A HERO for General Relativity

Abstract

HERO (Highly Eccentric Relativity Orbiter) is a space-based mission concept aimed to perform several tests of post-Newtonian gravity around the Earth with a preferably drag-free spacecraft moving along a highly elliptical path fixed in its plane undergoing a relatively fast secular precession. We considered two possible scenarios—a fast, 4-h orbit with high perigee height of 1047 km and a slow, 21-h path with a low perigee height of 642 km . HERO may detect, for the first time, the post-Newtonian orbital effects induced by the mass quadrupole moment J 2 of the Earth which, among other things, affects the semimajor axis a via a secular trend of ≃4–12 cm yr − 1 , depending on the orbital configuration. Recently, the secular decay of the semimajor axis of the passive satellite LARES was measured with an error as little as 0 . 7 cm yr − 1 . Also the post-Newtonian spin dipole (Lense-Thirring) and mass monopole (Schwarzschild) effects could be tested to a high accuracy depending on the level of compensation of the non-gravitational perturbations, not treated here. Moreover, the large eccentricity of the orbit would allow one to constrain several long-range modified models of gravity and accurately measure the gravitational red-shift as well. Each of the six Keplerian orbital elements could be individually monitored to extract the G J 2 / c 2 signature, or they could be suitably combined in order to disentangle the post-Newtonian effect(s) of interest from the competing mismodeled Newtonian secular precessions induced by the zonal harmonic multipoles J ℓ of the geopotential. In the latter case, the systematic uncertainty due to the current formal errors σ J ℓ of a recent global Earth’s gravity field model are better than 1 % for all the post-Newtonian effects considered, with a peak of ≃ 10 − 7 for the Schwarzschild-like shifts. Instead, the gravitomagnetic spin octupole precessions are too small to be detectable.