intensity depending on the mass of the
sun.[19]

4. So by knowing the length of year and distance of any planet from the
sun, the sun's mass can be calculated, in terms of that of the earth.

5. For the satellites, the force acting depends on the mass of _their_
central body, a planet. Hence the mass of any planet possessing a
satellite becomes known.

6. The force constraining the moon in her orbit is the same gravity as
gives terrestrial bodies their weight and regulates the motion of
projectiles. [Because, while a stone drops 16 feet in a second, the
moon, which is 60 times as far from the centre of the earth, drops 16
feet in a minute.]

* * * * *

7. The moon is attracted not only by the earth, but by the sun also;
hence its orbit is perturbed, and Newton calculated out the chief of
these perturbations, viz.:--

(The equation of the centre, discovered by Hipparchus.)

(_a_) The evection, discovered by Hipparchus and Ptolemy.

(_b_) The variation, discovered by Tycho Brahe.

(_c_) The annual equation, discovered by Tycho Brahe.

(_d_) The retrogression of the nodes, then being observed at
Greenwich by Flamsteed.

(_e_) The variation of inclination, then being observed at
Greenwich by Flamsteed.

(_f_) The progression of the apses (with an error of one-half).

(_g_) The inequality of apogee, previously unknown.

(_h_) The inequality of nodes, previously unknown.

8. Each planet is attracted not only by the sun but by the other
planets, hence their orbits are slightly affected by each other. Newton
began the theory of planetary perturbations.

9. He recognized the comets as members of the solar system, obedient to
the same law of gravity and moving in very elongated ellipses; so their
return could be predicted (_e.g._ Halley's comet).

10. Applying the idea of centrifugal force to the earth considered as a
rotating body, he perceived that it could not be a true sphere, and
calculated its oblateness, obtaining 28 miles greater equatorial than
polar diameter.

11. Conversely, from the observed shape of Jupiter, or any planet, the
length of its day could be estimated.

12. The so-calculated shape of the earth, in combination with
centrifugal force, causes the weight of bodies to vary with latitude;
and Newton calculated the amount of this variation. 194 lbs. at pole
balance 195 lbs. at equator.

13. A homogeneous sphere