17th Space Generation Congress (SGC), Bremen, Germany, 27-29 September 2018. Move an Asteroid Competition - 2018 Orbital analysis of a reusable CubeSat platform to relay communications for rovers on an asteroid Arunkumar Rathinama* a Australian Centre for Space Engineering Research, School of Electrical Engineering and Telecommunications, UNSW Sydney, Australia, [email protected] * Corresponding author Abstract In recent exploration missions to asteroids, landers/rovers based on the CubeSat platform are sent to investi- gate in-situ the suface of an asteroid. With increasing interest in small celestial body exploration and in-situ resource utilization, the future missions will have a more complex system of landers/rovers and spacecraft. In a current generic architecture of a orbiting spacecraft and a rover, the direct communication link between them is severly limited for nearly half the rotational period of the asteroid. This work presents a conceptual approach, having an additional reusable CubeSat orbiting around the asteroid to relay communications to the rovers. This work analyzes typical orbit orbital combinations of periodic, quasi-periodic and terminator orbits, to solve for a close approach window with a minimum ∆v between the trajectories of the master spacecraft and the CubeSat. The close approach orbital region is necessary for the master spacecraft to ren- dezvous, capture and dock the CubeSat platform. Numerical simulations were performed using the asteroid Castalia and a combination of orbital configurations for the master and CubeSat. We find that with both spacecraft in quasi-terminator orbits, the length of the rendezvous window is more consistent and the delta-v between the spacraft is minimized at closest approach. Keywords:(maximum 6 keywords) Nomenclature Acronyms/Abbreviations SRP Solar Radiation Pressure µSun Gravitational parameter of Sun (1.327 11 3 2 ⇥ ANH3BP Augmented Normalized Hill Three Body 10 km /s ) Problem µAst Gravitational parameter of Asteroid R Constant distance b/w Sun and Asteroid G1Solarfluxconstant(11017kgm3 /s2 /m2 ) 1. Introduction ⇥ σ Density (kg/m3) To date, asteroid exploration has been restricted to m/A Mass to projected area of spacecraft rendezvous, in-situ experiments, and sample-return 2 (kg/m ) missions. In recent years, mineral-rich asteroids be- N Mean motion came targets for space resource mining companies for J Jacobi integral in-situ resource extraction and utilization. The inter- ri Vector from variable field point to polyhe- dron vertex est from private enterprises towards mining will boost 3 3 future space exploration activities. This will increase Ee Edge dyad R ⇥ 2 3 3 Ff Face dyad R ⇥ the number of future missions and thus spacecraft are 2 1 Le Factor per-edge R expected to perform autonomously and coordinate 2 1 !f Factor per-face R with other specialized crafts/landers [1] or purpose 2 3 1 v Velocity vector R ⇥ built rover platforms. 2 3 1 ! Angular velocity vector R ⇥ 2 Experimental micro-platforms were used in pre- β Non-dimensional acceleration due to SRP vious exploration missions to conduct experiments 1 U Gravitational potential R 2 3 1 on asteroid surfaces. MINERVA, a lander that was U Gravitational attraction R ⇥ r 2 3 3 sent along with the first Hayabusa mission, unfortu- U Gravity gradient matrix R ⇥ rr2 1 2 nately couldn’t reach the asteroid because of an in- U Laplacian R r 2 correct timing of deployment [2]. MASCOT Lander [3] (based on the CubeSat platform), a part of the Move an Asteroid Competition - 2018 2018 Page 1 of 8 17th Space Generation Congress (SGC), Bremen, Germany, 27-29 September 2018. Hayabusa-2 mission, is to scout and perform scien- an opportunity for the master spacecraft to perform tific experiments on the asteroid’s surface. The lan- a minimal energy manoeuvre and capture the orbit- der is relatively small (28cm x 29cm x 21cm weighs ing CubeSat using the robotic arm and dock them. 9.8kg) when compared to Philae [4] that landed This work analyzes possible stable orbits around as- on⇠ the Comet 67P/Churyumov-Gerasimenko. It is teroids having such opertional configuration. Section equipped with four scientific instruments (MASCAM, 2 briefly discusses the dynamics around an asteroid, MicrOmega, MARA and MASMAG) [3] and has a computing the gravitational potential and the equa- limited operating time between 16 20 hours to ex- tions of motion near small celestial bodies. Section 3 plore the surface and collect useful⇠ scientific data. In discusses the di↵erent orbits such as periodic orbits, another exciting development, the first deep space quasi-periodic and terminator orbits and the cases for CubeSats Mars Cube One (MarCO) were launched numerical simulation. The results are discussed based along with NASA’s Insight lander and it is the first on the requirement of a close approach window with ever CubeSat platform flown in deep space. If their minimum ∆v between the trajectories. Section 4 pro- journey is successful, MarCO (A & B) will relay data vides a brief discussion of the results and the future of InSight’s entry, descent and landing back to Earth challenges. [5]. MarCO are based on a six unit CubeSat platform and the pair will carry their own communications 2. Dynamics near an asteroid and navigation experiments as they fly independently The dynamics in the vicinity of an asteroid are to Mars. The MASCOT-2 lander and two CubeSat extremely complex and the main factors that con- Opportunity Payload Inter-satellite Network Sensors tribute include irregular shape, mass distribution, ro- (COPINS) are also proposed for the future Asteroid tational period, solar perturbation (depending on as- Impact Mission mission [6]. Considering the progress teroid’s orbital position around the sun) and rare dis- of CubeSat technologies, future missions are expected turbances during close approach near the large plan- to carry more sophisticated CubeSat payloads for re- ets. connaissance purpose. 2.1 Gravity potential As interest in space resource mining grows, future The gravitational attraction of the asteroid is the missions are expected to carry and deploy purpose dominant factor a↵ecting the close proximity orbits built rover/lander platforms on the asteroid’s sur- around an asteroid. The asteroid’s shape and mass face. With rotation periods varying between 6 12 ⇠ distribution play a critical role in generating a non- hours for most NEAs [7] communications with a uniform gravity potential. Accurate computation rover/lander will be severly limited. A generic ateroid of potential is necessary for close proximity trajec- mission architecture comprised of a master space- tories to avoid collision with the asteroid’s surface. craft and CubeSat communications relay to support There are di↵erent established methods available in a lander/rover could allow for constant communica- the literature to calculate the gravitational poten- tions, reducing technical risk and increasing capabil- tial of a non-spherical body. These include spheri- ity. MarCOA &B will demonstrate that the CubeSat cal harmonic expansion, polyhedral approaches and is a platform capable of deliverying interplanetary mass concentration, each method has its own advan- communications. However, unlike Insight, missions tage and disadvantages. The polyhedral approach is to the asteroids will benefit from reusable CubeSat widely used to compute the gravity potential, attrac- communication relays as they will then be able to tion, gravity gradient and Laplace potential [8]. In visit multiple bodies. order to compute an accurate gravitational potential This work presents the possibility of a reusable we need a good shape model of the asteroid. Previ- CubeSat to relay communication to the rover de- ous asteroid exploration missions adopted a hovering ployed on the asteroid surface. The operation archi- approach during proximity operations, it would be tecture consists of a Master Spacecraft, a CubeSat interesting for future missions to find potential sta- (relay) platform and a rover on the asteroid surface. ble orbits. The gravitational potential U, attraction The CubeSat is assumed to be based on 6U platform U , gradient matrix U and the Laplacian 2U r rr r and equipped with a communications payload to re- of a constant density polyhedron [8] is given below. lay the data between the rover and miniature electric thrusters to perform orbit manoeuvres. The Cube- U = 1 Gσ r .E .r .L 2 e edges e e e e− Sat’s orbit is designed such that it frequently per- 2 (1) P1 forms a flyby of the master spacecraft, thus providing 2 Gσ f faces rf .Ff .rf .!f 2 P Move an Asteroid Competition - 2018 2018 Page 2 of 8 17th Space Generation Congress (SGC), Bremen, Germany, 27-29 September 2018. U = Gσ E .r .L + Gσ F .r .! 2.2 Equations of motion r − e e e f f f e edges f faces The equations of motion of a spacecraft (including 2X 2X (2) Coriolis and centripetal accelerations) defined in the body-fixed frame of an uniformly rotating asteroid U = Gσ E .L + Gσ F .! (3) rr e e f f are given by [10], e edges f faces 2X 2X r¨ +2! ˙r + ! ! r + !˙ r = U (5) ⇥ ⇥ ⇥ ⇥ r 2 U = Gσ !f (4) and the equations in scalar form are provided below. r − f faces 2 2X x¨ 2!y˙ = ! x Ux − 2 − In this work we consider the dynamics about aster- y¨ +2!x˙ = ! y + Uy (6) oid 4769 Castalia using the shape model available in z¨ = Uz [9]. The shape model of the asteroid shown in fig. 1, The spacecraft’s position and velocity is denoted by r consists of 4092 faces, 6138 edges and 2048 vertices. =[x,y,z] and v =[˙x, y,˙ z˙] respectively are represented 3 The density of the asteroid Castalia is 2.1 g.cm− and in the body-fixed frame centered on the asteroid. the rotational period is 4.07 hours [10].