In 1665 Newton began to suspect that this same gravitational pull might be the cause of the moon describing a circular orbit around the earth instead of running away at a tangent into space. The moon’s distance from the earth’s centre is 238,857 miles, or 60·27 times the radius of the earth. As the moon describes a circle of this size every month (27 days, 4 hours, 43 minutes, 11·5 seconds), we can calculate that its speed in its orbit is 2287 miles an hour. After one second it will have travelled 3350 feet, and if it kept to a strictly rectilinear course this would carry it 0·0044 feet further away from the earth. Thus, to keep in an exact circular orbit around the earth, it must fall 0·0044 feet in a second. This is far less than a body falls in a second at the earth’s surface, but Newton conjectured that the force of gravity must weaken as we recede from the earth’s surface. Actually a body at the earth’s surface falls 3632 times as fast as the moon’s earthward fall in its orbit. Now 3632 is the square of 60·27 (or 3632 = 60·27 × 60·27), whence Newton saw that the moon’s fall would be of exactly the right amount if the force of gravity fell off as the inverse square of the distance—that is to say, if it decreased just as rapidly as the square of the distance increased. As we shall see later, astronomical observation confirms the truth of this law in innumerable ways. This led Newton to put forward his famous law of gravitation according to which the gravitational pull of any body, such as the earth, falls off inversely as the square of the distance from the body. [Illustration: Fig. 3.] Professor C. V. Boys and others have measured the gravitational pull which a few tons of lead exert in the laboratory, and, with this knowledge, it is easy to calculate how many tons the earth must contain so as to exert its observed gravitational pull on bodies outside it. It is found that the earth’s weight must be just under six thousand million million million tons[3], or, as we shall write it, 6 × 10²¹ tons[4]. [3] Here, as throughout the book, we use the French or metric ton of a million grammes or 2204·5 lbs. The English ton of 2240 lbs. is equal to 1·0160 French tons. [4] The notation 6 × 10²¹ stands for the number formed by a 6 followed by 21 zeros, this shorthand notation being essential, in the interests of brevity, in discussing astronomical numbers. A million is 10⁶, a million million is 10¹² and so on. A similar notation is needed to express very small numbers. The expression 10⁻²¹ is written for 1/10²¹ and so on. Thus 6 × 10⁻⁶ stands for 6/1,000,000 or 0·000006. [Illustration: PLATE VII _Mt Wilson Observatory_ The Trifid Nebula _M_ 20 in Sagittarius]