Chapter 6, Problem 72GP

Newton had the data listed in Table 6–4, plus the relative sizes of these objects: in terms of the Sun’s radius R, the radii of Jupiter and Earth were 0.0997 R and 0.0109 R. Newton used this information to determine that the average density ρ(= mass/volume) of Jupiter is slightly less than of the Sun, while the average density of the Earth is four times that of the Sun. Thus, without leaving his home planet. Newton was able to predict that the composition of the Sun and Jupiter is markedly different than that of Earth. Reproduce Newton’s calculation and find his values for the ratios ρ_J/ρ_Sun and ρ_E/ρ_Sun (the modern values for these ratios are 0.93 and 3.91, respectively).