Solar Reflector Gravity Tractor for Asteroid Collision Avoidance

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1 olar eflector Gravity Tractor for steroid Collision voidance r. Jeff Wesley Fisher Fisher I/ strodynamics pecialist Conference & Exhibit Honolulu, HI 0 ugust, I/ strodynamics GT Created: of 14

2 steroid eflection by Gravity Tractor Multiple asteroid deflection concepts published in last 5 years epresentative deflection target: (9994) pophis iameter 30 m Mass 4.6e10 kg Impulsive deflection (nuclear explosive, kinetic impactor): Up to 1e9 N sec applied to asteroid instantaneously mple deflection capability, relatively brief operation Performance depends on asteroid composition, hence highly uncertain low Push: 0.1 to 1 N applied for months, years, or decades Provides precision necessary to avoid keyholes With sufficient operating time, can achieve offsets needed for collision avoidance Gravity Tractor (Lu & Love 005): Noncontact coupling of slow push spacecraft & asteroid via gravitational attraction Performance independent of all asteroid parameters except mass & radius I/ strodynamics GT Created: of 14

3 Gravity Tractor Using olar adiation Pressure Wie 007: olar ail can provide tow force for Gravity Tractor 90 m square, 8 yr operation (5 yr push, 3 yr coast) => pophis offset 30 km Perturbative acceleration depends on steroid mass eflector area & orientation Performance is insensitive to other asteroid characteristics olar eflector () mass is insignificant compared to asteroid mass need not be a gossamer structure! To achieve collision avoidance (6400 km offset) for pophis: Increase push time from 5 yr to 15 yr Grow reflecting area 36X to 300,000 m => 600 m diameter circle Comparable GT with Hall Effect electric propulsion would require 50 kw power I/ strodynamics GT Created: of 14

4 Two ynamics Paradigms Heliocentric dynamics govern deflection performance f olargravity f OtherodyGravity H* ody H (asteroid + GT) moves as point olar gravity balances inertial force to produce nominal orbit Gravity from other solar system bodies & solar pressure on asteroid also contribute olar pressure on perturbs orbit adial component effectively reduces m un Yields offset growth proportional to operating time Intrack component increases orbit energy Yields offset growth with square of operating time f folarpresson M H I d dt H steroid-centric dynamics govern hovering z H x H * f dh dt T ody (GT) acted on by f I steroid gravity force f & torque T olar pressure force f & torque T H basis is effectively inertial I f * M T Three-body and rotating reference frame loads are 4+ orders of magnitude smaller than f & f f I I d dt I/ strodynamics GT Created: of 14

5 Geometric Limits on Placement To avoid eclipse, minimum altitude fixed by: r r sa ta fs f ( saxh caz H ) r ta f s P c a pophis example: = 707 m caling with asteroid radius: r 3 r r olar pressure P & flight path angle g vary seasonally, so GT must maneuver hould vary a to maximize f c as( a g ) H r a a H g x H (intrack) r sa r Must vary gravity force to balance f pophis example: f = 1. to.3 N z H (toward sun) I/ strodynamics GT Created: of 14

6 Notional Mechanical Layout of 300,000 m 68 m I for comparison M = 40,000 kg 60 m 8 trusses form hexagonal backbone connecting 7 nodes 7 nodes support 10 panel trusses Each panel truss supports 10 panels, each 30 m by 100 m I solar array wings are 1 m by 34 m t r = 0.3 kg/m, M = 90,000 kg ize is unprecedented, but within existing technology Challenges: Launch expense ssembly/deployment 30 m 100 m I/ strodynamics GT Created: of 14

7 The Gravity Hitch Gravity gradient booms can provide roll & pitch torque For spacecraft that are small compared to distance from center of attracting body dimensions are comparable to altitude Generalized gravity gradient boom can provide propellantless control in 5 or 6 axes lso provides majority of gravity coupling Continuing tractor analogy, call this device the Gravity Hitch pophis Example: Central longitudinal mast, length 500 m 4 point masses i, 4000 kg each, on circle of radius 50 m Mechanisms translate each boom mass in 3 axes relative to 4 Mast 1 3 * * * I/ strodynamics GT Created: of 14

8 Gravity Hitch Geometry oom masses are 3.7X closer than * to Gravity acceleration is 14X stronger Gravity gradient is 103X stronger GH has only 16% of spacecraft mass, but produces 74% of gravity force Equilibrium: f * f + f = f * l x ( l)[( 4m M l) d ] 1 mm r [( ( r r ) ) 1 1 ] P c a l f l z This formula determines l for selected altitude and other parameters adial lines from to i lean away from longitudinal axis by s = 15 deg 1 3 d s f I/ strodynamics GT Created: of 14

9 Generating adial Force * * l z M M z f l elative displacement of i : Longitudinal, away from thru distance z Inertial displacements: * remains fixed * moves up as moves down, but z dominates No rotation Change in net gravity force: ominated by gradient at i mm M f zz (0.01 N/m) z 3 M 1 3 ange of ±50 m gives sufficient authority to overcome variation in solar pressure z f z M M z z x I/ strodynamics GT Created: of 14

10 Force ariation with ltitude & oom adial isplacement 1 Longitudinal Force due to Longitudinal isplacement = 600 m, l = 399 m = 700 m, l = 51 m = 800 m, l = 619 m 0.5 fz, N oom isplacement, m modeled with masscon distribution Nonrigid body effects modeled as shown on preceding charts Exemplar system accommodates ±100 m range of commanded altitude Provided boom mechanism has ±110 m of travel along mast I/ strodynamics GT Created: of 14

11 I/ strodynamics GT 11 of 14 Fisher Created: Generating Lateral Force & Torque X displacements of XZ-plane masses produce both X force & Y torque o do Y (in local coords) displacements of YZ-plane masses Move them differentially: x 1 = x 3, y 4 = y Then This is well conditioned, with inverse s with Z displacements, * moves slightly, but motions of i dominate otation is also nonzero, but insignificant ange of ±1 m sufficient for expected feedback signals m/m 8.6 N m/m 8.06 N N/m N/m c 1 c y x y x l l M s s m y T x f l l M y x y T x f y T x f m 11.5 m/n 7180 m/n m 11.9 m/n 7350 m/n c c 1 ) c (1 c 3 s s s s m

12 Generating Yaw Torque ingle boom GH can create yaw torque, but only correlated with lateral force Need more lateral separation between i, for example by splitting boom in two (no increase in mechanism count) Top view: 1 4 * 3 hould consider other options for yaw control: rticulated element(s) in to modulate solar pressure torque ynamic coupling I/ strodynamics GT Created: of 14

13 Work emaining GT dynamics & control concept has been proposed Gravity Hitch can provide 6-axis control with no consumables esign equations for sizing olar eflector & point mass Gravity Hitch have been developed High fidelity performance model in work Gravity force & torque model for arbitrary spacecraft mass distribution complete Lacking nonrigid body dynamics & efficient implementation of arbitrary asteroid mass distribution imulation also in work Example GH design establishes feasibility, but is not optimized in any way Much more efficient designs likely can be found eek lower mass, minimum number of drive mechanisms I/ strodynamics GT Created: of 14

14 Conclusions GT appears capable of collision avoidance for pophis class asteroid 100,000 kg spacecraft, 600 m diameter, 15 yr campaign Easily scales to smaller targets or deflection distances caling upward limited by geometric constraints Gravity Hitch turns size of into feature to provide 5- or 6-axis propellantless control dequate control authority Linear map decouples lateral force & torque GT worth consideration as alternative to olar-electric & Nuclear-Electric GTs Pro: Lower development risk Con: Higher reliability No consumables Higher launch mass More complex deployment/assembly More attractive for larger accelerations & longer mission durations More efficient GT designs likely to be found I/ strodynamics GT Created: of 14

A Gravitational Tractor for Towing Asteroids

1 A Gravitational Tractor for Towing Asteroids Edward T. Lu and Stanley G. Love NASA Johnson Space Center We present a concept for a spacecraft that can controllably alter the trajectory of an Earth threatening