In today’s gravity research there exists a number of gravitational theories which predict the existence of various corrections to the classical gravitational potential. In this paper using the different potentials that exist in the literature and with the help of Gauss’ planetary equations we examine the time rate of change of the Tisserand parameter as a function of the time rate of change of the three orbital elements involved. We find that the Tisserand parameter remains constant over a full orbital revolution in all the different potential resulting from the various theories. This fortifies and generalises the use of Tisserand parameter not only in case of Newtonian dynamics but also in more extended theories of gravity, thus ensuring its validity in determining the identity of a returning comet. Furthermore, we find that the parameter remains unchanged even in the case where a gravitational potential derived from a D-dimensional gravitational force, in the case where D = 4. Next quantization of orbits calculation is performed and the constancy of the Tisserand parameter is also recovered. Finally, assuming fractal orbits we obtain an expression for the fractal dimension of three well known Jupiter family comets in terms of their orbital elements and the constancy of the Tisserand parameter is also recovered.

在当今的引力研究中，存在许多引力理论，它们预测了对经典引力势的各种修正的存在。在本文中，利用文献中存在的不同势并借助高斯行星方程，我们检查了 Tisserand 参数的时间变化率作为所涉及的三个轨道元素的时间变化率的函数。我们发现，在不同理论产生的所有不同势中，蒂瑟兰德参数在整个轨道旋转过程中保持恒定。这不仅强化并推广了蒂瑟兰德参数的使用，不仅适用于牛顿动力学，而且适用于更广泛的引力理论，从而确保了其在确定返回彗星身份方面的有效性。此外，D维引力， D =4的情况。 接下来进行轨道量子化计算，也恢复了Tisserand参数的恒定性。最后，假设分形轨道，我们得到了三个著名木星族彗星的分形维数的轨道元素表达式，并且也恢复了 Tisserand 参数的恒定性。