Earth 'weighed' against the Sun

Having discovered that the size of the AU can be estimated in Earth radii using the telescope, there remains one task: to convert Earth's Kepler's constant to AU³/year², so that we can it with those of the Sun, Jupiter and Saturn:

• 1 AU ~ 24000 Earth radii, i.e. the radius of the Earth is ~ 4.2 x 10⁻⁵ AUs
• we cube this: ~ 7.4 x 10⁻¹⁴ and multiply our Kepler constant (297) by it
• 1 day is ~ 1/365 years
• we square this: ~ 7.5 x 10⁻⁶ and divide the above result by it 

In Solar System units, the Earth's Kepler constant is therefore ~ 3 x 10⁻⁶, i.e. about one 300,000th the value of that for the Sun. Hence, we suspect (pre-Cavendish) that the Earth's mass is the same proportion of the Sun's, one 300th the mass of Jupiter and one 100th the mass of Saturn.

Further, given the Sun's angular size is about one half a degree of arc, we can deduce that its radius is about one hundred Earth radii and its volume about that of one million Earths.

Hence the density of the Earth is about 3 times that of the Sun (and of Jupiter).