2.22 (a) The orbits of two bodies (stars, for example) with equal
masses, under the influence of their mutual gravity, are identical ellipses
with a common focus. That focus is not at the center of either star but
instead is located at the center of mass of the pair, midway between them.
The positions of the two bodies at three different times are indicated by the
pairs of numbers. (Notice that a line joining the bodies always passes
through the common focus.) (b) The orbits of two bodies, one of which is twice
as massive as the other. Again, the elliptical orbits have a common focus,
and the two ellipses have the same eccentricity. However, in accordance with
Newton's laws of motion, the more massive body moves more slowly, and in a
smaller orbit, staying closer to the center of mass (at the common focus). In
this particular case, the larger ellipse is twice the size of the smaller
one. (c) In this extreme case of a hypothetical planet orbiting the Sun, the
common focus of the two orbits lies inside the Sun.