Determination of Mercuryʹs 88 day libration and fluid core size from orbit

The requirements for determining the existence and size of the suspected fluid outer core of Mercury are discussed. The moment of inertia Cm of Mercuryʹs solid mantle and crust can be calculated from the amplitude of the 88 day forced libration in longitude and some auxiliary information, since the fluid core will not follow this motion unless its viscosity is much higher than expected. The libration amplitude can be determined from camera observations of the surface near periherm during the Mercury Orbiter mission, provided that the spacecraft location and the camera attitude are measured sufficiently well. The accuracies required are roughly 15 m in the spacecraft coordinate normal to the (polar) orbit plane and 15 arcsec in the camera attitude for 10% accuracy in Cm. The fluid core radius follows from Cm plus the total moment of inertia C and models for the composition and thermal history of the planet. Since maintaining a fluid core appears to require having perhaps 2 or 3% sulfur in the core, determination of the existence and size of the core will provide vital information on mixing of materials between different parts of the solar nebula. In this paper, the accuracy achievable for determining the spacecraft location with an X-band transponder system, as is planned for the mission, is investigated. A very preliminary covariance analysis was carried out based on 65 independent arcs starting every 10 days during the mission, with 6 h of tracking data around periherm for each arc. Gravity field coefficients up to degree and order 26 were solved for, and the effects of uncertainties in the other coefficients up to degree and order 36 were “considered”, along with the effects of uncertainties in some additional parameters. Six of the eight parameters included in the radiation pressure model were “considered” rather than solved for in order to make sure that model uncertainties were allowed for adequately. The 1 m assumed range measurement uncertainty was treated as a bias for each arc rather than a random error. The spacecraft location determination accuracy was found to be consistent with the requirements for measuring Cm to 10% or better accuracy if CmC is about 0.5, as suggested by current models.