AbstractUsing PREM as a reference model for the Earth density distribution we investigate the sensitivity of ORCA detector to deviations of the Earth (i) outer core (OC) density, (ii) inner core (IC) density, (iii) total core density, and (iv) mantle density, from their respective PREM densities. The analysis is performed by studying the effects of the Earth matter on the oscillations of atmospheric$$\nu _{\mu }$$νμ,$$\nu _e$$νe,$${\bar{\nu }}_\mu $$ν¯μand$${\bar{\nu }}_e$$ν¯e. We present results which illustrate the dependence of the ORCA sensitivity to the OC, IC, core and mantle densities on the type of systematic uncertainties used in the analysis, on the value of the atmospheric neutrino mixing angle$$\theta _{23}$$θ23, on whether the Earth mass constraint is implemented or not, and on the way it is implemented, and on the type – with normal ordering (NO) or inverted ordering (IO) – of the light neutrino mass spectrum. We show, in particular, that in the “most favorable” NO case of implemented Earth mass constraint, “minimal” systematic errors and$$\sin ^2\theta _{23}=0.58$$sin2θ23=0.58, ORCA can determine, e.g., the OC (mantle) density at$$3\sigma $$3σC.L. after 10 years of operation with an uncertainty of (− 18%)/+ 15% (of (− 6%)/+ 8%). In the “most disfavorable” NO case of “conservative” systematic errors and$$\sin ^2\theta _{23}=0.42$$sin2θ23=0.42, the uncertainty on OC (mantle) density reads (− 43%)/+ 39% ((− 17%/+ 20%), while for for$$\sin ^2\theta _{23} = 0.50$$sin2θ23=0.50and 0.58 it is noticeably smaller: (− 37)%/+ 30% and (− 30%)/+ 24% ((− 13%)/+ 16% and (− 11%/+ 14%)). We find also that the sensitivity of ORCA to the OC, core and mantle densities is significantly worse for IO neutrino mass spectrum.