Following Kepler's publication of his 3rd law of planetary motion1,
$$p^2 / r^3 = 1$$
in 1619, it would have been possible to use telescopic observations to arrive at an estimate of the orbital radii the Jovian moons observed by Galileo 1610, expressed in Earth orbital radii.2 Along with the observed periods of the moons, these radii could have been used in a Jovian version Kepler's formula to discover that (at least for Io, Europa, and Callisto3)
$$p^2 / r^3 \approx 1.053 \times 10^3$$
or as close as telescopic technology of the day would allow.
Did anyone at the time take this, or a similar approach, to arrive at the conclusion that there is an attribute the Sun and Jupiter in which they differ by a factor of approximately a thousand? That attribute, of course, turns out to be mass.
Did Kepler, Galileo, or any of their contemporaries perform this calculation in the early 1600s? If not, why?
1. For $p$ in Earth years and $r$ in Earth orbital radii (today's AU).
2. Applying trigonometry to the observed angular extent of the moons' orbits and the distance to Jupiter.
3. Ganymede produces a slightly different value.
Best Answer
No. Johannes Kepler published what is now known as his third law of planetary motion in 1619 (in his treatise Harmonices Mundi), but discovered it already on May 15, 1618. He simply related mean distance of a planet from the Sun to its mean angular motion, without a word about a mass, I think. He did write on gravity and mass (not the precise physical term) in a foreword to his earlier book Astronomia Nova.
Thanks to people (Rafael Gil Brand, Roger Ceragioli and R. H. van Gent) from H-ASTRO discussion forum I have the following update #1:
1, The original form of the third law (formulated for planets), freely traslated to English reads approximately:
"...it is absolutely certain and perfectly correct, that the ratio which exists between the periodic times of any two planets is precisely 3/2 of the ratio of the mean distances, i.e. of the spheres themselves, bearing in mind, however, that the arithmetic mean between both diameters of the elliptic orbit is slightly less than the longer diameter"
2, Although (as far as I know from my own experience with early observations of double stars by Galileo) it is virtually impossible to prove that an earlier observation/idea didn't exist, it seems that the first application of Kepler's Third Law to the Jovian satellite system, is found in Newton's Philosophiae Naturalis Principia Mathematica (2nd ed. of 1713), lib. III, prop. 8, resulting in 1/1033 solar mass.
It is possible that Riccioli had something about the topic in one of his monumental treatises published around the middle of the 17th century.
Update #2
Riccioli seem to discuss relation between elongation of Galilean satellites of Jupiter and their orbital periods both in his Almagestum Novum and Astronomia Reformata, and cites Vendelinus (Godefroy_Wendelin). The Wikipedia entry for him states:
"In 1643 he recognized that Kepler's third law applied to the satellites of Jupiter."
without further details.
Update #3 - Final answer
I repost here the final answer by Christopher Linton from H-ASTRO:
"Kepler, in the Epitome of Copernican Astronomy (1618-1621), did apply his third law to the Jovian satellites (in Art. 553). He got the data from Simon Mayr's World of Jupiter (Mundus Jovialis, 1614). He establishes that $T^2/a^3$ is roughly constant and concludes that the physical mechanism which causes the planets to move as they do is the same as that which causes the Jovian satellites to rotate around Jupiter."