National Aeronautics and Space Administration Manned Mission to NEO Study Jerry Condon, NASA/JSC/EG5 Jacob Williams, ESCG Elizabeth Davis, ESCG David Lee, NASA/JSC/EG5 Juan Senent, OSR Sept. 27, 2010 Run Methodology ΔVAD Patch conic assumptions. V∞EI ΔtAE Asteroid Earth departure epoch [1900 Cases]: Departure • Start: Jan 01, 2015 00:00:00 Earth Arrival Step: 5 days • ΔtS • End: Dec 31, 2040 00:00:00 Earth-Asteroid transfer time [72]: ΔVAA • Start: 30 days • Step: 5 days Asteroid Arrival • End: 360 days Asteroid stay time [6]: • Start: 7 days • Step 7 days • End: 42 days Asteroid-Earth transfer time [72]: • Start: 5 days Step: 5 days V∞ED • ΔtEA • End: 360 days 1900x72x6x72 = 59,097,600 cases per asteroid Earth Departure 5766 Asteroids 340,756,761,600 cases total. Run time of ~2 hrs on JSC cluster Pre-Decisional: For NASA Internal Use Only 2 Asteroid Cases JPL Small-Body Database Search Engine: http://ssd.jpl.nasa.gov/sbdb_query.cgi Export CSV file which is read by the program Input parameters: • Object group : NEOs • Object kind: Asteroids Damon Landau 9/1/2010: • Numbered state: All objects Assumed diameter > 50 m • Constraints: H (mag) ≤ 24.2 abs. vis. mag. < 24.2 • 5766 Asteroids in this set (as of 8-26-2010) - Note: without the H constraint, the total number is 7183. Output parameters: • SPK-ID • object fullname • Absolute magnitude: H (mag) • Rotation period: rot_per (h) • Keplerian elements - Epoch of osculation: epoch (MJD) - Semi-major axis: a (AU) - Eccentricity: e - Inclination: i (deg) Assuming these are in - Longitude of the ascending node: node (deg) J2000-ECLIPTIC frame - Argument of perihelion: peri (deg) - Mean anomaly: M (deg) Pre-Decisional: For NASA Internal Use Only 3 Run Case Each run case (a selected asteroid, departure epoch, transfer time and stay time) is: • 2 calls to SPICE spkgeo (to get the Earth’s state at arrival and departure) • 2 calls to the Kepler propagator (to get the Asteroid states at arrival and departure) [could also use SPICE for this, but Kepler propagator is faster] • 2 calls to Lambert targeter (outbound and inbound transfers) • Determination if the case is within the specified Δt, ΔV, and V∞ limits • If so, save data to output file. Only save solutions within specified limits: 2 2 • Earth Departure V∞ limit: 5.0 km/s [C3 = 25 km /s ] • Total Asteroid ΔV [Arrival + Departure] limit: 9.0 km/s • Earth Arrival V∞ limit: 7.0 km/s [VEI of 13.1 km/s at REI=121.92 km] • Total Mission Time limit: 365 days • Note: the data set limit can contain more than the acceptable range, and then be post-processed to show capability based on various constraints. Pre-Decisional: For NASA Internal Use Only 4 Tools Copernicus Toolkit Library • Using Gooding’s Lambert algorithm (no singularities: multi-rev, >180°, <180° transfers). Galaxy Computing Cluster • Each asteroid case is a different job that runs in parallel with the others. Asteroid Ephemeris: 1. Conic Orbit Elements: http://ssd.jpl.nasa.gov/sbdb_query.cgi 2. Full Ephemeris: HORIZONS. Earth Ephemeris • DE-421 via SPICE. Pre-Decisional: For NASA Internal Use Only 5 Sample Plots of Full Data Set Example Case All Data Points Pareto Front Min ΔV Boundary Pre-Decisional: For NASA Internal Use Only 6 Sample Plots of Full Data Set All Data Points Example Cases Pre-Decisional: For NASA Internal Use Only 7 Post Processing The post-processor sifts through the data files to return missions that meet various constraints Allows for examining the trends for specific vehicle capabilities. For each Asteroid, save 6 trajectories: • Min Total Ast ΔV [ΔVAA + ΔVAD ] • Min Earth Depart V∞ [V∞ED] • Min Ast Arrival ΔV [ΔVAA ] • Min Ast Depart ΔV [ΔVAD ] • Min Total [V∞ED + ΔVAA + ΔVAD + V∞EI] • Min Total Flight Time [ΔtEA + ΔtS + ΔtAE] For each Asteroid, accumulate two counts: • Number of possible missions • Number of unique departure epochs Pre-Decisional: For NASA Internal Use Only 8 Post Processing Assumptions: 3 2 • μE = 398600.436233 km /s • RE = 6378.14 km • Earth Escape Altitude = 400.0 km • EI Altitude = 125.0 km • Limits: - Departure epochs: 2016-2040 - C3 ≤ 24 km/s - ΔVAst ≤ 8.5 km/s - Stay Time = 14 days [subsequent runs will include all stay times] - Total Flight Time ≤ 360 days - VEI limit ≤ 12.5 km/s - ΔVTotal ≤ 12 km/s Pre-Decisional: For NASA Internal Use Only 9 CONIC ORBIT RESULTS Pre-Decisional: For NASA Internal Use Only 10 Post Processing Results: 239 NEOs Found Listed in order of most to least number of missions possible 1. (2001 QJ142) 41. (2006 SY5) 81. (2007 SG11) 121. (2010 MY1) 161. (2004 GB19) 201. (2002 NW16) 2. (1998 KG3) 42. (2007 EC) 82. (2003 YX1) 122. 101955 (1999 RQ36) 162. (1998 XN17) 202. (2007 YM56) 3. (2009 OS5) 43. (2001 KM20) 83. (2008 PG2) 123. (1994 CJ1) 163. 85585 Mjolnir (1998 FG2) 203. (2004 KG1) 4. (2003 SM84) 44. 25143 Itokawa (1998 SF36) 84. (2005 AJ3) 124. (2009 SC15) 164. (2010 KJ37) 204. (2008 WK60) 5. (1999 AO10) 45. (2006 CL9) 85. (2000 AE205) 125. (2000 TL1) 165. (2000 WG10) 205. (2005 YN128) 6. (2001 CQ36) 46. 141424 (2002 CD) 86. (2006 YF) 126. (2009 BL71) 166. (2010 PR10) 206. (2008 TT26) 7. (2004 JN1) 47. (2010 EX11) 87. (2010 CD55) 127. (2005 GE60) 167. (2009 EK1) 207. (2003 GS) 8. (2001 BB16) 48. (2004 EO20) 88. (2006 SU49) 128. (2002 RW25) 168. 136618 (1994 CN2) 208. (2008 GC110) 9. (2007 UY1) 49. 89136 (2001 US16) 89. (2009 WM105) 129. (2006 VP13) 169. (1999 SO5) 209. (1998 HK49) 10. (2006 FH36) 50. (2002 VU114) 90. (2006 KV89) 130. 216985 (2000 QK130) 170. (2009 DC1) 210. (2007 CT26) 11. (2006 XP4) 51. 65679 (1989 UQ) 91. (2008 FS6) 131. (2007 VW83) 171. (2004 UR) 211. (2008 JV19) 12. (2009 UY19) 52. (2008 FO) 92. (1999 SH10) 132. (2000 SL10) 172. (2004 BW18) 212. (2002 DQ3) 13. (1999 SF10) 53. (2005 FG) 93. 163000 (2001 SW169) 133. (2003 QU5) 173. (2008 TD2) 213. (2006 GB1) 14. (2010 HA) 54. (2008 MQ1) 94. (2005 RK3) 134. (2006 RJ1) 174. (2009 KT4) 214. (2006 SE6) 15. (2003 CA4) 55. (2010 CE55) 95. (1997 UR) 135. (2009 WZ104) 175. (2009 UX17) 215. (2009 JL1) 16. (2001 QC34) 56. (2004 FM17) 96. 3361 Orpheus (1982 HR) 136. (2004 MO3) 176. (2008 GE) 216. (2010 MS1) 17. (2003 EZ16) 57. (2009 RT1) 97. (2004 SR) 137. (2003 YN1) 177. (2007 TV18) 217. (2007 VD3) 18. (2006 WB) 58. (2009 QE34) 98. (2008 WN2) 138. (2006 VG13) 178. (2002 AO11) 218. 35107 (1991 VH) 19. (1998 HG49) 59. (2004 XG) 99. 208023 (1999 AQ10) 139. (2007 CN26) 179. (2005 WA) 219. 162783 (2000 YJ11) 20. (2005 TF45) 60. (2005 YR3) 100. (2009 SQ104) 140. (2007 WU3) 180. (2008 SO) 220. 163249 (2002 GT) 21. (2005 YA37) 61. (2002 SR) 101. (2002 LT38) 141. (2001 XP88) 181. (2008 CP) 221. 163364 (2002 OD20) 22. 225312 (1996 XB27) 62. (2007 SQ6) 102. (2005 AZ28) 142. (2002 AW) 182. (2010 HX107) 222. (2003 GX) 23. (2007 PS9) 63. 10302 (1989 ML) 103. (2010 FC) 143. (2009 UD2) 183. (2010 CF19) 223. (2001 EC16) 24. (2005 CD69) 64. 65717 (1993 BX3) 104. 52381 (1993 HA) 144. (2010 FK) 184. (2000 OK8) 224. (2010 DJ77) 25. 162173 (1999 JU3) 65. (2009 DC12) 105. (1999 NW2) 145. (1999 FA) 185. (2004 BH11) 225. (2000 CO101) 26. (2000 YS134) 66. 207945 (1991 JW) 106. (2009 KY1) 146. (2000 WP19) 186. (2004 CO49) 226. (2002 FW1) 27. (2008 EV5) 67. (2006 CT) 107. (2008 VA15) 147. (2009 DL46) 187. 162162 (1999 DB7) 227. (2003 OT13) 28. (2002 XY38) 68. (2002 TC70) 108. (2008 CO) 148. 98943 (2001 CC21) 188. (2010 GP67) 228. (2003 FQ6) 29. (2009 TP) 69. (1996 BG1) 109. (2005 ML13) 149. (1994 UG) 189. (2000 CE59) 229. (2005 RZ2) 30. 99942 Apophis (2004 MN4) 70. (2008 DG5) 110. (1997 XR2) 150. (2001 VB76) 190. (2010 JT39) 230. (2006 MB) 31. (2006 XW) 71. (2009 PD) 111. (2006 GB) 151. (2001 VC2) 191. 154019 (2002 CZ9) 231. (2007 TE66) 32. (2004 EU22) 72. (2008 RH1) 112. (2009 RH) 152. (2006 EW52) 192. (2002 DU3) 232. (1997 WB21) 33. (2000 SJ344) 73. (2007 UP6) 113. (2006 KL21) 153. (2006 KQ1) 193. (2004 HQ1) 233. (1998 VD32) 34. (2003 GA) 74. 163899 (2003 SD220) 114. (2008 BX2) 154. (2008 HS3) 194. (2005 BY2) 234. (2000 AF205) 35. (2002 NV16) 75. (2006 QQ23) 115. 4660 Nereus (1982 DB) 155. (2004 FJ31) 195. (2006 DM) 235. (2004 FK2) 36. (2007 UW1) 76. (1999 RA32) 116. (2006 SF6) 156. (2007 LT) 196. (2003 GY) 236. (2004 XJ) 37. (2004 WH1) 77. (2002 GR) 117. (2002 BF25) 157. (2009 SA100) 197. (2004 JX20) 237. (2006 OT9) 38. (2006 YP) 78. (2006 XY) 118. 152563 (1992 BF) 158. 164207 (2004 GU9) 198. 139622 (2001 QQ142) 238. (2010 AF30) 39. (2000 EA14) 79. (2002 TD60) 119. (2000 AC6) 159. (2004 PJ2) 199. (2002 JX8) 239. 226554 (2003 WR21) 40. (2008 PW4) 80. (2002 OA22) 120. 228502 (2001 TE2) 160. 138404 (2000 HA24) 200. (2005 EH94) Pre-Decisional: For NASA Internal Use Only 11 Post Processing Results: Available Missions Pre-Decisional: For NASA Internal Use Only 12 Post Processing Results: Best Cases – Lowest Total ΔV Earth- Asteroid- Total Earth Asteroid Asteroid Earth DV Earth Asteroid DV Earth Asteroid Earth Mission Departure Arrival DV Departure Arrival VInf C3 Asteroid DV Total V EI Asteroid Departure Stay Time Escape Transfer Transfer Time VInf Mag Mag DV Mag Mag (km2/s2) Total (km/s) (km/s) Date (day (km/s) Time (day) Time (day) (days) (km/s) (km/s) (km/s) (km/s) (km/s) (2009 UY19) 4/24/2040 85 14 260 359 4.755 0.237 0.656 4.841 22.607 4.173 0.894 5.067 12.084 (2001 10/3/2035 170 14 175 359 2.692 1.248 0.775 3.816 7.245 3.505 2.023 5.528 11.711 QJ142) (2007 UY1) 3/10/2021 195 14 145 354 4.406 0.958 0.616 5.202 19.410 4.037 1.574 5.611 12.233 99942 Apophis 5/7/2028 265 14 70 349 3.686 1.576 0.506 5.400 13.588 3.786 2.082 5.868 12.319 (2004 MN4) 207945 5/23/2027 110 14 235 359 4.610 1.097 0.662 5.156 21.250 4.115 1.760 5.875 12.214 (1991 JW) (2001