Page:Popular Science Monthly Volume 12.djvu/240

This page has been validated.
228
THE POPULAR SCIENCE MONTHLY.

the centre. There is no force acting directly from the centre. That which is often called centrifugal is really centripetal force, for the tension of the string in the following experiment is hot caused by any force acting on the body from the centre, but it is caused by a force drawing the body out of its rectilineal course, and toward the centre, compelling it to move in a curve.

Suppose the body E (Fig. 1) moves with a certain velocity in the PSM V12 D240 Planetary motion and gravity.pngFig. 1. curve E C D, and that the string E S feels a known tension, just equal to its strength. Now, double the velocity, and the strength of the string must be increased fourfold to keep it from breaking, for the force drawing the body toward the centre must then be four times as great to keep it moving in the curve. Or, suppose the body moves from A toward B with a known velocity, and that on reaching E is acted upon by the string. The body is then made to take a curvilinear motion, and the string feels a tension drawing the body not directly from but toward the centre, and equal to a force necessary to keep the body from moving in a straight line. It may be remarked that, as action and reaction are equal, the tension is felt both ways. But the reader can easily see what I mean.

This law of motion can be still better illustrated by a reference to one of the satellites of the planet Neptune. The mean distance of this satellite is nearly equal to the distance of our moon from the earth. We may assume these distances to be exactly equal. Then, as at the same distance the centripetal force must increase as the square of the velocity, to keep the body moving in the curve, and as the velocity of this moon of Neptune is about four and a half times greater than that of our moon, the centripetal force, or the force of gravity produced by Neptune on this moon, must be (4.5)2 about twenty times as great as is the centripetal force or the gravitating power our earth produces on its moon. In other words, the planet Neptune is about twenty times as heavy as our earth, for weight is nothing else than the measure of gravity.

The preceding statements are sufficient to show what is meant by centrifugal and centripetal forces. Let us now see how these act on bodies moving in large and small curves, and how the waters on the earth's surface are driven by centrifugal force toward a line tangent to her orbit. Since the length of the orbital curve of the earth is