Instability of the planetary orbits for space-time dimensions higher than four

TL;DR

This paper demonstrates that planetary orbits are only stable in space-times with four or fewer dimensions, highlighting the instability in higher-dimensional models.

Contribution

It provides a clear, didactic proof that planetary orbit stability is limited to four-dimensional space-time, extending understanding of higher-dimensional physics.

Findings

Planetary orbits are stable only in four or fewer dimensions.

Higher dimensions lead to orbital instability.

The proof is accessible and pedagogical.

Abstract

It is shown that in a Minkowski space of total space-time dimension $D=d+1$, the orbits of the planetary motion are stable only if the total dimension of space-time is $D\le 4$. The proof is performed in a fully didactic way.