发表机构
Institute of Astronomy, V. N. Karazin Kharkiv National University; Zentrum für Astronomie, Institut für Theoretische Astrophysik, Universität Heidelberg; Smead Department of Aerospace Engineering Sciences, University of Colorado Boulder（哈尔科夫国立大学天体物理研究所; 海德堡大学天文学中心理论天体物理研究所; 科罗拉多大学博尔德分校斯米德航空航天工程科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文解析求解热传导方程，建立了小行星表面单元雅科夫斯基效应的4项解析表达式，精度达15%，并拟合出0.15%精度的表达式，优于传统3参数拟合，进而给出球形小行星的雅科夫斯基力表达式。
AI 中文摘要
我们研究了由小行星上一个平面表面单元产生的雅科夫斯基效应如何依赖于热参数。然后，我们将雅科夫斯基力在球形小行星的表面上进行积分。在本系列的后续文章中，我们将研究形状更复杂的天体的雅科夫斯基力，并计算小行星轨道的变化。利用微扰理论，我们解析地求解了表面单元下的一维热传导方程，并利用该解解析地计算了热参数大和小极限情况下的雅科夫斯基效应。然后，我们解析地将这两个解拼接起来，得到一个对热参数大和小都适用的雅科夫斯基效应的近似表达式。我们通过将其与热传导方程的数值解结果进行比较来验证它。最后，我们拟合近似解析表达式中的参数，以提高与数值结果的一致性。我们得到了一个表面单元的雅科夫斯基效应的完全解析表达式，该表达式由4项组成，对于任何热参数值，精度可达15%。我们还提出了一个相同形式的拟合表达式，其精度可达0.15%。这两者都大大优于传统的3参数拟合，后者产生的误差高达50%，特别是对于小的热参数值，其误差约为2倍。最后，我们应用新的形式体系来评估作用在球形小行星上的雅科夫斯基力的解析表达式，最终得到了一个对于0倾角、圆轨道小行星精度为0.1%的拟合表达式，以及一个对于一般情况精度较低的表达式。
英文摘要
We investigate how the Yarkovsky effect created by one flat surface element on the asteroid depends on the thermal parameter. Then we integrate the Yarkovsky force over the surface of a spherical asteroid. In the next articles of the series, we will investigate the Yarkovsky force for bodies of more complicated shape and compute the change of the asteroid's orbit. Using perturbation theory, we analytically solve the one-dimensional heat conduction equation under the surface element and use the solution to analytically compute the Yarkovsky effect in the limiting cases of big and small thermal parameters. Then we analytically sew the two solutions to obtain an approximate expression for the Yarkovsky effect valid for both large and small thermal parameters. We verify it by comparing it to the results of the numerical solution of the heat conduction equation. Finally, we fit the parameters in an approximate analytical expression to improve the agreement with the numerical results. We obtain a fully analytical expression for the Yarkovsky effect of one surface element, which is composed of 4 terms and is precise for any value of the thermal parameter up to the accuracy of 15%. We also propose a fitted expression of the same form, which is precise up to 0.15%. They both much supersede the traditionally used 3-parameter fit, which produces an error up to 50% and, in particular, is about a factor of 2 wrong for small values of thermal parameters. Finally, we apply the new formalism to evaluate an analytical expression for the Yarkovsky force acting on a spherical asteroid, ending up in a 0.1%-accurate fitted expression for an asteroid with 0 obliquity on a circular orbit and a less accurate expression for the general case.
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