The Mathematical Principles of Natural Philosophy, Book III: Of the System of the World
Phænomenon IV
That the fixed stars being at rest, the periodic times of the five primary planets, and (whether of the sun about the earth, or) of the earth about the sun, are in the sesquiplicate proportion of their mean distances from the sun.
This proportion, first observed by Kepler, is now received by all astronomers; for the periodic times are the same, and the dimensions of the orbits are the same, whether the sun revolves about the earth, or the earth about the sun. And as to the measures of the periodic times, all astronomers are agreed about them. But for the dimensions of the orbits, Kepler and Bullialdus, above all others, have determined them from observations with the greatest accuracy; and the mean distances corresponding to the periodic times differ but insensibly from those which they have assigned, and for the most part fall in between them; as we may see from the following table.
The periodic times with respect to the fixed stars, of the planets and earth revolving about the sun, in days and decimal parts of a day.
♄ ♃ ♂ ♁ ♀ ☿
10759,275 4332,514 686,9785 365,2565 224,6176 87,9692.
The mean distances of the planets and of the earth from the sun.
♄ ♃ ♂
According to Kepler 951000 519650 152350
" to Bullialdus 954198 522520 152350
" to the periodic times 954006 520096 152369
♁ ♀ ☿
According to Kepler 100000 72400 38806
" to Bullialdus 100000 72398 38585
" to the periodic times 100000 72333 38710
As to Mercury and Venus, there can be no doubt about their distances from the sun; for they are determined by the elongations of those planets from the sun; and for the distances of the superior planets, all dispute is cut off by the eclipses of the satellites of Jupiter. For by those eclipses the position of the shadow which Jupiter projects is determined; whence we have the heliocentric longitude of Jupiter. And from its heliocentric and geocentric longitudes compared together, we determine its distance.