This paper has a didactic aim. Indeed, starting from the well-known principle of free fall discovered by Galileo Galilei, we want to make some reflections that we consider useful for secondary school students. Being the acceleration invariant with respect to Galilei’s transformations, it is useful to underline that the free fall in a gravitational field is independent of the mass of the body that falls only if the attractive mass is an inertial frame. In general, the corrections to the motion of a test particle falling in a gravitational field due to its mass can be easily calculated avoiding misinterpretations of Galileo’s principle. Moreover, it may be useful to observe that, in the case of periodic motions, these corrections increase with time and would lead, over the centuries, to not negligible effects.

中文翻译：

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行星轨道周期的质量依赖校正

本文具有教学目的。的确，从伽利略·伽利利（Galileo Galilei）发现的众所周知的自由落体原理开始，我们想作一些思考，我们认为这些思考对中学生有用。作为相对于伽利略变换而言的加速度不变性，有必要强调指出，引力场中的自由落体仅与吸引力的质量是惯性系时才下降的物体的质量无关。通常，可以很容易地计算出由于质量而落入重力场的测试粒子运动的校正，从而避免误解伽利略原理。此外，可能有用的是观察到，在周期性运动的情况下，这些校正会随着时间的流逝而增加，并且在数个世纪之内将导致不可忽略的影响。