The Orbits of Planets

Proposition 15 Problem 1

Find the principal diameters of the orbits of the planets.

They are in the sub-sesquiplicate proportion of the periodic times, by Prop. 15, Book 1. Then they are augmented in the proportion of the sum of the masses of matter in the sun and each planet to the first of two mean proportionals betwixt that sum and the quantity of matter in the sun, by Prop. 60, Book 1.

Proposition 16 Problem 2

Find the eccentricities and aphelions of planets

This Problem is resolved by Proposition 18, Book 1.

Proposition 17 Theorem 15

The rotations of the planets are uniform. The libration of the moon is caused by its rotation.

This is proven by the First Law of Motion, and Cor. 22, Prop 66 Book 1.

• Jupiter, with respect to the fixed stars, rotates in 9h 56m
• Mars in 24h 39m
• Venus in 23h
• Earth in 23h 56m
• Sun in 25.5 days
• The moon in 27 days 7h 43m

The sun’s spots return in 27.5 days relative to the Earth. Relative to the stars, it rotates in 25.5 days.

But because the lunar day, arising from its uniform revolution about its axis, is menstrual, that is, equal to the time of its periodic revolution in its orb, therefore the same face of the moon will be always nearly turned to the upper focus of its orb; but, as the situation of that focus requires, will deviate a little to one side and to the other from the earth in the lower focus; and this is the libration in longitude; for the libration in latitude arises from the moon’s latitude, and the inclination of its axis to the plane of the ecliptic.

This theory of the libration of the moon, Mr. N. Mercator in his Astronomy, published at the beginning of the year 1676, explained more fully out of the letters I sent him. The utmost satellite of Saturn seems to revolve about its axis with a motion like this of the moon, respecting Saturn continually with the same face; for in its revolution round Saturn, as often as it comes to the eastern part of its orbit, it is scarcely visible, and generally quite disappears; which is like to be occasioned by some spots in that part of its body, which is then turned towards the earth, as M. Cassini has observed.

So also the utmost satellite of Jupiter seems to revolve about its axis with a like motion, because in that part of its body which is turned from Jupiter it has a spot, which always appears as if it were in Jupiter’s own body, whenever the satellite passes between Jupiter and our eye.