Two planets with orbital period ratio approximately 10:1 have been discovered around the star HD 83443 .
The inner and more massive planet , HD 83443 b , 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 \pm 0.008 , in spite of efficient tidal damping .
This is a consequence of its secular interactions with HD 83443 c whose orbital eccentricity e _ { 2 } = 0.42 \pm 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 \equiv ( k _ { 2 } / k _ { 2 J } ) ( 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 .