Location and stability of distant retrograde orbits around the Moon

2020 ◽  
Vol 494 (2) ◽  
pp. 2727-2735
Author(s):  
P Pires ◽  
O C Winter

ABSTRACT Recently has grown the interest of placing natural or artificial objects in the neighbourhood of the Moon. We numerically investigate a region of retrograde orbits around the Moon associated with the C Family of periodic orbits and the quasi-periodic orbits that oscillate around them (Broucke 1968; Winter 2000). We have given continuity to Winter (2000) investigations by introducing a more realistic dynamical scenario, one based on the four-body Sun–Earth–Moon–particle problem. Our results showed that the region of stability diminished to approximately 4 ${{\ \rm per\ cent}}$, the original size encountered for the circular-restricted three-body problem (CRTBP), mainly due to the Sun’s gravitational perturbations. None the less, the size of the region continues to be significant and we were able to found distant retrograde orbits (DROs) around the Moon with eccentricity following e = 2.259 63 × 10−6a + 0.238 45 (standard error of 1 ${{\ \rm per\ cent}}$) and semimajor axis values of the initial osculating orbits, varying between 110 000 and 185 000 km, remaining stable for a time span of 104 lunar periods. This set of distant orbits from the Moon are characterized by a narrow range of acceptable initial positions (0.8–0.83) and velocities of ∼0.5, in the rotating Earth–Moon frame. The out of plane amplitude oscillations of $\pm 15\, 000$ km presented by these DROs are a natural outcome of the significant Moon’s inclination of 5.15°. Some results presented on this work can be useful for lunar missions, such as the ones that would require prolonged stays around the satellite and use stable distant orbits as ‘parking’ orbits, such as the advanced concepts of NASA’s Asteroid Redirect Mission, proposed a few years ago.

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Aminu Abubakar Hussain ◽  
Aishetu Umar

This paper studies the motion of a third body near the 1st family of the out-of-plane equilibrium points, L6,7, in the elliptic restricted problem of three bodies under an oblate primary and a radiating-triaxial secondary. It is seen that the pair of points (ξ0,0,±ζ0) which correspond to the positions of the 1st family of the out-of-plane equilibrium points, L6,7, are affected by the oblateness of the primary, radiation pressure and triaxiality of the secondary, semimajor axis, and eccentricity of the orbits of the principal bodies. But the point ±ζ0 is unaffected by the semimajor axis and eccentricity of the orbits of the principal bodies. The effects of the parameters involved in this problem are shown on the topologies of the zero-velocity curves for the binary systems PSR 1903+0327 and DP-Leonis. An investigation of the stability of the out-of-plane equilibrium points, L6,7 numerically, shows that they can be stable for 0.32≤μ≤0.5 and for very low eccentricity. L6,7 of PSR 1903+0327 and DP-Leonis are however linearly unstable.


2020 ◽  
Vol 18 (01) ◽  
pp. 2150005 ◽  
Author(s):  
Elbaz I. Abouelmagd ◽  
Abdullah A. Ansari ◽  
M. H. Shehata

We analyze the existence of equilibrium points for a particle or dust grain in the framework of unperturbed and perturbed Robe’s motion. This particle is moving in a spherical nebula consisting of a homogeneous incompressible fluid, which is considered as the primary body. The second primary body creates the modified Newtonian potential. The perturbed mean motion and equations of motion are found. The equilibrium points (i.e. collinear, noncollinear and out–of–plane points), along with the required conditions of their existence are also analyzed. We emphasize that this analysis can be used to study the oscillations of the Earth’s core under the attraction of the Moon and it is also applicable to study the motion of underwater vehicles.


1994 ◽  
Vol 04 (04) ◽  
pp. 865-884 ◽  
Author(s):  
PAU ATELA ◽  
ROBERT I. McLACHLAN

We study the global bifurcation diagram of the two-parameter family of ODE’s that govern the charged isosceles three-body problem. (The classic isosceles three-body problem and the anisotropic Kepler problem (two bodies) are included in the same family.) There are two major sources of periodic orbits. On the one hand the “Kepler” orbit, a stable orbit exhibiting the generic bifurcations as the multiplier crosses rational values. This orbit turns out to be the continuation of the classical circular Kepler orbit. On the other extreme we have the collision-ejection orbit which exhibits an “infinite-furcation.” Up to a limiting value of the parameter we have finitely many periodic orbits (for each fixed numerator in the rotation number), passed this value there is a sudden birth of an infinite number of them. We find that these two bifurcations are remarkably connected forming the main “skeleton” of the global bifurcation diagram. We conjecture that this type of global connection must be present in related problems such as the classic isosceles three-body problem and the anisotropic Kepler problem.


1996 ◽  
Vol 240 (2) ◽  
pp. 273-293 ◽  
Author(s):  
C. G. Zagouras ◽  
E. Perdios ◽  
O. Ragos

2013 ◽  
Vol 40 (1) ◽  
pp. 135-146
Author(s):  
Aleksandar Tomic

Newton's formula for gravity force gives greather force intensity for atraction of the Moon by the Sun than atraction by the Earth. However, central body in lunar (primary) orbit is the Earth. So appeared paradox which were ignored from competent specialist, because the most important problem, determination of lunar orbit, was inmediately solved sufficiently by mathematical ingeniosity - introducing the Sun as dominant body in the three body system by Delaunay, 1860. On this way the lunar orbit paradox were not canceled. Vujicic made a owerview of principles of mechanics in year 1998, in critical consideration. As an example for application of corrected procedure he was obtained gravity law in some different form, which gave possibility to cancel paradox of lunar orbit. The formula of Vujicic, with our small adaptation, content two type of acceleration - related to inertial mass and related to gravity mass. So appears carried information on the origin of the Moon, and paradox cancels.


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