scholarly journals Gravity assists gravitational scattering and the perturbation rings in the Solar system

2021 ◽  
Vol 2090 (1) ◽  
pp. 012084
Author(s):  
A Grushevskii
Keyword(s):  
Solar System ◽  
Coulomb Field ◽  
Necessary Condition ◽  
Three Body Problem ◽  
Gravity Assist ◽  
Gravitational Scattering ◽  
Gravity Assists ◽  
Sphere Of Influence ◽  
Three Body ◽  
Gravitational Capture

Abstract One of the types of gravitational scattering in the Solar system within the framework of the model of the restricted three-body problem (R3BP) is gravity assist maneuvers of the “particles of insignificant mass” [1] (spacecraft, asteroids, comets, etc.). For their description, a physical analogy with the beam scattering of charged α particles in a Coulomb field is useful. However, unlike the scattering of charged particles, there are external restrictions for the possibility of gravity assists executing related from the restricted size of planet’s sphere of influence. At the same time, internal restrictions for the gravity assists performance estimated by the effective radii of planets are known from the literature on R3BP [2] (gravitational capture by the planet, falling into it). They depend from the particle asymptotic velocity relative the planet. For obvious reasons, their influence cuts off the possibility of effective gravity assists performance [3]. In this work the generalized estimates of the sizes of the near-planetary regions (“perturbation rings”), falling into which is a necessary condition for the implementation of gravity assists, are presented. The detailed analysis shows that Neptune and Saturn have the characteristic “perturbation rings” of the largest sizes in the Solar system, and Jupiter occupies only the fourth place in this checklist.

scholarly journals Rutherford’s extended formula and optimization of the gravity assists beam modelling in the Solar system

2021 ◽  
Vol 2090 (1) ◽  
pp. 012083
Author(s):  
A Grushevskii ◽  
Yu Golubev ◽  
V Koryanov ◽  
A Tuchin ◽  
D Tuchin
Keyword(s):  
Solar System ◽  
Interplanetary Space ◽  
Coulomb Field ◽  
Gravity Assist ◽  
Space Flights ◽  
Modern Methods ◽  
Gravitational Scattering ◽  
Gravity Assists ◽  
Effective Use ◽  
Α Particles

Abstract Rutherford’s formula for the scattering of charged α-particles in the Coulomb field can be easily generalized to the case of gravitational scattering. The extended Rutherford formula for the gravitational scattering is presented. One of the types of the gravitational scattering in the Solar system is the gravity assist maneuvers. In this paper, an effective gravitational scattering cross-section is introduced by analogy for them and the generalized Rutherford formula for gravitational scattering is presented out when performing gravity assists. Modern methods of the ballistic design of the interplanetary space flights using gravity assist maneuvers around planets [1-3] are associated with the need to calculate a lot of trajectories (i.e. of the phase beams). For their effective use it is necessary to study the structure of non-linear flyby gravitational scattering using the Rutherford’ formula and to construct the corresponding effective modelling using according regularized phase beams. It is shown that with using of such approach, it is possible to significantly increase the efficiency of the recurrent procedure for the gravity assists chains searching for ballistic scenarios of the modern interplanetary flights.

Orbits of Trojan Asteroids

1974 ◽  
Vol 62 ◽  
pp. 63-69 ◽  
Author(s):  
G. A. Chebotarev ◽  
N. A. Belyaev ◽  
R. P. Eremenko
Keyword(s):  
Solar System ◽  
Body Problem ◽  
Equations Of Motion ◽  
Orbital Evolution ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Trojan Asteroids ◽  
Actual Motion ◽  
Three Body

In this paper the orbital evolution of Trojan asteroids are studied by integrating numerically the equations of motion over the interval 1660–2060, perturbations from Venus to Pluto being taken into account. The comparison of the actual motion of Trojans in the solar system with the theory based on the restricted three-body problem are given.

scholarly journals Orbital stability of high inclination asteroids

1996 ◽  
Vol 172 ◽  
pp. 187-192
Author(s):  
N. A. Solovaya ◽  
E. M. Pittich
Keyword(s):  
Solar System ◽  
Body Problem ◽  
Equations Of Motion ◽  
Orbital Stability ◽  
Dynamical Model ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

The orbital evolutions of fictitious asteroids with high inclinations have been investigated. The selected initial orbits represent asteroids with movement, which corresponds to the conditions of the Tisserand invariant for C = C (L1) in the restricted three body problem. Initial eccentricities of the orbits cover the interval 0.0–0.4, inclinations the interval 40–80°, and arguments of perihelion the interval 0–360°. The equations of motion of the asteroids were numerically integrated from the epoch March 25, 1991 forward within the interval of 20,000 years, using a dynamical model of the solar system consisting of all planets. The orbits of the model asteroids are stable at least during the investigated period.

scholarly journals Gravitational Capture of Asteroids by Gas Drag

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
E. Vieira Neto ◽  
O. C. Winter
Keyword(s):  
Body Problem ◽  
Giant Planets ◽  
Three Body Problem ◽  
Irregular Satellites ◽  
Whole Process ◽  
Orbital Configuration ◽  
Temporary Capture ◽  
Three Body ◽  
Gravitational Capture ◽  
Gas Drag

Several irregular satellites of the giant planets were found in the last years. Their orbital configuration suggests that these satellites were asteroids captured by the planets. The restricted three-body problem can explain the dynamics of the capture, but the capture is temporary. It is necessary some kind of dissipative effect to turn the temporary capture into a permanent one. In this work we study an asteroid suffering a gas drag at an extended atmosphere of a planet to turn a temporary capture into a permanent one. In the primordial Solar System, gas envelopes were created around the planet. An asteroid that was gravitationally captured by the planet got its velocity reduced and could been trapped as an irregular satellite. It is well known that, depending on the time scale of the gas envelope, an asteroid will spiral and collide with the planet. So, we simulate the passage of the asteroid in the gas envelope with its density decreasing along the time. Using this approach, we found effective captures, and have a better understanding of the whole process. Finally, we conclude that the origin of the irregular satellites cannot be attributed to the gas drag capture mechanism alone.

scholarly journals Gravity assists gravitational scattering and the perturbation rings in the Solar system

2021 ◽  
pp. 1-26 ◽  
Author(s):  
Yury Filippovich Golubev ◽  
Alexey Vasilyevich Grushevskii ◽  
Victor Vladimirovich Korianov ◽  
Andrey Georgievich Tuchin ◽  
Denis Andreevich Tuchin
Keyword(s):  
Solar System ◽  
Gravitational Scattering ◽  
Gravity Assists

scholarly journals Stability of the Moons Orbits in Solar System in the Restricted Three-Body Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Sergey V. Ershkov
Keyword(s):  
Solar System ◽  
Effective Mass ◽  
Body Problem ◽  
Equations Of Motion ◽  
Centre Of Mass ◽  
Three Body Problem ◽  
Dynamical Parameter ◽  
Lagrange Form ◽  
Elliptic Orbits ◽  
Three Body

We consider the equations of motion of three-body problem in aLagrange form(which means a consideration of relative motions of 3 bodies in regard to each other). Analyzing such a system of equations, we consider in detail the case of moon’s motion of negligible massm3around the 2nd of two giant-bodiesm1,m2(which are rotating around their common centre of masses on Kepler’s trajectories), the mass of which is assumed to be less than the mass of central body. Under assumptions of R3BP, we obtain the equations of motion which describe the relative mutual motion of the centre of mass of 2nd giant-bodym2(planet) and the centre of mass of 3rd body (moon) with additional effective massξ·m2placed in that centre of massξ·m2+m3, whereξis the dimensionless dynamical parameter. They should be rotating around their common centre of masses on Kepler’s elliptic orbits. For negligible effective massξ·m2+m3it gives the equations of motion which should describe aquasi-ellipticorbit of 3rd body (moon) around the 2nd bodym2(planet) for most of the moons of the planets in Solar System.

scholarly journals On solar system dynamics in general relativity

2017 ◽  
Vol 14 (09) ◽  
pp. 1750117 ◽  
Author(s):  
Emmanuele Battista ◽  
Giampiero Esposito ◽  
Luciano Di Fiore ◽  
Simone Dell’Agnello ◽  
Jules Simo ◽  
...  
Keyword(s):  
General Relativity ◽  
Solar System ◽  
System Dynamics ◽  
Body Problem ◽  
The Sun ◽  
Three Body Problem ◽  
Lagrangian Points ◽  
The Earth ◽  
Solar System Dynamics ◽  
Three Body

Recent work in the literature has advocated using the Earth–Moon–planetoid Lagrangian points as observables, in order to test general relativity and effective field theories of gravity in the solar system. However, since the three-body problem of classical celestial mechanics is just an approximation of a much more complicated setting, where all celestial bodies in the solar system are subject to their mutual gravitational interactions, while solar radiation pressure and other sources of nongravitational perturbations also affect the dynamics, it is conceptually desirable to improve the current understanding of solar system dynamics in general relativity, as a first step towards a more accurate theoretical study of orbital motion in the weak-gravity regime. For this purpose, starting from the Einstein equations in the de Donder–Lanczos gauge, this paper arrives first at the Levi-Civita Lagrangian for the geodesic motion of planets, showing in detail under which conditions the effects of internal structure and finite extension get canceled in general relativity to first post-Newtonian order. The resulting nonlinear ordinary differential equations for the motion of planets and satellites are solved for the Earth’s orbit about the Sun, written down in detail for the Sun–Earth–Moon system, and investigated for the case of planar motion of a body immersed in the gravitational field produced by the other bodies (e.g. planets with their satellites). At this stage, we prove an exact property, according to which the fourth-order time derivative of the original system leads to a linear system of ordinary differential equations. This opens an interesting perspective on forthcoming research on planetary motions in general relativity within the solar system, although the resulting equations remain a challenge for numerical and qualitative studies. Last, the evaluation of quantum corrections to location of collinear and noncollinear Lagrangian points for the planar restricted three-body problem is revisited, and a new set of theoretical values of such corrections for the Earth–Moon–planetoid system is displayed and discussed. On the side of classical values, the general relativity corrections to Newtonian values for collinear and noncollinear Lagrangian points of the Sun–Earth–planetoid system are also obtained. A direction for future research will be the analysis of planetary motions within the relativistic celestial mechanics set up by Blanchet, Damour, Soffel and Xu.

scholarly journals Orbits of Minor Bodies of the Solar System in the Circular Restricted Three-Body Problem

2017 ◽  
Vol 13 (1) ◽  
pp. 29-48
Author(s):  
Jeremy B Tatum Mandyam N Anandaram
Keyword(s):  
Solar System ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
The Sun ◽  
Three Body Problem ◽  
Third Body ◽  
Circular Orbits ◽  
Three Body

A brief introduction to the circular restricted three-body problem (CR3BP) is given where a third body of negligible mass moves under the combined gravitational- centrifugal potential of two co-rotating massive bodies restricted to circular orbits. The equipotential contours of a variety of two body systems in the solar system are presented along with interesting orbits of Trojans, Hildas, Thule in the Sun-Jupiter system, the libration of Pluto in the Sun-Neptune system and choreographic orbits.

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