  Using PREM as a reference model for the Earth density distribution we
investigate in the present article the sensitivity of the 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 $\nu_{\mu}$, $\nu_e$, $\bar{\nu}_\mu$
and $\bar{\nu}_e$. We present results which, in particular, 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 $\theta_{23}$, 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
$\sin^2\theta_{23}=0.58$, ORCA can determine, e.g., the OC (mantle) density at
$3\sigma$ C.L. after 10 years of operation with an uncertainty of (-18\%)/+15\%
(of (-6\%)/+8\%). In the "most unfavourable" NO case of "conservative"
systematic errors and $\sin^2\theta_{23}=0.42$, the uncertainty reads
(-43\%)/+39\% ((-17\%/+20\%), while for for $\sin^2\theta_{23} = 0.50$ and 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 outer core,
core and mantle densities is significantly worse for IO neutrino mass spectrum.
