Mrs. B. First draw a line from the earth to the sun representing the force of attraction; then describe the force of projection at a right angle to it.
Caroline. The earth will then move in the curve G I, of the parallelogram G H I K.
Mrs. B. You recollect that a body acted upon by two forces, moves through a diagonal, in the same time that it would have moved through one of the sides of the parallelogram, were it acted upon by one force only. The earth has passed through the diagonals of these three parallelograms, in the space of three months, and has performed one quarter of a circle; and on the same principle it will go on till it has completed the whole of the circle. It will then recommence a course, which it has pursued ever since it first issued from the hand of its Creator, and which there is every reason to suppose it will continue to follow, as long as it remains in existence.
Emily. What a grand and beautiful effect resulting from so simple a cause!
Caroline. It affords an example, on a magnificent scale, of the curvilinear motion, which you taught us in mechanics. The attraction of the sun is the centripetal force, which confines the earth to a centre; and the impulse of projection, the centrifugal force, which impels the earth to quit the sun, and fly off in a tangent.
Mrs. B. Exactly so. 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 carpenter's square, as A, B, C; ([fig. 2. plate 6.]) the point B will be a right angle, the sides of the square being perpendicular to each other; after having done this you are to describe a small circle at the angular point B, representing the earth, and to fasten the extremity of one of the legs of the square to a fixed point A, which we shall consider as the sun. Thus situated, the two sides of the square will represent both the centrifugal and centripetal forces; A B, representing the centripetal, and B C, the centrifugal force; if you now draw it round the fixed point, you will see how the direction of the centrifugal force varies, constantly forming a tangent to the circle in which the earth moves, as it is constantly at a right angle with the centripetal force.
Emily. The earth then, gravitates towards the sun, without the slightest danger either of approaching nearer, or receding further from it. How admirably this is contrived! If the two forces which produce this curved 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.
Mrs. B. What will you say, my dear, when I tell you, that these two forces are not, in fact, so proportioned as to produce circular motion in the earth? We actually revolve round the sun in an elliptical or oval orbit, the sun being situated in one of the foci or centres of the oval, so that the sun is at some periods much nearer to the earth, than at others.
Caroline. You must explain to us, at least, in what manner we avoid the threatened destruction.