Axis Of Maximum Inertia Research Articles

Effects of Grain Alignment with Magnetic Fields on Grain Growth and the Structure of Dust Aggregates

Abstract Dust grains drift through the interstellar medium and are aligned with the magnetic field. Here we study the effect of grain alignment and motion on grain growth in molecular clouds (MCs). We first discuss the characteristic timescales of alignment of the grain axis of maximum inertia ( a ˆ 1) with its angular momentum (J; i.e., internal alignment) and alignment of J with the magnetic field ( B ; i.e., external alignment). We determine the maximum grain size with efficient internal ( a max , aJ ) and external ( a max , JB ) alignment for composite grains. For the MC density of n H ∼ 103–108 cm−3, we find that external alignment can occur for very large grains, but internal alignment only occurs for grains smaller than a max , aJ ∼ 2 μ m . The presence of iron clusters within dust grains or suprathermal rotation increases a max , aJ to ∼10–50 μm. We then study the growth of aligned grains drifting through the gas. Due to the motion of aligned grains across the magnetic field, gas accretion would increase the grain elongation rather than decrease, as expected from the growth of randomly oriented grains. Coagulation by grain collisions also increases grain elongation, leading to the increase of elongation with the grain size. The coagulation of aligned grains forms dust aggregates that contain elongated binaries comprising a pair of grains with parallel short axes. Grains within dust aggregates in 67P/Churyumov–Gerasimenko obtained by Rosetta have the grain elongation increasing with the grain radius, implying that such dust aggregates might form from aligned grains.

The eccentric case of a fast-rotating, gravity-gradient-perturbed satellite attitude solution

A closed-form first-order perturbation solution for the attitude evolution of a triaxial space object in an elliptical orbit is presented. The solution, derived using the Lie–Deprit method, takes into account gravity-gradient torque and is facilitated by an assumption of fast rotation of the object. The formulation builds on the earlier implementation of Lara and Ferrer, which assumes a circular orbit. The previously presented work—which assumes spin about an object’s axis of maximum inertia—is further extended by the explicit presentation of the transformations required to apply the solution to an object spinning about its axis of minimum inertia. Additionally, several numerical analyses are presented to more completely assess the utility of the solution. These studies (1) validate the elliptical solution, (2) assess the impact of varying the small parameter of the perturbation procedure, (3) analyze the assumption of fast rotation, and (4) apply the solution to the common and important scenario of a tumbling rocket body.

Rapid Charged Geosynchronous Debris Perturbation Modeling of Electrodynamic Disturbances

Charged space objects experience small perturbative torques and forces from their interaction with Earth’s magnetic field. These small perturbations can change the orbits of lightweight, uncontrolled debris objects dramatically even over short periods. This paper investigates the effects of the isolated Lorentz force, the effects of including or neglecting this and other electromagnetic perturbations in a full propagation, and then analyzes for which objects electromagnetic effects have the most impact. It is found that electromagnetic forces have a negligible impact on their own. However, if the center of charge is not collocated with the center of mass, electromagnetic torques are produced which do impact the attitude, and thus the position by affecting the direction and magnitude of the solar radiation pressure force. The objects for which electrostatic torques have the most influence are charged above the kilovolt level, have a difference between their center of mass and center of charge, have highly attitude-dependent cross-sectional area, and are not spinning stably about an axis of maximum inertia. Fully coupled numerical simulation illustrate the impact of electromagnetic disturbances through the solar radiation pressure coupling.

Radiation-induced torques on spheroids

Radiation-induced torques on ellipsoids of revolution are discussed. Exact formulae for the thermal YORP torques are given in terms of elliptic integrals. It is demonstrated that in the absence of thermal inertia, the average values of dynamically significant projections of these torques are zero if a spheroid rotates around the axis of maximum inertia and if there are no resonances between rotation and orbital motion. The thermal lag leads to a systematic drift in the obliquity, but it does not affect the rotation period. The direct radiation pressure torques on spheroids are shown to be zero.

Radiation-induced torques on spheroids

Radiation-induced torques on ellipsoids of revolution are discussed. Exact formulae for the thermal YORP torques are given in terms of elliptic integrals. It is demonstrated that in the absence of thermal inertia, the average values of dynamically significant projections of these torques are zero if a spheroid rotates around the axis of maximum inertia and if there are no resonances between rotation and orbital motion. The thermal lag leads to a systematic drift in the obliquity, but it does not affect the rotation period. The direct radiation pressure torques on spheroids are shown to be zero.

Long‐term rotation and mantle dynamics of the Earth, Mars, and Venus

In response to internal and surface tectonic processes the terrestrial planets have the ability to displace the axis of rotation with respect to the mantle. This behavior is quantified by means of a nondimensional number, defined here as the rotational number Ro, that allows classification of the planets into two categories, the first containing Mars and the Earth, where true polar wander is a feasible mechanism, and the second, to which Venus belongs, where rotation equilibrium is attained by means of mega‐wobbles driven by internal mass anomalies. The number Ro is related to the timescale characterizing the readjustment of the equatorial bulge during long‐term polar motion and to the length of the sidereal day. If these two timescales are well separated, the planet experiences true polar wander. Nonlinear Liouville equations for stratified viscoelastic bodies with linear Maxwell rheology are solved in order to assess the relevance of surface and mantle processes in driving long‐term rotation instabilities in the terrestrial planets. The amount of true polar wander estimated for the Earth and Mars is reproduced correctly by our modeling with mantle viscosities and lithospheric thickness consistent with other studies. The major difference between the Earth and Mars is the driving mechanism, subduction for the Earth and lithospheric loading for Mars. When mantle viscosities similar to those of the Earth are considered for Venus, the most updated estimate for the offset of about 0.5° between the rotation axis and the axis of maximum inertia is well reproduced during the mega‐wobbles induced by internal mass redistribution. We show that the degree 2 topography of these three planets can be affected by their rotation, which is responsible for the dominance of the sectorial component on the Earth and Mars and for the zonal component on Venus.

A Torque-Free Flexible Model Gyro

The present investigation is concerned with the behavior of an elastic, oblate, torquefree gyro model. The model has been devised such that it represents accurately arbitrarily large attitudes and arbitrarily large deformations. All simplifying assumptions are incorporated into the model before the theory is applied. The subsequent theoretical development is consequently exact; i.e., the expressions for inertia moments, angular moments, kinetic and elastic energies are all exact. Also, the mass center of the model gyro does not shift within the gyro. Equations remain tractable and the practicing engineer can readily get a feel for the phenomena uncovered. The model is composed of a rigid massless rod connected elastically to a rigid massive disk. At the tip of each rod there is a point mass. The nonlinear equations of quasistatic motion are derived using Euler’s law, and a floating coordinate frame. Following the analysis, various numerical examples are investigated and the results are plotted. The total mechanical energy of the system is determined, and the condition for existence of an energy trap state (minimum energy state at an attitude other than zero) is obtained. When trapped, the gyro is in effect rigid, has a stable attitude, and rotates around the principal axis of maximum inertia, which in turn is collinear with the space-fixed angular momentum vector.

Determination of the earth’s pole of rotation from laser range observations to satellites

The methods of using earth satellites for determining the motion of the earth’s axis of rotation and of the earth’s principal axis of maximum inertia are discussed.