CONSTRAINTS ON DENSITY MODELS FROM RADIAL MOMENTS - APPLICATIONS TO EARTH, MOON, AND MARS

Few objective constraints exist on radial density variations in planet ary interiors. Even if the mean density and mean moment of inertia wer e known with perfect accuracy, they would only provide integral constr aints on the density models. However, among the family of monotonic ra dial density models with a given mean density and mean moment of inert ia, the simple two-layer piecewise constant models have useful extrema l properties. The model has only three parameters, an inner density, a n outer density, and a transition radius. Once the radial moment const raints are applied, there is only one remaining degree of freedom. If the outer region density is somehow specified, then the inner region d ensity of the two-layer model provides a firm lower bound on central d ensity of monotonic models. Likewise, if an upper bound on central den sity call be provided, then the two-layer model provides a lower bound on outer region density. An envelope of acceptable density models can be generated by scanning the transition depth from the center to the surface. Any monotonic model with specified mean density and mean iner tial moment must lie within that envelope. Resulting extremal density envelopes for the Earth, Moon, and Mars are compared to published radi al density profiles. For the Moon, the moment constraints are quite re strictive. For the Earth, which is more centrally condensed, the allow ed envelope of density profiles is rather broad. Mars is an intermedia te case. Present geodetic and astrometric observations only constrain the Martian mean moment of inertia to lie somewhere in the range 0.325 less than or equal to I/MR(2) < 0.365. However, our analysis shows th at any value within that range can be accommodated without invoking ge ochemically implausible density minima or maxima.