Horava–Lifshitz gravity: calculation of radar signal delay contribution in the vicinity of the Sun in the Kehagias–Sfetsos solution

There has been a renewed interest in the recent years for the study of gravitational theories alternative to General Relativity (GR). This results from current observations that seem to question the role of General Relativity theory at large distances, i.e., galactic and cosmological ones. An example of such theories is that of Modified Newtonian Dynamics or (MOND). In an effort for a description of gravitation in a quantum framework Horava has recently proposed the Horava–Lifshitz gravity (HL). Our goal is to study the effect of radar signal delays in the vicinity of the sun for the Kehagias–Sfetsos space-time solution of the Horava–Lifshitz modified gravity. For that we use a spherically symmetric modified solar system space-time metric and we calculate the radar signal delay correction as a function of the non-dimensional HL parameter ψ. Next expressing ψ as a function of the planetary orbital elements we derive an expression for the Kehagias–Sfetsos radar time delay solution, which next calculate for all the planets in the solar system excluding Pluto. Finally, for the planets Mercury to Neptune, we obtain radar time delays in the range of \(531\times 10^{-9}~\mathrm{ps} \le t_{\mathit{KS}_{\mathit{MER}}} \le 5379.86~\mathrm{ps}\) for the planets Mercury to Neptune.