51. _The Moon held in her Orbit by Gravity._--Newton compared the distance _mN_ that the moon is drawn to the earth in a given time, with the distance a body near the surface of the earth would be pulled toward the earth in the same time; and he found that these distances are to each other inversely as the squares of the distances of the two bodies from the centre of the earth. He therefore concluded that _the moon is drawn to the earth by gravity_, and that the _intensity of gravity decreases as the square of the distance increases_. [Illustration: Fig. 62.] 52. _Any Body whose Orbit is a Conic Section, and which moves according to Kepler's Second Law, is acted upon by a Force varying inversely as the Square of the Distance._--Newton compared the distance which any body, moving in an ellipse, according to Kepler's Second Law, is drawn towards the sun in the same time in different parts of its orbit. He found these distances in all cases to vary inversely as the square of the distance of the planet from the sun. Thus, in Fig. 62, suppose a planet would move from _K_ to _B_ in the same time that it would move from _k_ to _b_ in another part of its orbit. In the first instance the planet would be drawn towards the sun the distance _AB_, and in the second instance the distance _ab_. Newton found that _AB : ab = (SK)^2 : (Sk)^2_. He also found that the same would be true when the body moved in a parabola or a hyperbola: hence he concluded that _every body that moves around the sun in an ellipse, a parabola, or a hyperbola, is moving under the influence of gravity_. [Transcriber's Note: In Newton's equation above, (SK)^2 means to group S and K together and square their product. In the original book, instead of using parentheses, there was a vinculum, a horizontal bar, drawn over the S and the K to express the same grouping.] [Illustration: Fig. 63.] 53. _The Force that draws the Different Planets to the Sun Varies inversely as the Squares of the Distances of the Planets from the Sun._--Newton compared the distances _jK_ and _eF_, over which two planets are drawn towards the sun in the same time, and found these distances to vary inversely as the squares of the distances of the planets from the sun: hence he concluded that _all the planets are held in their orbits by gravity_. He also showed that this would be true of any two bodies that were revolving around the sun's centre, according to Kepler's Third Law. 54. _The Copernican System._--The theory of the solar system which originated with Copernicus, and which was developed and completed by Kepler and Newton, is commonly known as the _Copernican System_. This system is shown in Fig. 64. [Illustration: Fig. 64.] II. THE SUN AND PLANETS. I. THE EARTH. Form and Size.