Potential Launch Opportunities for a SmallSat Mission around the Moon Injected during a Lunar Flyby En Route to Mars

<table class="table-group" id="tab5"><tr><td><table class="table"><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Periapsis altitude at deployment (km)</td><td class="align_center" rowspan="2">Periapsis velocity at deployment (km/s)</td><td class="align_center" colspan="3">Delta-V for an orbiter mission (km/s)</td><td class="align_center">Delta-V for an impactor mission (km/s)</td></tr><tr class="thead"><td class="align_center"><span style="width: 27.6661ptpx;"><svg height="12.0131pt" id="M192" style="vertical-align:-3.272799pt" version="1.1" viewbox="-0.0498162 -8.7403 27.6661 12.0131" width="27.6661pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M600 0V24L339 665L311 657L43 24V0H600ZM497 50H107L303 539L497 50Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.327,0)"><path d="M702 650H468V614C550 604 550 590 527 521C500 434 457 318 402 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182C232 159 261 135 261 91C261 48 227 21 190 21C130 21 85 79 68 145L41 140C41 104 51 36 58 22C75 7 121 -12 172 -12C252 -12 337 35 337 126C337 195 286 231 210 262C166 281 126 304 126 348C126 388 152 417 191 417C240 417 274 378 294 318L319 325Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,20.983,3.132)"><path d="M380 106C343 72 306 56 265 56C195 56 116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 449 144 421 103 376S37 269 37 201C37 88 109 -12 232 -12C263 -12 332 6 395 84L380 106ZM225 412C281 412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,24.896,3.132)"><path d="M390 111C344 68 312 56 269 56C212 56 118 102 118 241C118 346 175 401 241 401C277 401 312 388 342 360C350 352 355 349 361 349C372 349 394 371 394 392C394 403 391 411 378 422C362 436 329 449 288 449H287C250 449 190 432 138 392C71 341 37 274 37 197C37 90 112 -12 238 -12C297 -12 363 32 407 90L390 111Z"></path></g></svg></span></td><td class="align_center"><span style="width: 36.1516ptpx;"><svg height="12.0497pt" id="M194" style="vertical-align:-3.3094pt" version="1.1" viewbox="-0.0498162 -8.7403 36.1516 12.0497" width="36.1516pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M600 0V24L339 665L311 657L43 24V0H600ZM497 50H107L303 539L497 50Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.327,0)"><path d="M702 650H468V614C550 604 550 590 527 521C500 434 457 318 402 172H399C363 266 284 469 255 549C240 592 240 603 313 614V650H15V614C77 608 93 594 124 517C165 413 259 172 327 -11H377C455 195 546 422 579 500C619 595 637 607 702 614V650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,17.57,3.132)"><path d="M861 0V28C774 35 771 41 768 147L759 509C756 612 762 614 851 622V650H681L449 149L221 650H57V622C148 613 153 609 144 479L130 271C123 166 117 123 111 88C104 46 85 34 26 28V0H259V28C192 35 169 42 167 90C166 130 166 173 170 256L185 541H187L411 7H431L675 555H679L683 147C683 41 680 35 598 28V0H861Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,25.596,3.132)"><path d="M381 665C170 665 44 498 44 318C44 125 188 -15 369 -15C552 -15 703 117 703 333C703 534 550 665 381 665ZM359 629C491 629 601 517 601 306C601 114 502 21 390 21C249 21 146 158 146 346S248 629 359 629Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,32.311,3.132)"><path d="M303 0V28C221 34 213 39 213 125V525C213 610 221 616 303 622V650H38V622C120 616 128 610 128 525V125C128 40 120 34 38 28V0H303Z"></path></g></svg></span></td><td class="align_center"><span style="width: 36.1516ptpx;"><svg height="12.0497pt" id="M195" style="vertical-align:-3.3094pt" version="1.1" viewbox="-0.0498162 -8.7403 36.1516 12.0497" width="36.1516pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M600 0V24L339 665L311 657L43 24V0H600ZM497 50H107L303 539L497 50Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.327,0)"><path d="M702 650H468V614C550 604 550 590 527 521C500 434 457 318 402 172H399C363 266 284 469 255 549C240 592 240 603 313 614V650H15V614C77 608 93 594 124 517C165 413 259 172 327 -11H377C455 195 546 422 579 500C619 595 637 607 702 614V650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,17.57,3.132)"><path d="M861 0V28C774 35 771 41 768 147L759 509C756 612 762 614 851 622V650H681L449 149L221 650H57V622C148 613 153 609 144 479L130 271C123 166 117 123 111 88C104 46 85 34 26 28V0H259V28C192 35 169 42 167 90C166 130 166 173 170 256L185 541H187L411 7H431L675 555H679L683 147C683 41 680 35 598 28V0H861Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,25.596,3.132)"><path d="M381 665C170 665 44 498 44 318C44 125 188 -15 369 -15C552 -15 703 117 703 333C703 534 550 665 381 665ZM359 629C491 629 601 517 601 306C601 114 502 21 390 21C249 21 146 158 146 346S248 629 359 629Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,32.311,3.132)"><path d="M303 0V28C221 34 213 39 213 125V525C213 610 221 616 303 622V650H38V622C120 616 128 610 128 525V125C128 40 120 34 38 28V0H303Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td class="align_left">198.084</td><td class="align_center">2.444</td><td class="align_center">0.874</td><td class="align_center">0.021</td><td class="align_center">0.895</td><td class="align_center">0.896</td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>SmallSat mission characteristics for the year 2031 for the orbiter and impactor mission case.</div>

Mathematical Problems in Engineering

tab5

Table 5

Table 5: Potential Launch Opportunities for a SmallSat Mission around the Moon Injected during a Lunar Flyby En Route to Mars 