Third-order Analytical Solutions around Non-collinear Equilibrium Points of a Contact Binary Asteroid

2014 ◽  
Author(s):  
Jinglang Feng ◽  
Ron Noomen ◽  
Jianping Yuan ◽  
Boudewijn Ambrosius
Keyword(s):  
Analytical Solutions ◽  
Equilibrium Points ◽  
Third Order ◽  
Binary Asteroid ◽  
Contact Binary

scholarly journals Evaluation of hillslope storage with variable width under temporally varied rainfall recharge

2021 ◽  
Author(s):  
Ping-Cheng Hsieh ◽  
Tzu-Ting Huang
Keyword(s):  
Groundwater Flow ◽  
Analytical Solutions ◽  
Water Conservation ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Time Discretization ◽  
Third Order ◽  
Analytical And Numerical Solutions ◽  
Rainfall Recharge ◽  
Integral Transform Technique

Abstract. This study discussed water storage in aquifers of hillslopes under temporally varied rainfall recharge by employing a hillslope-storage equation to simulate groundwater flow. The hillslope width was assumed to vary exponentially to denote the following complex hillslope types: uniform, convergent, and divergent. Both analytical and numerical solutions were acquired for the storage equation with a recharge source. The analytical solution was obtained using an integral transform technique. The numerical solution was obtained using a finite difference method in which the upwind scheme was used for space derivatives and the third-order Runge–Kutta scheme was used for time discretization. The results revealed that hillslope type significantly influences the drains of hillslope storage. Drainage was the fastest for divergent hillslopes and the slowest for convergent hillslopes. The results obtained from analytical solutions require the tuning of a fitting parameter to better describe the groundwater flow. However, a gap existed between the analytical and numerical solutions under the same scenario owing to the different versions of the hillslope-storage equation. The study findings implied that numerical solutions are superior to analytical solutions for the nonlinear hillslope-storage equation, whereas the analytical solutions are better for the linearized hillslope-storage equation. The findings thus can benefit research on and have application in soil and water conservation.

scholarly journals Shape model and spin-state analysis of PHA contact binary (85990) 1999 JV6 from combined radar and optical observations

2019 ◽  
Vol 631 ◽  
pp. A149
Author(s):  
A. Rożek ◽  
S. C. Lowry ◽  
M. C. Nolan ◽  
P. A. Taylor ◽  
L. A. M. Benner ◽  
...  
Keyword(s):  
Physical Model ◽  
Spin State ◽  
Rotation Period ◽  
Optical Observations ◽  
Shape Model ◽  
Optical Photometry ◽  
Binary Asteroid ◽  
Radar Images ◽  
Yorp Effect ◽  
Contact Binary

Context. The potentially hazardous asteroid (85990) 1999 JV6 has been a target of previously published thermal-infrared observations and optical photometry. It has been identified as a promising candidate for possible Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect detection. Aims. The YORP effect is a small thermal-radiation torque considered to be a key factor in spin-state evolution of small Solar System bodies. In order to detect YORP on 1999 JV6 we developed a detailed shape model and analysed the spin-state using both optical and radar observations. Methods. For 1999 JV6, we collected optical photometry between 2007 and 2016. Additionally, we obtained radar echo-power spectra and imaging observations with Arecibo and Goldstone planetary radar facilities in 2015, 2016, and 2017. We combined our data with published optical photometry to develop a robust physical model. Results. We determine that the rotation pole resides at negative latitudes in an area with a 5° radius close to the south ecliptic pole. The refined sidereal rotation period is 6.536787 ± 0.000007 h. The radar images are best reproduced with a bilobed shape model. Both lobes of 1999 JV6 can be represented as oblate ellipsoids with a smaller, more spherical component resting at the end of a larger, more elongated component. While contact binaries appear to be abundant in the near-Earth population, there are only a few published shape models for asteroids in this particular configuration. By combining the radar-derived shape model with optical light curves we determine a constant-period solution that fits all available data well. Using light-curve data alone we determine an upper limit for YORP of 8.5 × 10−8 rad day−2. Conclusions. The bifurcated shape of 1999 JV6 might be a result of two ellipsoidal components gently merging with each other, or a deformation of a rubble pile with a weak-tensile-strength core due to spin-up. The physical model of 1999 JV6 presented here will enable future studies of contact binary asteroid formation and evolution.

Radar observations and a physical model of contact binary Asteroid 4486 Mithra

Icarus ◽  
2010 ◽  
Vol 208 (1) ◽  
pp. 207-220 ◽  
Author(s):  
Marina Brozovic ◽  
Lance A.M. Benner ◽  
Christopher Magri ◽  
Steven J. Ostro ◽  
Daniel J. Scheeres ◽  
...  
Keyword(s):  
Physical Model ◽  
Radar Observations ◽  
Binary Asteroid ◽  
Contact Binary

A High Order Time Advancement Scheme for Prediction of Solidification Processes

2010 ◽  
Vol 297-301 ◽  
pp. 779-784 ◽  
Author(s):  
A. Abbasnejad ◽  
M.J. Maghrebi ◽  
H. Basirat Tabrizi
Keyword(s):  
Analytical Solutions ◽  
Second Order ◽  
High Order ◽  
Kutta Method ◽  
Third Order ◽  
Runge Kutta Method ◽  
Solidification Processes ◽  
Order Scheme ◽  
High Order Time ◽  
Good Agreement

The aim of this study is the simulation of alloys and pure materials solidification. A third order compact Runge-Kutta method and second order scheme are used for time advancement and space derivative modeling. The results are compared with analytical and semi-analytical solutions and show very good agreement.

Spacecraft trajectory tracking and parameter estimation around a splitting contact binary asteroid

2020 ◽  
Vol 171 ◽  
pp. 280-289
Author(s):  
Tiago M. Silva ◽  
Jean-Baptiste Bouvier ◽  
Kathleen Xu ◽  
Masatoshi Hirabayashi ◽  
Koki Ho
Keyword(s):  
Parameter Estimation ◽  
Trajectory Tracking ◽  
Binary Asteroid ◽  
Spacecraft Trajectory ◽  
Contact Binary

scholarly journals Analysis of the orbital stability close to the binary asteroid (90) Antiope

2020 ◽  
Vol 496 (2) ◽  
pp. 1645-1654
Author(s):  
S Aljbaae ◽  
A F B A Prado ◽  
D M Sanchez ◽  
H Hussmann
Keyword(s):  
Gravitational Field ◽  
Equilibrium Points ◽  
Orbital Stability ◽  
Solar Radiation Pressure ◽  
Equal Mass ◽  
Orbital Dynamics ◽  
Full Potential ◽  
Mass Ratio ◽  
Binary Asteroid ◽  
Polyhedral Shape

ABSTRACT We provide a generalized discussion on the dynamics of a spacecraft around the equal-mass binary asteroid (90) Antiope, under the influence of solar radiation pressure at the perihelion and aphelion distances of the asteroid from the Sun. The polyhedral shape of the components of this asteroid is used to accurately model the gravitational field. Five unstable equilibrium points are determined and classified into two cases that allow classifying of the motion associated with the target as always unstable. The dynamical effects of the mass ratio of our binary system are investigated. We tested massless particles initially located at the periapsis distance on the equatorial plane of the primary of our binary asteroid. Bounded orbits around our system are not found for the longitudes λ ∈ {60, 90, 120, 240, 270, 300}. We also discuss the orbital dynamics in the full potential field of (90) Antiope. The tested motions are mainly dominated by the binary’s gravitational field; no significant effects of the SRP are detected. For λ = 180°, less perturbed orbits are identified between 420 and 700 km from the centre of the system, that corresponds to orbits with Δa < 30 km and Δe < 0.15. All the orbits with initial periapsis distance smaller than 350 km either collide with components of our asteroid or escape from the system.

scholarly journals Surface dynamics, equilibrium points and individual lobes of the Kuiper Belt object (486958) Arrokoth

2020 ◽  
Vol 496 (4) ◽  
pp. 4154-4173 ◽  
Author(s):  
A Amarante ◽  
O C Winter
Keyword(s):  
Equilibrium Points ◽  
Kuiper Belt ◽  
Rotation Period ◽  
Radial Symmetry ◽  
Irregular Shape ◽  
Orbital Energy ◽  
Dynamic Features ◽  
Kuiper Belt Object ◽  
Contact Binary ◽  
Power Curves

ABSTRACT The New Horizons space probe led the first close flyby of one of the most primordial and distant objects left over from the formation of the Solar system, the contact binary Kuiper Belt object (486958) Arrokoth. This is composed of two progenitors, the lobes called Ultima and Thule. In the current work, we investigate Arrokoth’s surface in detail to identify the location of equilibrium points and also we explore each lobe’s individual dynamic features. We assume that Arrokoth’s irregular shape is a homogeneous polyhedra contact binary. We explore its dynamic characteristics numerically by computing its irregular binary geopotential in order to study its quantities, such as geometric height, oblateness, ellipticity and zero-power curves. The stability of Arrokoth Hill was also explored through zero-velocity curves. Arrokoth’s external equilibrium points have no radial symmetry due to its highly irregular shape. We identified even equilibrium points concerning its shape and spin rate: i.e. four unstable external equilibrium points and three inner equilibrium points, where two points are linearly stable, with an unstable central point that has a slight offset from its centroid. Moreover, the large and small lobes each have five equilibrium points with different topological structures from those found in Arrokoth. Our results also indicate that the equatorial region of Arrokoth’s lobes is an unstable area due to the high rotation period, while its polar locations are stable resting sites for surface particles. Finally, the zero-power curves indicate the locations around Arrokoth where massless particles experience enhancing and receding orbital energy.

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