matera and Grasse), with intensities of the order of a few photons return. The reflectors of Apollo 15 mission on the lunar surface have a surface area of about 3400 cm2, while the one of the reflectors of Apollo 11 and 14 of is in the order 1000 cm2. Recent studies, however, demonstrate that a single retroreflector, with 15 cm diameter, could be tracked similarly to the ones of Apollo 11/14 [24], [25]. The scientific payloads of the LOC will collect several science data to be transmitted to ground and to increase performances a parallel communication chain could be established toward the high-altitude satellite to increase the number of connections with the Moon Orbiter. Transmissions can be made adapting off-the-shelf UHF transponders (the first simple solution using 400 MHz systems today used by most of the cubesat missions) or using more recent S-band equipment able to provide higher performances. The UHF systems are already available, and they could allow the development of a reliable system which could not require a very high pointing accuracy, therefore with lower constrains on the on-board AOCS. On the contrary advanced systems such as X-band transponder could increase the data-rate, but they would require additional on-board resources to be subtracted from the payloads. Parallel communication systems could be used at the same time to provide main and backup options and to cope with different constrains encountered during the different mission phases. For example, the UHF link could be very useful during the first part of the mission when tether operations could reduce pointing accuracy and high datarate payloads are not active, and S-band or X-band transponder could be necessary after orbit insertion and during the science phase to support telemetry download.

Fig. 6. Termination phase: periapsis evolution for LOC satellite before Moon impact.

Fig. 7. 3-D impression of LOC.

Fig. 8. 3-D impression of HOC.

4. Future developments

magnetosphere close to the swirls fields. LOC will collect dust particles during all trajectory arcs around pericenter; initial trajectories will have a 26 km pericenter altitude, but dust analysis will be conducted also at much lower heights once LOC will be put in a “spiralling” and impacting orbit with the Moon due to the higher-order harmonics of the Moon's gravity field. LOC could also map the lunar surface with a mini SAR at the lowest altitudes in order to investigate Moon stratigraphy at scales comparable to those of optical images. Power required by mini SAR is less 1 W, compatible with power available on designed cubesats. Multiple, low altitude revolutions over the same area will supply large data sets that are essential for unambiguous 3-D mapping of the lunar subsurface. The

Ongoing research work is focusing on further optimization of the design of the proposed cubesats configuration, addressing in detail the definition of LOC and HOC subsystems: thermal control, power and distribution, radio communication system, scientific payloads. The work is performed mainly through thesis work of students of the master's degree of Aerospace Engineering at the University of Padova. Special attention is given to the Tether deployment system design: trade-off of tether performance vs size, analysis of release system and monitoring sensors, implementation of control laws; analysis of tether cut mechanism. Starting from the baseline mission scenarios the team is also 7

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defining scientific operation timelines: operative and idle modes, instrument activation and data acquisition sequences, pre-planned tasks and autonomous tasks. Ground Segment and Operations design are also considered, with the definition and characterization of the communication windows and communication links among the small satellites and the Mission Control Center at ground. Tracking feasibility is currently analysed in a dedicated study considering the laser facility by Italian Space Agency in Matera and requirements for orientation of the optical aperture to Earth.

[4] Brett W. Denevi, et al., The distribution and extent of lunar swirls, Icarus 273 (2016) 53–57. [5] T.D. Glotch, J.L. Bandfield, P.G. Lucey, et al., Formation of lunar swirls by magnetic field standoffof the solar wind, Nat. Commun. 6 (2015) 6189, https://doi.org/10. 1038/ncomms7189. [6] I. Garrick-Bethell, J.W. Head, C.M. Pieters, Magnetic fields, spectral properties, and dust transport at lunar swirls, Icarus 212 (2011) 480–492. [7] P.H. Schultz, L.J. Srnka, Cometary collisions on the moon and mercury, Nature 284 (1980) 22–26. [8] M. Horányi, et al., A permanent, asymmetric dust cloud around the Moon, Nature 522 (7556) (2015) 324–326. [9] O.E. Berg, H. Wolf, J.W. Rhee, Lunar soil movement registered by the Apollo17 cosmic dust experiment, in: H. Elsässer, H. Fechtig (Eds.), Interplanetary Dust and Zodiacal Light, Springer-Verlag, Berlin, 1976, pp. 233–237. [10] L. Chappaz, R. Sood, H.J. Melosh, K.C. Howell, D.M. Blair, C. Milbury, M.T. Zuber, Evidence of large empty lava tubes on the Moon using GRAIL gravity, Geophys. Res. Lett. 44 (2017) 105–112, https://doi.org/10.1002/2016GL071588. [11] Kaku, et al., Detection of intact lava tubes at marius hills on the moon by SELENE (kaguya) lunar radar sounder, GRL 44 (2017) 10155–10161. [12] D.G. Angelis, J. Wilson, M. Clowdsley, J. Nealy, D. Humes, J. Clem, Lunar lava tube radiation safety analysis, J. Radiat. Res. 43 (Suppl) (2002) S41–S45. [13] Sood Rohan, H. Jay Melosh, Kathleen Howell, Lunar advanced radar orbiter for subsurface sounding (LAROSS): lava tube exploration mission, Adv. Astronaut. Sci. 158 (2016). [14] M.L. Cosmo, E.C. Lorenzini (Eds.), Tethers in Space Handbook, vol. 4, National Aeronautics and Space Administration, 1997. [15] Michiel Kruijff, Erik J. van Der Heide, Qualification and in-flight demonstration of a European tether deployment system on YES2, Acta Astronaut. 64 (2009) 882–905. [16] J. Peláez, M. Ruiz Delgado, E.C. Lorenzini, Strategies for maximizing a satellite lifetime by tether-mediated orbital injection, J. Astronaut. Sci. 45 (2) (1997) 205–231. [17] R. Mantellato, A. Valmorbida, E.C. Lorenzini, Thrust-aided librating deployment of tape tethers, J. Spacecraft Rockets 52 (No. 5) (2015) 1395–1406, https://doi.org/ 10.2514/1.A33273.(2015). [18] V.V. Beletsky, E.M. Levin, first ed., Dynamics of Space Tether Systems, Advances in the Astronautical Sciences vol. 83, American Astronautical Society Publication, 1993. [19] E.C. Lorenzini, S.B. Bortolami, C.C. Rupp, F. Angrilli, Control and flight performance of tethered satellite small expendable deployment system-II, J. Guid. Contr. Dynam. 19 (4) (1996) 1148–1156. [20] E.C. Lorenzini, J.A. Carroll, In-orbit experimentation with the small expendabletether deployment system, ESA J. 15 (1) (1991) 27–33. [21] E. Grün, H.A. Zook, H. Fechtig, R.H. Giese, Collisional balance of the meteoritic complex, Icarus 62 (2) (1985) 244–272. [22] S.B. Khan, J.R. Sanmartin, Survival probability of round and tape tethers against debris impact, J. Spacecraft Rockets 50 (3) (2013) 603–608. [23] C. Bettanini, F. Esposito, S. Debei, C. Molfese, G. Colombatti, A. Aboudan, the DREAMS experiment flown on the ExoMars 2016 mission for the study of Martian environment during the dust storm season, Measurement 122 (2018) 484–493. [24] Jean O. Dickey, et al., Lunar laser ranging: a continuing legacy of the Apollo program, Science 265 (5171) (1994) 482–490. [25] Merton E. Davies, Tim R. Colvin, Lunar coordinates in the regions of the Apollo landers, J. Geophys. Res.: Plan 105 (E8) (2000) 20277–20280.

5. Conclusions The small propulsive capacity of cubesats has limited their ability to carry out scientific explorations. This paper presents a strategy for fast and accurate transfer of two cubesats into eccentric orbits around the Moon starting from a typical delivery circular orbit at 500 km of altitude. The technique is almost propellantless as it utilizes a long, thin tether to inject the two cubesats into the desired orbit through momentum exchange. Specifically, from the presented calculations, the lower orbit is eccentric with a 460 km altitude aposelenium and a 26 km altitude periselenium that allows a long-term stability of the orbit. The orbit inclination will provide a complete coverage for lowaltitude observation of the Moon's surface. The higher satellite, tracked optically from Earth, will provide the position of the lower satellite through an additional inter-satellite radio link to the lower cubesat. With such configuration the two Cubesat mission would provide reliable data on Moon dust, magnetosphere and subsurface geological structures providing scientific clues on Moon dust cloud and grains, SWIRLs and configuration of lava tubes. Appendix A. Supplementary data Supplementary data related to this article can be found at https:// doi.org/10.1016/j.actaastro.2018.09.005. References [1] M. Fuller, S.M. Cisowski, Lunar paleomagnetism, in: J.A. Jacobs (Ed.), Geomagnetism, vol. 2, Academic Press Ltd., London, 1987, pp. 307–455. [2] B.P. Weiss, S.M. Tikoo, The lunar dynamo, Science 346 (2014) 1198. [3] M.B. Syal, P.H. Schultz, Cometary impact effects at the Moon: implications for lunar swirl formation, Icarus 257 (2015) 194–206.

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