as the distance of a planet from the
sun in various parts of its orbit is sometimes greater, and sometimes
less, than its mean distance.

The planet Venus has the nearest approach to a circular orbit, as there
are only 500,000 miles between the mean, and greatest and least
distances, but both Mercury and Mars show great differences between
their greatest and least distances from the sun.

If, therefore, the orbits of a planet are not exactly circular, what is
their exact shape? Kepler solved this problem, and proved that the exact
path of a planet round its central body the sun was that of an ellipse,
or an elongated circle. Thus he gave to the world the first of his
famous laws which stated that each planet revolves round the sun in an
orbit which has an elliptic form, the sun occupying one of the Foci.

Not only is the orbit of a planet round the sun elliptic in form, but
the path of the moon round the earth, or the path of any satellite, as
for example a satellite of Mars or Jupiter or Saturn, is also that of an
ellipse, the planet round which it revolves occupying one of the Foci.

It has also been found that certain comets have orbits which cannot be
distinguished from that of an elongated ellipse, the sun occupying one
of the Foci.

Now let us apply the Law of Gravitation to Kepler's First Law, and note
carefully its application.

[Illustration: Fig: 1.]

Let _A_, _B_, _C_, _D_ be an ellipse representing the orbit of the earth,
and let _S_ represent the sun situated at one of the Foci.

We will suppose that the earth is projected into space at the point _A_,
then according to the First Law of Motion, it would proceed in a
straight line in the direction of _A_ _E_, if there were no other force
acting upon the earth. But it is acted upon by the attraction of the
sun, that is the Centripetal Force which is exerted along the straight
line _S_ _A_ (Art. 20), which continues to act upon it according to the
principle already explained in Arts. 21 and 22.

Now, according to the Second Law of Motion and the Parallelogram of
Forces, instead of the earth going off at a tangent in the direction of
_A_ _E_, it will take a mean path in the direction of _A_ _B_, its path
being curved instead of being a straight line.

If the sun were stationary in space, then the mean distance, that is,
the length of the imaginary straight line joining the sun _S_ _A_ to the
earth, would remain unaltered. The Radius Vector _S_ _A_, o