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Surface gravity of rotating dumbbell shapes
Astrophysics and Space Science ( IF 1.9 ) Pub Date : 2021-03-10 , DOI: 10.1007/s10509-021-03934-6
Wai-Ting Lam , Marian Gidea , Fredy R. Zypman

We investigate the problem of determining the shape of a rotating celestial object – e.g., a comet or an asteroid – under its own gravitational field. More specifically, we consider an object symmetric with respect to one axis – such as a dumbbell – that rotates around a second axis perpendicular to the symmetry axis. We assume that the object can be modeled as an incompressible fluid of constant mass density, which is regarded as a first approximation of an aggregate of particles.

In the literature, the gravitational field of a body is often described as a multipolar expansion involving spherical coordinates (Kaula, 1966). In this work we describe the shape in terms of cylindrical coordinates, which are most naturally adapted to the symmetry of the body, and we express the gravitational potential generated by the rotating body as a simple formula in terms of elliptic integrals. An equilibrium shape occurs when the gravitational potential energy and the rotational kinetic energy at the surface of the body balance each other out. Such an equilibrium shape can be derived as a solution of an optimization problem, which can be found via the variational method. We give an example where we apply this method to a two-parameter family of dumbbell shapes, and find approximate numerical solutions to the corresponding optimization problem.



中文翻译:

旋转哑铃形状的表面重力

我们研究确定在其自身引力场下确定旋转天体(例如,彗星或小行星)的形状的问题。更具体地说,我们认为一个对象相对于一个轴对称(例如哑铃),该对象围绕垂直于对称轴的第二个轴旋转。我们假设可以将对象建模为质量密度恒定的不可压缩流体,这被视为粒子集合的第一近似值。

在文献中,人体的引力场通常被描述为涉及球坐标的多极膨胀(Kaula,1966)。在这项工作中,我们用圆柱坐标来描述形状,而圆柱坐标最自然地适合于物体的对称性,并且用椭圆积分将旋转物体产生的重力势表示为简单公式。当重力势能和身体表面的旋转动能相互平衡时,就会出现平衡形状。这种平衡形状可以作为优化问题的解决方案而得出,该问题可以通过变分方法找到。我们举一个例子,说明如何将此方法应用于两个参数的哑铃形状系列,

更新日期:2021-03-10
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