In Chapter 16 of Astronomia nova, Kepler describes and applies a method for finding the parameters of what he will call the vicarious hypothesis: a model that still assumes circular orbits and an equant point, but does not assume the bisection of the eccentricity, that is, that the center of the orbit is halfway between the equant point and the Sun. The method allows Kepler to find independently both centers in a very elegant way, but its application is tedious. He confesses that he had to apply it seventy times over a period of 5 years to obtain trustable results. Years earlier, when Kepler arrived to work with Tycho, he found that Tycho and Longomontanus had rejected bisection and somehow had obtained a ratio between eccentricities that, as Kepler himself highlights, happened to be very close to the one Kepler would later find after so much effort. Kepler does not say how Tycho and Longomontanus obtained their parameters and, to the best of my knowledge, there is no single published work that attempts to answer this question. Still, it is a very interesting question to ask how they arrived at values so close to those that took so much pain for Kepler to obtain. Recently, I published a paper describing a method Tycho used for finding Saturn’s parameters. In this paper, I show that by applying this method to the data of Tychonic observations of oppositions, it is possible to arrive at parameters very close to those that we know Tycho found. In this way, I argue that this is the method Tycho applied for obtaining Mars’s parameters. The simplicity of the Tychonic method contrasts with the complexity of Kepler’s.

在《天文学新星》第16章中，开普勒描述并应用了一种方法来寻找他所谓的替代假设的参数。：一个模型，该模型仍假定圆轨道和等点，但不假定偏心率的二等分，即，轨道的中心位于等点和太阳之间的一半。该方法允许开普勒以非常优雅的方式独立地找到两个中心，但是其应用很繁琐。他承认，为了获得可信赖的结果，他必须在5年的时间内应用70次。几年前，当开普勒到达第谷工作时，他发现第谷和Longomontanus拒绝了二等分，并且以某种方式获得了偏心率之间的比率，正如开普勒本人所强调的那样，恰好与开普勒后来发现的那部分相差甚远。努力。开普勒没有透露第谷和隆戈蒙塔努斯是如何获得参数的，据我所知，没有任何出版的作品试图回答这个问题。但是，询问它们如何达到与开普勒难以承受的痛苦如此接近的价值仍然是一个非常有趣的问题。最近，我发表了一篇论文，描述了第谷草用于查找土星参数的方法。在本文中，我证明了通过将这种方法应用于反对派的强音观测资料，可以得出非常接近我们知道的第谷发现的参数。这样，我认为这是第谷用来获取火星参数的方法。Tychonic方法的简单性与开普勒方法的复杂性形成对比。我发表了一篇论文，描述了Tycho用于查找土星参数的方法。在本文中，我证明了通过将这种方法应用于反对派的强音观测资料，可以得出非常接近我们知道的第谷发现的参数。这样，我认为这是第谷用来获取火星参数的方法。Tychonic方法的简单性与开普勒方法的复杂性形成对比。我发表了一篇论文，描述了Tycho用于查找土星参数的方法。在本文中，我证明了通过将这种方法应用于反对派的强音观测资料，可以得出非常接近我们知道的第谷发现的参数。这样，我认为这是第谷用来获取火星参数的方法。Tychonic方法的简单性与开普勒方法的复杂性形成对比。