caa a22 4500 44586303X CHVBK 20180317145449.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s10569-010-9330-2 doi (NATIONALLICENCE)springer-10.1007/s10569-010-9330-2 Analytical investigations of quasi-circular frozen orbits in the Martian gravity field [Elektronische Daten] [Xiaodong Liu, Hexi Baoyin, Xingrui Ma] Frozen orbits are always important foci of orbit design because of their valuable characteristics that their eccentricity and argument of pericentre remain constant on average. This study investigates quasi-circular frozen orbits and examines their basic nature analytically using two different methods. First, an analytical method based on Lagrangian formulations is applied to obtain constraint conditions for Martian frozen orbits. Second, Lie transforms are employed to locate these orbits accurately, and draw the contours of the Hamiltonian to show evolutions of the equilibria. Both methods are verified by numerical integrations in an 80 × 80 Mars gravity field. The simulations demonstrate that these two analytical methods can provide accurate enough results. By comparison, the two methods are found well consistent with each other, and both discover four families of Martian frozen orbits: three families with small eccentricities and one family near the critical inclination. The results also show some valuable conclusions: for the majority of Martian frozen orbits, argument of pericentre is kept at 270° because J 3 has the same sign as J 2; while for a minority of ones with low altitude and low inclination, argument of pericentre can be kept at 90° because of the effect of the higher degree odd zonals; for the critical inclination cases, argument of pericentre can also be kept at 90°. It is worthwhile to note that there exist some special frozen orbits with extremely small eccentricity, which could provide much convenience for reconnaissance. Finally, the stability of Martian frozen orbits is estimated based on the trace of the monodromy matrix. The analytical investigations can provide good initial conditions for numerical correction methods in the more complex models. Springer Science+Business Media B.V., 2011 Mars nationallicence Frozen orbits nationallicence Lagrangian formulations nationallicence Stability nationallicence Lie transforms nationallicence Hamiltonian systems nationallicence Liu Xiaodong School of Aerospace, Tsinghua University, 100084, Beijing, China aut Baoyin Hexi School of Aerospace, Tsinghua University, 100084, Beijing, China aut Ma Xingrui School of Aerospace, Tsinghua University, 100084, Beijing, China aut Celestial Mechanics and Dynamical Astronomy Springer Netherlands 109/3(2011-03-01), 303-320 0923-2958 109:3<303 2011 109 10569 https://doi.org/10.1007/s10569-010-9330-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10569-010-9330-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Liu Xiaodong School of Aerospace, Tsinghua University, 100084, Beijing, China aut NATIONALLICENCE 700 1- Baoyin Hexi School of Aerospace, Tsinghua University, 100084, Beijing, China aut NATIONALLICENCE 700 1- Ma Xingrui School of Aerospace, Tsinghua University, 100084, Beijing, China aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Springer Netherlands 109/3(2011-03-01), 303-320 0923-2958 109:3<303 2011 109 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer