The mass,gravity field,and ephemeris of Mercury

This paper represents a final report on the gravity analysis of radio Doppler and range data generated by the Deep Space Network (DSN) with Mariner 10 during two of its encounters with Mercury in March 1974 and March 1975. A combined least-squares fit to Doppler data from both encounters has resulted in a determination of two second degree gravity harmonics, J₂ = (6.0 ± 2.0) × 10⁻⁵ and C₂₂ = (1.0 ± 0.5) × 10⁻⁵, referred to an equatorial radius of 2439 km, plus an indication of a gravity anomaly in the region of closest approach of Mariner 10 to Mercury in March 1975 amounting to a mass deficiency of about GM = −0.1 km³sec⁻². An analysis is included that defends the integrity of previously published values for the mass of Mercury (H. T. Howard et al. 1974, Science 185, 179–180; P. B. Esposito, J. D. Anderson, and A. T. Y. Ng 1978, COSPAR: Space Res. 17, 639–644). This is in response to a published suggestion by R. A. Lyttleton (1980, Q. J. R. Astron. Soc. 21, 400–413; 1981, Q. J. R. Astron. Soc. 22, 322–323) that the accepted values may be in error by more than 30%. We conclude that there is no basis for being suspicious of the earlier determinations and obtain a mass GM = 22,032.09 ± 0.91 km³sec⁻² or a Sun to Mercury mass ratio of 6,023,600 ± 250. The corresponding mean density of Mercury is 5.43 ± 0.01 g cm⁻³. The one-sigma error limits on the gravity results include an assessment of systematic error, including the possibility that harmonics other than J₂and C₂₂ are significantly different from zero. A discussion of the utility of the DSN radio range data obtained with Mariner 10 is included. These data are most applicable to the improvement of the ephemeris of Mercury, in particular the determination of the precession of the perihelion.