An improved lunar moment of inertia determination: a proposed strategy

Abstract

The current error of 0.0025 on the lunar homogeneity parameterI/MR 2 is dominated by the uncertainties in theC 20 andC 22 gravity harmonics. This error level is equivalent to a 4.20 gm cm−3 density uncertainty for a lunar interior model having a core 300 km in radius. Covariance analyses are performed using Doppler data from the relay satellite of the proposed Lunar Polar Orbiter mission to determine an optimum reduction strategy which obtains an order of magnitude improvement in the gravity estimates. Error studies show the long-arc reduction method obtains results which are an order of magnitude more accurate than the short-arc technique. The nominal 4000 km circular orbit of the relay satellite is very sensitive to the unmodeled effects of gravity harmonics of degree 5 through 9. Results from this orbital geometry indicate that it may not be possible to achieve the desired order of magnitude accuracy improvement. A modified orbit having the identical orbital conditions as the nominal one, but with a larger semi-major axis of 7000 km is studied. Results show the desired order of magnitude improvement can be achieved when a complete fourth degree and order model and some fifth and sixth degree terms are estimated while considering the unmodeled effects of the remaining harmonics through degree and order eight. Studies also show a 50% additional improvement inC 22 can be achieved if differential differenced Doppler is also processed with the direct Doppler. The improved uncertainty inI/MR 2 reduces the core density error from 4.20 gm cm−3 to 0.1 gm cm−3 for the case of a lunar density model having a 300 km core radius.