具有椭圆截面的均匀环面的外引力势：I.用两个巨大的圆圈表示
Outer gravitational potential of a homogeneous torus with an elliptical cross-section: I. Representation by two massive circles
摘要：
本文讨论了均匀椭圆截面环面的引力势。我们提出了一个新的表达式，它的引力势是有效的，在空间的任何一点，通过建模的环面与一组大规模的圆（无限薄环）。我们发现外势可以用两个质量为环面质量一半的大质量圆的势来表示，具有很好的精度。这些大质量圆在沿长轴的两点处与椭圆形截面相交，这两点在相反的方向上，并且在到截面的焦点的距离的一半处。相同的公式适用于两种情况：扁圆和长轴横截面。对于环面的长截面的情况下，到大质量圆的距离是虚的和共轭的，但是在这种情况下环面势的值是实的。所得到的近似是鲁棒的误差图显示。
英文摘要：
This paper deals with the gravitational potential of a homogeneous torus with elliptical cross-section. We present a new expression for its gravitational potential which is valid in any point of the space, obtained by modeling the torus with a set of massive circles (infinitely thin rings). We found that the outer potential can be represented with good accuracy by the potential of two massive circles with masses which are half of the torus mass. These massive circles intercept the elliptical cross-section at two points along the major axis which are in opposite directions and at half of the distances to the foci of the cross-section. The same formula works for both cases: oblate and prolate cross-sections. For the case of the prolate cross-section of the torus the distances to massive circles are imaginary and conjugate ones but the values of the torus potential for this case are real. The obtained approximation is robust as the error maps show.
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