When at the beginning of 1600, Kepler arrived to work with Tycho Brahe, Longomontanus, Tycho’s principal assistant, who was working with a model for Mars that predicted with remarkable accuracy its longitudes at oppositions. According to Kepler, this hypothesis “represented all these oppositions within a distance of two minutes in longitude.” The model, however, was unsuccessful in predicting longitudes at other elongations from the Sun, and latitudes even at opposition. Much has been said on how Kepler developed his model after this meeting, arriving finally at the so-called first two laws published in his Astronomia Nova in 1609. By contrast, Longomontanus’ attempt, published as a final model in his Astronomia Danica, has received little scholarly attention. In this paper, I will systematically analyse and explain this model. Even if Longomontanus’ solution is not as elegant as Kepler’s, it deserves scholarly attention, both because it solves the problems posed by the model that he and Tycho were working on when Kepler arrived and because it offers an interesting though heterodox solution that, by contrast, helps to highlight the elegance and simplicity of Kepler’s own solution.

中文翻译：

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Longomontanus 的火星经度模型

1600 年初，开普勒与第谷的主要助手第谷·布拉赫（Longomontanus）一起工作，后者正在研究一个火星模型，该模型以惊人的准确度预测了对冲时的经度。根据开普勒的说法，这个假设“代表了经度两分钟距离内的所有这些对立。” 然而，该模型未能成功预测太阳其他经度处的经度，甚至在对冲时也无法预测纬度。关于开普勒如何在这次会议之后发展他的模型，最终达到了 1609 年发表在他的新天文学中的所谓的前两条定律，已经说了很多。相比之下，朗格蒙塔努斯的尝试，在他的天文学中作为最终模型发表，已经很少受到学术界的关注。在本文中，我将系统地分析和解释这个模型。