AAS 14-276 WHAT DOES IT TAKE TO CAPTURE AN ASTEROID? A CASE STUDY ON CAPTURING ASTEROID 2006 RH120 Hodei Urrutxua,∗ Daniel J. Scheeres,y Claudio Bombardelli∗, Juan L. Gonzalo∗ and Jes ´usPelaez´ ∗ The population of “temporarily captured asteroids” offers attractive candidates for as- teroid retrieval missions. Once captured, these asteroids have lifetimes ranging from a few months up to several years in the vicinity of the Earth.1 One could potentially extend the duration of such temporary capture phases by acting upon the asteroid with slow deflection techniques that conveniently modify their trajectories, in order to allow for an affordable access to an asteroid for in-situ study. In this paper we present a case study on asteroid 2006 RH120, which got temporarily captured in 2006-2007 and is the single known member of this category up to date. We study what it would have taken to prolong its capture and estimate that deflecting the asteroid with 0:27 N for less than 6 months and a total ∆V barely 32 m/s, would have sufficed to extend the capture for over 5 additional years. MOTIVATION The growing interest in the study of asteroids, their formation, composition or internal structure, is often hindered by the lack of material samples and the difficulty of measuring certain physical features without in-situ scientific experiments. Hence, the idea of capturing and bringing an asteroid into the vicinity of the Earth has gained popularity in recent years, as proven by many papers attempting to propose asteroid captures,2,3,4,5,6 or most recently the NASA’s Asteroid Retrieval Initiative.7 Such kind of Earth delivery missions would allow an affordable access to asteroids along with a remarkable outcome in their scientific study, the possibility of resource utilization and eventually the development of new exploration technologies for the new-coming era of manned spaceflight. However, according to the Asteroid Retrieval Feasibility Study in Ref.7, accomplishing such a missions comes with a great economical cost; the nominally targeted asteroid is 2008 HU4 of approximately 500 ton mass and 7-8 m diameter, and the idea is to capture it and place it in a high lunar orbit, where it would be energetically in a favourable location to support human exploration beyond cislunar space. Omitting the Earth escape trajectory, heliocentric transfer and rendez-vous with the asteroid, the sole cost of deflecting 2008 HU4 in order to bring it into lunar orbit via a lunar fly-by is estimated in a ∆V of approximately 170 m/s. This arises the question of how much does it really take to bound an asteroid in Earth orbit and whether capturing an asteroid could be done more cheaply by targeting a different kind of asteroid or pursuing a different capture strategy. In this regards, we come to propose a novel conceptual approach to enable an affordable access to asteroids in the Earth vicinity. A special population of small asteroids that become temporarily captured in the Earth-Moon system has recently been discovered. While only a single member of this class of asteroids has been confirmed to date, namely asteroid 2006 RH120, rigorous calculations show that there is a significant flux of these temporary ∗Space Dynamics Group, School of Aeronautical Engineering, Technical University of Madrid (UPM). http://sdg.aero.upm.es/ yCelestial and Spaceflight Mechanics Laboratory, Colorado Center for Astrodynamics Research, The University of Colorado at Boulder. http://ccar.colorado.edu/scheeres/Scheeres 1 visitors,1 such that at any given time there are about a dozen half-meter-sized objects and at least two meter- sized objects, and one ∼ 10 meter object would be temporarily captured every 50 years. Once captured, these NEAs can remain bound to the Earth-Moon system for times ranging from a few months up to several years. The mean lifetime of this population is predicted to be 9.5 months, during which time they make almost 3 orbits about the Earth. Hence, the availability of a population of temporarily captured natural satellites of the Earth-Moon system, or “minimoons”, brings into the game new possibilities to provide humanity with access to asteroids in “our own backyard”. The only issue would be for how long we could guarantee them to be bound in the vicinity of the Earth, and if by a convenient modification of their orbits we could make them remain close enough to Earth for a longer time, and at what energetic cost or ∆V . This paper contains a numerical study on what it would have taken to extend the temporary capture phase of one such minimoon, namely the asteroid 2006 RH120, during its latest 2006-2007 temporary capture. Though the current study is founded in a past scenario, its results remain representative of the temporarily captured population of asteroids and it serves as a Case Study for any future minimoon of similar characteristics that we might encounter. To support this assessment, the study is also extended to other 9 temporarily captured virtual asteroids. REPRODUCING THE TEMPORARY CAPTURE OF 2006 RH120 The asteroid 2006 RH120 is a small sized NEA, with a diameter of about 5 meters, that was discovered on 14 September 2006 during its last temporary capture that extended until June 2007. The complexity of the temporary capture of a NEA around the Earth, along with the chaoticity proper of a n- a 1:033271548165328 AU body problem, suggests the use of numerical propagation e 0:02448611507535683 - techniques in order to reproduce the asteroid orbit in both i 0:5953070470775252 deg its heliocentric and geocentric trajectories. However, we Ω 51:14274388312688 deg wanted to find the simplest model that would describe the ! 10:07298372371885 deg dynamics and the outcoming trajectories reliably, hoping M 33:64154746771107 deg that a model as ideal as possible would ease the study by enabling the use of analytical techniques, thus helping us to Table 1: Orbital elements of 2006RH120 at get a better insight in the capture dynamics and how to ex- JD 2456000.5 in heliocentric ecliptic J2000.0 ploit them for our benefit. For that, and taking 2006 RH120 frame, as obtained from JPL 45 ephemeris as testbed, we undertook some numerical experiments in order to draw some conclusions and find out the most con- a 0:9873022869878605 AU venient dynamical setting to balance our interests. e 0:01914526201748496 - For our numerical simulations we have initially consid- i 0:7974471215924634 deg ered the initial conditions for 2006 RH120 given in Table1, Ω 278:6483110626849 deg which are its heliocentric orbital elements on March 14th ! 136:132656110278 deg 2012, after the temporary capture phase. Alternatively, ini- M 74:85730211872003 deg tial conditions were also available at an epoch during the capture, corresponding to February 1st 2007 (see Table2), Table 2: Orbital elements of 2006RH120 at which seem more suitable for our study. Its mass has been JD 2454132.5 in heliocentric ecliptic J2000.0 frame, as obtained from JPL 47 ephemeris estimated assuming a spherical body of 5 meters of diame- ter and a density ρ = 2000 kg/m3. The very first thing we noticed is that the use of high precision numerical ephemerides is required, since otherwise the temporary capture phase is missed. Any attempt to use simplified ephemerides (analytical ephemerides, circularized orbits, . ) would yield the temporary capture phase to disappear. The necessity to use numerical ephemerides has further implications, as the fact that the Jacobi constant is not a constant any more (idem for the Hill-Jacobi constant), as shown in Fig.1. This is very easily understood if we realize that even if the Sun, Earth-Moon Barycenter (EMB) and 2006 RH120 were the only bodies 2 -0.185 -0.85 3.0014 2720 3.0012 -0.19 -0.9 3.001 2700 -0.195 3.0008 -0.95 3.0006 2680 -0.2 3.0004 -0.205 -1 3.0002 2660 3 -0.21 -1.05 2640 2.9998 Jacobi Constant (-) Hill-Jacobi Constant (-) Jacobi Constant (MJ/kg) Constant Jacobi 2.9996 -0.215 Hill-Jacobi Constant (MJ/kg) 2620 2.9994 -1.1 Jacobi Constant (MJ/kg) -0.22 Hill-Jacobi Constant (MJ/kg) Jacobi Constant (-) 2.9992 Hill-Jacobi Constant (-) 2600 2.999 -0.225 -1.15 2000 2002 2004 2006 2008 2010 2012 2006.5 2007 2007.5 2008 Fractional Year Fractional Year Figure 1: Dimensional and non-dimensional values of the Jacobi constant and the Hill-Jacobi constant for 2006 RH120 during its temporary capture between years 2006 and 2007 considered in our propagation, this wouldn’t be an ideal three-body problem, not even an elliptic three-body problem, because the relative positions of Sun and EMB being given by ephemeris tacitly imply a n-body problem, since the computation of planetary ephemeris inherently considers the perturbations of other third bodies, even if these are being omitted in our problem. Consequently, the Hill constant is not preserved as a constant any longer and proves of little practical use in our case study. Also note that the normalization of the Jacobi and Hill-Jacobi constants is not trivial, since the normalizing magnitudes (distances and angular velocities) also come from ephemerides, so they are not constants but rather vary with time. Consequently, there also seems to be no point in using the Hill equations when 2006 RH120 is inside the Hill sphere of the Earth, since the use of ephemerides invalidates the underlying hypothesis on which the Hill equations are built, and their use results in imprecision in the propagation of the orbit. 0.01 0.01 GMAT Our Propagator 0.005 0.005 Hill Sphere Moon Orbit 0 Hill Sphere 0 Y (AU) Y (AU) Moon Orbit -0.005 -0.005 JPL 47 Our Propagator -0.01 -0.01 -0.01 0 0.01 -0.01 0 0.01 X (AU) X (AU) Figure 2: Trajectory of 2006 RH120 during it temporary capture phase.