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

$1047\phantom{\rule{0.166667em}{0ex}}\mathrm{km}$ and a slow, 21-h path with a low perigee height of

$642\phantom{\rule{0.166667em}{0ex}}\mathrm{km}$ . 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

$\mathrm{cm}\phantom{\rule{0.166667em}{0ex}}{\mathrm{yr}}^{-1}$ , 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

$0.7\phantom{\rule{0.166667em}{0ex}}\mathrm{cm}\phantom{\rule{0.166667em}{0ex}}{\mathrm{yr}}^{-1}$ . 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

${J}_{\ell}$ of the geopotential. In the latter case, the systematic uncertainty due to the current formal errors

${\mathsf{\sigma}}_{{J}_{\ell}}$ of a recent global Earth’s gravity field model are better than

$1\%$ for all the post-Newtonian effects considered, with a peak of

$\simeq {10}^{-7}$ for the Schwarzschild-like shifts. Instead, the gravitomagnetic spin octupole precessions are too small to be detectable.

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