ttract one another at all, but only moved under the influence of the
sun, they would move in orbits having the form of ellipses. They are
found to move very nearly in such orbits, only the actual path deviates
from an ellipse, now in one direction and then in another, and it
slowly changes its position from year to year. These deviations are due
to the pull of the other planets, and by measuring the deviations we
can determine the amount of the pull, and hence the mass of the planet.

The reader will readily understand that the mathematical processes
necessary to get a result in this way must be very delicate and
complicated. A much simpler method can be used in the case of those
planets which have satellites revolving round them, because the
attraction of the planet can be determined by the motions of the
satellite. The first law of motion teaches us that a body in motion, if
acted on by no force, will move in a straight line. Hence, if we see a
body moving in a curve, we know that it is acted on by a force in the
direction towards which the motion curves. A familiar example is that
of a stone thrown from the hand. If the stone were not attracted by the
earth, it would go on forever in the line of throw, and leave the earth
entirely. But under the attraction of the earth, it is drawn down and
down, as it travels onward, until finally it reaches the ground. The
faster the stone is thrown, of course, the farther it will go, and the
greater will be the sweep of the curve of its path. If it were a
cannon-ball, the first part of the curve would be nearly a right line.
If we could fire a cannon-ball horizontally from the top of a high
mountain with a velocity of five miles a second, and if it were not
resisted by the air, the curvature of the path would be equal to that
of the surface of our earth, and so the ball would never reach the
earth, but would revolve round it like a little satellite in an orbit
of its own. Could this be done, the astronomer would be able, knowing
the velocity of the ball, to calculate the attraction of the earth as
well as we determine it by actually observing the motion of falling
bodies around us.

Thus it is that when a planet, like Mars or Jupiter, has satellites
revolving round it, astronomers on the earth can observe the attraction
of the planet on its satellites and thus determine its mass. The rule
for doing this is very simple. The cube of the distance between the
planet and satellite is