Equilibrium Points and Related Periodic Motions in the Restricted Three-Body Problem with Angular Velocity and Radiation Effects

<div>The rotating coordinate system (O<i>xy</i>) with angular velocity <svg height="6.1673pt" id="M18" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 8.42472 6.1673" width="8.42472pt" 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="M615 290C615 392 563 448 529 448C511 448 491 441 484 434L483 425C518 400 546 349 546 273C546 158 504 46 417 46C381 46 356 77 356 142C356 184 380 293 392 334L387 340L307 323C305 288 296 228 287 188C265 94 221 52 180 52C144 52 112 89 112 171C112 278 164 372 241 430L226 454C106 394 23 288 23 155C23 40 79 -12 139 -12C184 -12 245 32 285 85C292 31 322 -12 376 -12C423 -12 470 18 501 45C570 104 615 184 615 290Z" id="g113-246"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="638" vert-adv-y="638"></glyph.data></g></svg> relative to the inertial frame (O<i>XY</i>). The two primaries and the massless body are denoted by <svg height="12.9866pt" id="M19" style="vertical-align:-4.3507pt" version="1.1" viewbox="-0.0498162 -8.6359 18.3401 12.9866" width="18.3401pt" 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 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z" id="g113-81"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="617" vert-adv-y="617"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.656,3.132)"><path d="M389 0V32C297 37 291 46 291 118V635C234 612 176 595 109 583V556L161 554C203 551 207 548 207 497V118C207 46 201 37 110 32V0H389Z" id="g58-47"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,11.088,3.132)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z" id="g50-45"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="237" vert-adv-y="237"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,13.244,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 317 408 376 408 465C408 569 328 635 237 635C178 635 131 610 100 575L42 494L67 471C94 511 138 565 205 565C277 565 321 518 321 435C321 348 259 269 195 195C146 136 89 82 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g58-48"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg> and <svg height="11.9316pt" id="M20" style="vertical-align:-3.2957pt" version="1.1" viewbox="-0.0498162 -8.6359 11.727 11.9316" width="11.727pt" 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 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z" id="g113-81"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="617" vert-adv-y="617"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.656,3.132)"><path d="M290 377C321 398 342 415 358 430C379 451 389 475 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C113 529 154 573 208 573C263 573 303 542 303 482C303 409 233 371 141 341L149 308C165 313 190 319 215 319C272 319 341 284 341 193C342 97 293 43 222 43C162 43 123 71 96 94C89 101 80 101 70 94C61 87 47 73 46 60C44 48 49 36 62 23S118 -12 165 -12C238 -12 430 62 430 223C430 298 379 359 290 375V377Z" id="g58-49"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg>, respectively.</div>

Advances in Astronomy

fig1

Figure 1

Figure 1: Equilibrium Points and Related Periodic Motions in the Restricted Three-Body Problem with Angular Velocity and Radiation Effects 