### Accessibility of the Resources of Near Earth Space Using Multi-Impulse Transfers

Joan-Pau Sanchez, Colin McInnes
2010 AIAA/AAS Astrodynamics Specialist Conference   unpublished
Most future concepts for exploration and exploitation of space require a large initial mass in low Earth orbit. Delivering this mass requires overcoming Earth's natural gravity well, which imposes a distinct obstacle to space-faring. An alternative for future space progress is to search for resources in-situ among the near Earth asteroid population. This paper examines the scenario of future utilization of asteroid resources. The near Earth asteroid resources that could be transferred to a
more » ... ansferred to a bound Earth orbit are determined by integrating the probability of finding asteroids inside the Keplerian orbital element space of the set of transfers with an specific energy smaller than a given threshold. Transfers are defined by a series of impulsive maneuvers and computed using the patched-conic approximation. The results show that even moderately low energy transfers enable access to a large mass of resources. Nomenclature a = semi-major axis of an orbit, AU b = exponent parameter of power law size distribution, 2.354 C = constant parameter of power law size distribution, 942 D = asteroid diameter, km or m e = eccentricity of an orbit f = portion of material with {a,e,i} capturable with an insertion v lower than a given limit H = absolute magnitude h = percentage of {a,e,i}-orbits that can be phased with the Earth with a v lower than a limit i = inclination of an orbit, deg m = mass of the asteroid, kg M = mean anomaly of an orbit, deg M[Du-Dlo]= total asteroid mass between upper and lower diameter, kg MOID cap = maximum MOID at which a perigee insertion is possible with a given maneuver, AU. N = number of asteroids p = semi-latus rectum of an orbit, AU P = probability of finding an capturable asteroid within a volume in Keplerian element space {a,e,i} r a = apoapsis altitude, AU r enc = distance from the Sun of the intersection point, AU r p = periapsis altitude, AU e t = time at the encounter or intersection point, s m t = time of the phasing maneuver, s enc n v = normal Cartesian component of the orbital velocity at the intersection point, AU/s enc r v = radial Cartesian component of the orbital velocity at the intersection point, AU/s plX v = asteroid velocity at the Earth plane crossing point, AU/s 0 v = orbital velocity of the asteroid, AU/s * jpau.sanchez@strath.ac.uk, member AIAA, Research Fellow, v  = hyperbolic excess velocity, AU/s ∆i = inclination change of the asteroid, deg ∆M = difference in mean anomaly of the asteroid, deg ∆n = change of asteroid mean motion, rad/s v  = increment of velocity inc v  = impulsive v to change asteroid inclination, AU/s cap v  = v for final Earth capture, AU/s ∆v lev = delta-velocity-v ∞ leveraging maneuver, AU/s . thres v  = maximum allowed v, AU/s a  = semi-major axis change due to an impulse maneuver, AU t v  = tangential impulse provided by phasing maneuver, AU/s = flight path angle, rad or deg  = true anomaly of an orbit, rad or deg enc  = true anomaly of the intersection point, rad or deg   = gravitational constant of the Earth, 1.19069x10 -19 AU 3 /s 2 Sun  = gravitational constant of the Sun, 3.96438x10 -14 AU 3 /s 2   .  = probability density function a  = asteroid density, kg/m 3  = argument of the ascending node of an orbit, rad or deg  = argument of the perigee of an orbit, rad or deg   = Earth"s mean angular velocity, rad/s MOID0 = periapsis argument at which MOID is zero Suffixes: |  = referent to Earth max | = maximum value allowed min | = minimum value allowed Acronyms: MOID = Minimum Orbital Intersection Distances NEA = Near Earth Asteroid