Perihelion of Mercury Based on the magnitude of time dilation around the sun and the change in time dilation based on the radius from the sun.
Is there an easy way to calculate the Perihelion of Mercury?
 A: Yes. If we consider the extension of Newtonian gravity that allows the position dependent gravitational time dilation (measurable lapse function), we could obtain the equation for perihelion precession of Mercury that matches observations and coincides with the first correction of the full GR equation. This could be seen in this essay:

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*Hansen, D., Hartong, J., & Obers, N. A. Gravity between Newton and Einstein. Essay for the 2019 Essay Competition of the Gravity Research Foundation, doi, arXiv:1904.05706.

Abstract

Statements about relativistic effects are often subtle. In this essay we will demonstrate that the three classical tests of general relativity, namely perihelion precession, deflection of light and gravitational redshift, are passed perfectly by an extension of Newtonian gravity that includes gravitational time dilation effects while retaining a non-relativistic causal structure. This non-relativistic gravity theory arises from a covariant large speed of light expansion of Einstein's theory of gravity that does not assume weak fields and which admits an action principle.

Perihelion precession would be described by eq. (14) of the essay. Note, that this  would be an easy way (of calculation) only for someone who is already reasonably familiar with GR formalism (or at least with differential geometry).
