scholarly journals On the secondary’s rotation in a synchronous binary asteroid

2020 ◽  
Vol 493 (1) ◽  
pp. 171-183
Author(s):  
H S Wang ◽  
X Y Hou
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Spin Orbit ◽  
Binary Asteroid ◽  
Classical Spin ◽  
Long Period ◽  
Period Orbit ◽  
Short Period ◽  
Orbit Eccentricity ◽  
Binary Asteroid System

ABSTRACT This article studies the secondary’s rotation in a synchronous binary asteroid system in which the secondary enters the 1:1 spin-orbit resonance. The model used is the planar full two-body problem, composed of a spherical primary plus a triaxial ellipsoid secondary. Compared with classical spin-orbit work, there are two differences: (1) influence of the secondary’s rotation on the mutual orbit is considered and (2) instead of the Hamiltonian approach, the approach of periodic orbits is adopted. Our studies find the following. (1) The genealogy of the two families of periodic orbits is the same as that of the families around triangular libration points in the restricted three-body problem. That is, the long-period family terminates on to a short-period orbit travelling N times. (2) In the limiting case where the secondary’s mass is negligible, our results can be reduced to classical spin-orbit theory, by equating the long-period orbit with free libration and the short-period orbit with the forced libration caused by orbit eccentricity. However, the two models show obvious differences when the secondary’s mass is non-negligible. (3) By studying the stability of periodic orbits for a specific binary asteroid system, we are able to obtain the maximum libration amplitude of the secondary (which is usually less than 90°) and the maximum mutual orbit eccentricity that does not break the secondary’s synchronous state. We also find an anti-correlation between the secondary’s libration amplitude and the orbit eccentricity. The (65803) Didymos system is taken as an example to show the results.

scholarly journals Libration-induced Orbit Period Variations Following the DART Impact

2021 ◽  
Vol 2 (6) ◽  
pp. 242
Author(s):  
Alex J. Meyer ◽  
Ioannis Gkolias ◽  
Michalis Gaitanas ◽  
Harrison F. Agrusa ◽  
Daniel J. Scheeres ◽  
...  
Keyword(s):  
Momentum Transfer ◽  
Binary Asteroid ◽  
Long Period ◽  
Short Period ◽  
Planetary Defense ◽  
Period Variations ◽  
Post Impact ◽  
Binary Asteroid System ◽  
Orbit Period ◽  
The Impact

Abstract The Double Asteroid Redirection Test (DART) mission will be the first test of a kinetic impactor as a means of planetary defense. In late 2022, DART will collide with Dimorphos, the secondary in the Didymos binary asteroid system. The impact will cause a momentum transfer from the spacecraft to the binary asteroid, changing the orbit period of Dimorphos and forcing it to librate in its orbit. Owing to the coupled dynamics in binary asteroid systems, the orbit and libration state of Dimorphos are intertwined. Thus, as the secondary librates, it also experiences fluctuations in its orbit period. These variations in the orbit period are dependent on the magnitude of the impact perturbation, as well as the system’s state at impact and the moments of inertia of the secondary. In general, any binary asteroid system whose secondary is librating will have a nonconstant orbit period on account of the secondary’s fluctuating spin rate. The orbit period variations are typically driven by two modes: a long period and a short period, each with significant amplitudes on the order of tens of seconds to several minutes. The fluctuating orbit period offers both a challenge and an opportunity in the context of the DART mission. Orbit period oscillations will make determining the post-impact orbit period more difficult but can also provide information about the system’s libration state and the DART impact.

On the post-impact spin state of the secondary component of the Didymos-Dimorphos binary asteroid system

2020 ◽  
Author(s):  
Harrison Agrusa ◽  
Kleomenis Tsiganis ◽  
Ioannis Gkolias ◽  
Derek Richardson ◽  
Alex Davis ◽  
...  
Keyword(s):  
Spin State ◽  
Uniform Density ◽  
Dynamical Structure ◽  
Spin Orbit ◽  
Binary Asteroid ◽  
Planetary Defense ◽  
Out Of Plane ◽  
Post Impact ◽  
Binary Asteroid System ◽  
Binary Orbit

<p>NASA’s Double Asteroid Redirection Test (DART) is designed to be the first demonstration of a kinetic impactor for planetary defense against a small body impact hazard. The target is the smaller component of the Didymos-Dimorphos binary asteroid system. The DART impact will abruptly change the relative velocity of the secondary (Dimorphos), increasing the binary eccentricity and exciting librations in the secondary. The observed change in the binary orbit period will be used to infer the “beta factor”, or the momentum transfer efficiency, an important parameter used in planetary defense. The post-impact spin and librational dynamics are expected to be highly dependent on the momentum transferred to the target (i.e., beta) and the shape of the secondary, which is still unconstrained.</p> <p>In this work, we explore the possible post-impact spin state of Dimorphos, as a function of its shape and beta, assuming it has an ellipsoidal shape and that both bodies have a uniform density. We have conducted attitude dynamics simulations with a modified 3-D spin-orbit model, accounting for the secondary’s shape and the primary’s oblateness, to understand the underlying dynamical structure of the system. In addition, we have used the radar-derived polyhedral shape model of Didymos in high-fidelity Full Rigid Two-Body Problem (FR2BP) simulations to capture the fully three-dimensional nature of the problem. We consider the outcomes from a simplified planar impact, where the DART momentum is transferred within the binary orbit plane, opposite the motion of Dimorphos, in addition to a more realistic case that accounts for the full DART velocity vector (which contains out-of-plane components).</p> <p>With both simulation tools, we produce the expected signatures of the 1:1 and 2:1 secondary resonances between the free and forced libration periods, corresponding to axial ratios of a/b = 1.414 and a/b = 1.087, respectively. For moderate values of beta (~3), we find that the libration amplitude can exceed ~40 degrees in most cases. For some possible axial ratios, it is even possible to achieve a libration amplitude exceeding 40 degrees with beta values as low as 1. In addition, both codes reveal that the secondary may be attitude unstable in many cases, and can enter a chaotic tumbling state for larger values of beta (~5). In some cases, Dimorphos is able to break from its assumed 1:1 spin-orbit resonance.</p> <p>In the case with a more realistic impact geometry (where some momentum is transferred out-of-plane), the results are relatively similar. The most noticeable difference is in the cases that result in a chaotic tumbling state. In those cases, the characteristic timescale for entering the chaotic tumbling state is much shorter – typically only several orbit periods are required. We also discuss the feasibility of detecting the post-impact spin state of Dimorphos with ground-based observations.</p> <p>This study was supported in part by the DART mission, NASA Contract # NNN06AA01C to JHU/APL. The work of K.T. and I.G. is supported by the EC Horizon 2020 research and innovation programme, under grant agreement No. 870377 (project "NEO-MAPP"). Some of the simulations herein were carried out on The University of Maryland Astronomy Department’s YORP cluster, administered by the Center for Theory and Computation.</p>

scholarly journals The Evolution of Comet Orbits

1976 ◽  
Vol 25 (Part1) ◽  
pp. 445-464 ◽  
Author(s):  
Edgar Everhart
Keyword(s):  
Solar System ◽  
Body Problem ◽  
List Type ◽  
Type Number ◽  
Distant Source ◽  
Origin And Evolution ◽  
Long Period ◽  
Jacobi Integral ◽  
Short Period ◽  
Stellar Perturbations

AbstractThis review states and defends seven conclusions on the origin of comets and the evolution of their orbits:1.There is a N-½ law of survival of comets against ejection on hyperbolic orbits, where N is the number of perihelion passages.2.The short-period comets are not created by single close encounters of near-parabolic comets with Jupiter.3.Observable long-period comets do not evolve into observable short-period comets.4.Unobservable long-period comets with perihelia near Jupiter can evolve into observable short-period comets.5.Long-period comets cannot have been formed or created within the planetary region of the solar system. (This conclusion is somewhat qualified because of possible effects of stellar perturbations. )6.It is possible that some of ths short-period comets could have been formed inside the orbit of Neptune, but it is certain that others have the same distant source as the long-period comets.7.The circularly-restricted 3-body problem, and its associated Jacobi integral, are not valid approximations to use in studying origin and evolution of comets.

The capture of comets

1974 ◽  
Vol 22 ◽  
pp. 187-191
Author(s):  
Hans Rickman
Keyword(s):  
The Sun ◽  
Capture Process ◽  
Long Period ◽  
Limited Role ◽  
Period Orbit ◽  
Short Period

The expression: “Capture of a comet” may lead thoughts primarily to the single encounter mechanism, when a comet happens to pass very close to Jupiter and is at once “captured” into Jupiter’s family of comets, getting an aphelion just outside Jupiter’s orbit, but I would rather suggest that any evolution from a long-period orbit far from the Sun to a short-period orbit, making use of different kinds of perturbations, may be termed a “capture process”, and it is evident that single encounters must play a rather limited role in such evolutions.

Semi-analytical orbital dynamics around the primary of a binary asteroid system

2020 ◽  
Vol 495 (3) ◽  
pp. 3307-3322
Author(s):  
Yue Wang ◽  
Tao Fu
Keyword(s):  
Binary System ◽  
Analytical Model ◽  
Body Problem ◽  
Equilibrium Points ◽  
Dynamical Model ◽  
Orbital Dynamics ◽  
Binary Asteroid ◽  
Binary Asteroid System ◽  
Averaged Model

ABSTRACT The orbital dynamics in the vicinity of a binary asteroid system has been studied extensively, motivated by the special dynamical environment and possible exploration missions. Equilibrium points, periodic orbits, and invariant manifolds have been investigated in many studies based on the model of the Restricted Full Three Body Problem (RF3BP). In this paper, a new semi-analytical orbital dynamical model around the primary of a binary system is developed as a perturbed two-body problem. The solution includes the effect of the primary's oblateness and the secondary's third-body gravity. The semi-analytical dynamical model, also denoted as the averaged model, is obtained by using the averaging process and Lagrange planetary equations in terms of the Milankovitch orbital elements. This semi-analytical model enables much faster orbital propagations than the non-averaged counterpart, and is particularly useful in orbital stability analysis and the design of long-term passively stable orbits and orbits with specific performance, e.g. frozen orbits. The applicability of the semi-analytical model is then discussed. Two parameters describing relative magnitudes of both perturbations w.r.t. the primary's point mass gravity and the third parameter related to the orbital period ratio w.r.t. the secondary are defined to provide indicators for the validity of the averaged model. The validity boundaries in terms of the three parameters are given based on numerical simulations, by comparing with the full orbital model. The application to a real binary system, 2003 YT1, has shown that the averaged solution has a high precision in the long-term orbital propagation.

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

2015 ◽  
Vol 2015 ◽  
pp. 1-21 ◽  
Author(s):  
E. A. Perdios ◽  
V. S. Kalantonis ◽  
A. E. Perdiou ◽  
A. A. Nikaki
Keyword(s):  
Angular Velocity ◽  
Body Problem ◽  
Equilibrium Points ◽  
Velocity Variation ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Long Period ◽  
Short Period ◽  
Three Body

The paper deals with a modification of the restricted three-body problem in which the angular velocity variation is considered in the case where the primaries are sources of radiation. In particular, the existence and stability of its equilibrium points in the plane of motion of the primaries are studied. We find that this problem admits the well-known five planar equilibria of the classical problem with the difference that the corresponding collinear points may be stable depending on the parameters of the problem. For all planar equilibria, sufficient parametric conditions for their stability have been established which are used for the numerical determination of the stability regions in various parametric planes. Also, for certain values of the parameters of the problem for which the equilibrium points are stable, the short and long period families have been computed. To do so, semianalytical expressions have been found for the determination of appropriate initial conditions. Special attention has been given to the continuation of the long period family, in the case of the classical restricted three-body problem, where we show numerically that periodic orbits of the short period family, which are bifurcation points with the long period family, are connected through the characteristic curve of the long period family.

Discussion following the presentation by F. Deubner

1977 ◽  
Vol 36 ◽  
pp. 69-74
Keyword(s):  
List Type ◽  
The Sun ◽  
Type Number ◽  
Harmonic Motion ◽  
Locally Excited ◽  
Long Period ◽  
Coherent Wave ◽  
Short Period ◽  
Global Modes

The discussion was separated into 3 different topics according to the separation made by the reviewer between the different periods of waves observed in the sun :1) global modes (long period oscillations) with predominantly radial harmonic motion.2) modes with large coherent - wave systems but not necessarily global excitation (300 s oscillation).3) locally excited - short period waves.

scholarly journals Isolation and Analysis of Six timeless Alleles That Cause Short- or Long-Period Circadian Rhythms in Drosophila

Genetics ◽  
2000 ◽  
Vol 156 (2) ◽  
pp. 665-675
Author(s):  
Adrian Rothenfluh ◽  
Marla Abodeely ◽  
Jeffrey L Price ◽  
Michael W Young
Keyword(s):  
Nuclear Translocation ◽  
Phase Response Curve ◽  
Fixed Number ◽  
Constant Darkness ◽  
Genetic Screens ◽  
Protein Levels ◽  
Long Period ◽  
Short Period ◽  
Molecular Oscillation ◽  
New Alleles

Abstract In genetic screens for Drosophila mutations affecting circadian locomotion rhythms, we have isolated six new alleles of the timeless (tim) gene. Two of these mutations cause short-period rhythms of 21–22 hr in constant darkness, and four result in long-period cycles of 26–28 hr. All alleles are semidominant. Studies of the genetic interactions of some of the tim alleles with period-altering period (per) mutations indicate that these interactions are close to multiplicative; a given allele changes the period length of the genetic background by a fixed percentage, rather than by a fixed number of hours. The timL1 allele was studied in molecular detail. The long behavioral period of timL1 is reflected in a lengthened molecular oscillation of per and tim RNA and protein levels. The lengthened period is partly caused by delayed nuclear translocation of TIML1 protein, shown directly by immunocytochemistry and indirectly by an analysis of the phase response curve of timL1 flies.

scholarly journals Wave Force Characteristics of Large-Sized Offshore Wind Support Structures to Sea Levels and Wave Conditions

2019 ◽  
Vol 9 (9) ◽  
pp. 1855
Author(s):  
Youn-Ju Jeong ◽  
Min-Su Park ◽  
Jeongsoo Kim ◽  
Sung-Hoon Song
Keyword(s):  
Shallow Water ◽  
Wave Height ◽  
Wave Force ◽  
Diffraction Effect ◽  
Support Structures ◽  
Sea Levels ◽  
Irregular Wave ◽  
Long Period ◽  
Short Period ◽  
Period Wave

This paper presents the results of wave force tests conducted on three types of offshore support structures considering eight waves and three sea levels to investigate the corresponding wave forces. As a result of this study, it is found that the occurrence of shoaling in shallow water induces a significant increase of the wave force. Most of the test models at the shallow water undergo a nonlinear increase of the wave force with higher wave height increasing. In addition, the larger the diameter of the support structure within the range of this study, the larger the diffraction effect is, and the increase in wave force due to shoaling is suppressed. Under an irregular wave at the shallow water, the wave force to the long-period wave tends to be slightly higher than that of the short period wave since the higher wave height component included in the irregular wave has an influence on the shoaling. In addition, it is found that the influence of shoaling under irregular wave becomes more apparent in the long period.

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