Fig. 2. 



INTRODUCTION TO ASTRONOMY. xxxi 



the sun is the centripetal force, which confines the earth to a centre ; and 

 the impulse of projection the force which impels the earth to quit the sun 

 and fly off in a tangent, and which, therefore, by the inertia of the body, 

 produces the centrifugal force. 



A simple mode of illustrating the effect of these combined forces on the 

 earth is to cut a slip of card in the form of 

 a right angle (Jig. 2), to describe a small circle 

 at the angular point representing the earth, 

 arid to fasten the extremity of one of the legs of 

 the angle to a fixed point, which we shall con- 

 sider as the sun. Thus situated, the lines 

 forming the angle will represent both the forces 

 which act upon the earth ; and if you draw it 

 round the fixed point, you will see how the di- 

 rection of the force which opposes the centri- 

 petal force varies, constantly forming a tangent 

 to the circle in which the earth moves, as it 

 is constantly at a right angle with the centri- 

 petal force. You will naturally conclude that if the two forces which 

 produce this circular motion had not been so accurately adjusted, 

 one would ultimately have prevailed over the other, and we should 

 either have approached so near the sun as to have been burnt, or 

 have receded so far from it as to have been frozen. But we have de- 

 scribed the earth as moving in a circle, merely to render the explanation 

 more simple, for in reality these two forces are not so proportioned as to 

 produce circular motion ; and the earth's orbit, or path which it describes 

 round the sun, is not circular but elliptical or oval. 



Let us suppose that when the earth is at A (fig. 3) its projectile force 



Fig. 3. 



does not give it a velocity sufficient 

 to counterbalance that of gravity, so 

 as to enable these powers conjointly 

 to carry it round the sun in a circle ; 

 the earth instead of describing the 

 line A C, as in the former figure, 

 will approach nearer the sun in the 

 line A B. Under these circum- 

 stances, it will be asked what is to 

 prevent our approaching nearer and 

 nearer the sun till we fall into it ; for 

 its attraction increases as we advance 

 towards it. There also seems to be 

 another danger. As the earth ap- 

 proaches the sun, the direction of its 

 motion is no longer perpendicular to 

 that of attraction, but inclines more 

 nearly to it. When the earth reaches that part of its orbit at B, the 

 force of projection would carry it to D, which brings it nearer the 

 sun instead of bearing it away from it; so that being driven, by 

 one power, and drawn by the other towards this centre of destruc- 

 tion, it would seem impossible for us to escape. But nature abounds in 

 resources. The earth continues approaching the sun with an accelerated 

 motion, till it reaches the point E : the projectile force now impels it 

 in the direction E F. Here then the two forces act perpendicularly 

 to each other, and the earth is situated as in the preceding figure, yet it 



