_{1}p

_{2}(1 - e

_{1}e

_{2}cosD) is at least as large as p

_{1}

^{2}(1 - e

_{2}

^{2}) + p

_{2}

^{2}(1 - e

_{1}

^{2}) __________________________________________________

__Bonus problem__Suppose that the ellipses were in distinct planes, given by their normals L1 and L2. Now what is the intersection condition?

__Note__:

The title refers to the fact that planetary orbits are ellipses with common focus.