Just as the earth’s gravitational pull keeps the moon perpetually describing circles around it, so the sun’s gravitational pull keeps the earth and all the other planets describing circles around the sun. Knowing the distance of any planet from the sun, and also its speed in its orbit, we can calculate the distance this planet falls towards the sun in a second. This tells us the amount of the sun’s gravitational pull, and from this we can calculate that the sun’s weight must be about 332,000 times the weight of the earth, or almost exactly 2 × 10²⁷ tons. Whichever of the planets we use, we obtain exactly the same weight for the sun. This not only gives us confidence in our result, but incidentally it also provides striking confirmation of the truth of Newton’s law of gravitation, for if this law were inexact or untrue, the different planets would not all tell exactly the same story as to the sun’s weight. Einstein has recently shewn that the law is not absolutely exact, but the amount of inexactness is inappreciable except for the nearest planet, Mercury, and even here it is so exceedingly small that we need not trouble about it for our present purpose. Just as we can weigh the sun and earth by studying the motion of a body gripped by their gravitational pull—or “in their gravitational fields,” as the mathematician would say—so we can weigh any other body which keeps a second small body moving round it by its gravitational attraction. The motions of Jupiter’s satellites make it possible to weigh Jupiter; its weight is found to be about 1·92 × 10²⁴ tons, which is 317 times that of the earth, although only ¹/₁₀₄₇ of that of the sun. Similarly the weight of Saturn is found to be 5·71 × 10²³ tons or about 94·9 times that of the earth. WEIGHING THE STARS. And now we come to a striking application of the principles just explained—when we observe two stars in the sky describing orbits about one another, we can weigh the stars from a study of their orbits. Generally the problem is not quite so simple as those we have just discussed. For its adequate treatment, we must once again levy toll on the mathematical work of Newton. We have seen that a projectile fired horizontally with a speed of 4·90 miles a second, would describe endless circles round the earth. What would happen if it were fired in some other direction and with some other speed?