Astronomical constants and planetary ephemerides deduced from radar and optical observations

A number of astronomical constants have been deduced by processing planetary radar data spannng the interval from 1959 to July 1966 and U. S. Naval Observatory optical data extending from 1950 to 1965. Results obtained using general relativity [Newtonian] theory with their formal standard errors are: a.u., 499.004786[499.004785]i0.000005 light sec; Mercury radius, 2434[2440]+2 km Venus radius, 6056[6056] 1 km; Mercury mass, 6021000[6029000]+53000; Venus mass, 408250[408450] 120; earth plus moon mass, 328900[328950]+6O; Mars mass, 3111000[3107000] 9000; earth-moon mass ratio 81.3030 [81.3024] 0.005. The planetary masses are given as inverses in terms of the solar mass. Corresponding mass density ratios are 0.9528[0.9527] 0.0008 for Venus/earth and 0.995[0.986] 0.009 for Mercury/earth. The orbital elements of Mercury, Venus, and the earth-moon barycenter were obtained simultaneously and the accompanying formal standard errors are substantially lower than heretofore achieved. The over-all goodness-of-fit measure 1N - E( )i/ffi]2 Ni-1 was 0.63 for general relativity theory and 0.65 for Newtonian theory. Only for the fraction of data com- prising time-delay observations of Mercury was a significant difference between the two theories noted; for this fraction general relativity gave E =0.7 and Newtonian theory 1.3.