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 divided
by the square of the time of revolution of the satellite. The
quotient is a number which is proportional to the mass of the
planet. The rule applies to the motion of the moon round the earth
and of the planets round the sun. If we divide the cube of the
earth's distance from the sun, say 93,000,000 miles, by the square
of 365 1/4, the days in a year, we shall get a certain quotient.
Let us call this number the sun-quotient. Then, if we divide the
cube of the moon's distance from the earth by the square of its
time of revolution, we shall get another quotient, which we may
call the earth-quotient. The sun-quotient will come out about
330,000 times as large as the earth-quotient. Hence it is
concluded that the mass of the sun is 330,000 times that of the
earth; that it would take this number of earths to make a body as
heavy as the sun.

I give this calculation to illustrate the principle; it must not
be supposed that the astronomer proceeds exactly in this way and
has only this simple calculation to make. In the case of the moon
and earth, the motion and distance of the former vary in
consequence of the attraction of the sun, so that their actual
distance apart is a changing quantity. So what the astronomer