  Two planets with orbital period ratio approximately 10:1 have been discovered
around the star HD 83443. The inner and more massive planet, HD 83443b, has the
smallest semi-major axis among all currently known exoplanets. Unlike other
short period exoplanets, it maintains a substantial orbital eccentricity,
e_1=0.079+/- 0.008, in spite of efficient tidal damping. This is a consequence
of its secular interactions with HD 83443c whose orbital eccentricity
e_2=0.42+/-0.06. Dissipation, associated with tides the star raises in the
inner planet, removes energy but not angular momentum from its orbit, while
secular interactions transfer angular momentum but not energy from the inner to
the outer planet's orbit. The outward transfer of angular momentum decreases
the tidal decay rate of the inner planet's orbital eccentricity while
increasing that of the outer planet. The alignment of the apsides of the
planets' orbits is another consequence of tidal and secular interactions. In
this state the ratio of their orbital eccentricities, e_1/e_2, depends upon the
secular perturbations the planets exert on each other and on additional
perturbations that enhance the inner planet's precession rate. Tidal and
rotational distortions of the inner planet along with general relativity
provide the most important of these extra precessional perturbations, each of
which acts to reduce e_1/e_2. Provided the planets' orbits are coplanar, the
observed eccentricity ratio uniquely relates sin i and
C=(k_2/k_{2J})(R_1/R_J)^5, where the tidal Love number, k_2, and radius, R_1,
of the inner planet are scaled by their Jovian equivalents.
