Abstract
THE prominence you give to M. F. Ollive's note in Comptes rendus, tome 157, No. 26, induces me to point out that M. Ollive's so-called empirical formula is really a simple statement about the densities of the planets. The formula is r3 = kRR′v′2, where r is the mean radius of any planet, R its mean distance from the Sun, R′ the mean distance of any satellite from its primary, and v′ the mean orbital velocity of the satellite. v′2R′ for any satellite can be replaced by γM, where γ is the gravitation constant, and M is the mass of its primary, since we can ignore the mass of the planet as compared with its primary. We get then r3 = k′RM, where k′ is a new constant. But M = ¾πρr3 where ρ is the mean density of a planet. Thus we get Rρ = constant. This is what M. Ollive's formula amounts to. In other words, his formula does not derive any generality by the introduction of the satellites. The fact that his results for the various satellites of any given primary agree inter se is merely Kepler's third law.
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BRODETSKY, S. The Densities of the Planets. Nature 93, 33 (1914). https://doi.org/10.1038/093033a0
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DOI: https://doi.org/10.1038/093033a0
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