Abstract

A mean-element differential equation system is solved analytically in the first approximation in a small parameter to investigate the orbital evolution of an asteroid moving under the attraction of the Sun and additional perturbing acceleration \({\mathbf{P}} = {\mathbf{P}}{\kern 1pt}' {\text{/}}{{r}^{2}}\), which arises due to the Yarkovsky effect. Here, \(r\) is the heliocentric distance; the modulus of \({\mathbf{P}}{\kern 1pt} '\) is small in comparison with the main acceleration caused by the attraction of the Sun; the vector \({\mathbf{P}}{\kern 1pt} '\) components (\(S,\;T,\;W\)) are constant in a reference frame with the origin in the central body and axes directed along the radius vector, the transversal (perpendicular to the radius vector in the osculating plane in the direction of motion), and the binormal (directed along the area vector). The values of \(S\), \(T\), \(W\), which are necessary for considering the Yarkovsky effect, can be found either as additional parameters when determining the orbit from observations or by using thermophysical models of the Yarkovsky acceleration. The first approach requires high-precision astrometry for a long period of time; the second one requires knowing the asteroid’s thermophysical characteristics and rotation parameters. In this paper, the semimajor axis drift is calculated for 23 asteroids with transversal acceleration determined by the first approach, taken from different publications. Comparative analysis shows good agreement with the results obtained in other works. Within the second approach, a linear thermophysical model for the Yarkovsky force for spherical asteroids and equations for the force components in a radius-vector-bound reference frame serves as a basis for determining nongravitational parameters for the asteroid 1685 Toro (1948 OA): \({{A}_{1}} = S{\text{/}}r_{0}^{2} = (7.96_{{ - 3.48}}^{{ + 2.72}}) \times {{10}^{{ - 15}}}\) AU/d², \({{A}_{2}} = T{\text{/}}r_{0}^{2} = ( - 3.24_{{ - 0.57}}^{{ + 0.42}}) \times {{10}^{{ - 15}}}\) AU/d², \({{A}_{3}} = W{\text{/}}r_{0}^{2} = 0\) (\({{r}_{0}} = \) 1 AU). The next step for 1685 Toro is to find the eccentricity drift, semimajor axis drift, and mean anomaly drift and estimate the asteroid’s displacement from the nonperturbed position over 1000 revolutions around the Sun (1600 yr). Considering the uncertainties for the parameters \({{A}_{1}}\) and \({{A}_{2}}\), the advancement in the mean anomaly is \(2.50' \) to \(3.28' \), and the displacement is 143 000 to 188 000 km.

中文翻译：

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扰动加速度随平方反比定律变化的中心场运动：在Yarkovsky效应中的应用

摘要

用一个小参数对一阶均值微分方程组进行解析求解，以研究小行星在太阳的吸引力和附加扰动加速度下运动的轨道演化\（{\ mathbf {P}} = {\ mathbf {P}} {\ kern 1pt}'{\ text {/}} {{r} ^ {2}} \），这是由于Yarkovsky效应而产生的。在这里，\（r \）是日心距；\（{\ mathbf {P}} {\ kern 1pt}'\）的模量与由太阳的吸引力引起的主要加速度相比较小；向量\（{\ mathbf {P}} {\ kern 1pt}'\）分量（\（S，\; T，\; W \））在参考系中是恒定的，其原点在中心体中，并且轴沿半径矢量，横向（垂直于在运动方向上的切平面中的半径矢量）和双法线（沿着面积矢量定向） ）。的值\（S \） ，\（T \） ，\（W \）可以根据考虑确定Yarkovsky效应的必要条件找到，这可以作为从观测中确定轨道时的附加参数，也可以使用Yarkovsky加速度的热物理模型找到。第一种方法需要长时间的高精度天体测量。第二个要求知道小行星的热物理特征和旋转参数。在本文中，计算了23种小行星的半长轴漂移，这些小行星的横向加速度由第一种方法确定，取自不同的出版物。对比分析显示与其他工作中获得的结果吻合良好。在第二种方法中，\（{{{A} _ {1}} = S {\ text {/}} r_ {0} ^ {2} =（7.96 _ {{-3.48}} ^ {{+ 2.72}}）\次{{ 10} ^ {{--15}}} \） AU / d ²，\（{{A} _ {2}} = T {\ text {/}} r_ {0} ^ {2} =（-3.24_ {{-0.57}} ^ {{+ 0.42}}）\ times {{10} ^ {{-15}}} \） AU / d ²，\（{{A} _ {3}} = W {\文本{/}} r_ {0} ^ {2} = 0 \）（\（{{r} _ {0}} = \） 1 AU）。1685年托罗（Toro）的下一步是找到偏心率漂移，半长轴漂移和平均异常漂移，并估计小行星在围绕太阳（1600年）旋转1000圈后从非扰动位置的位移。考虑参数\（{{A} _ {1}} \）和\（{{A} _ {2}} \）的不确定性，平均异常的进展为\（2.50'\）到\（3.28'\），位移为143 000至188 000 km。