At perigee, the distance to the Earth is already rmin, which is what you want it to be, but the capsule is moving too fast to stay on a circular orbit (put differently, the gravitational force ...At perigee, the distance to the Earth is already rmin, which is what you want it to be, but the capsule is moving too fast to stay on a circular orbit (put differently, the gravitational force of the Earth at that point is too weak to bend the orbit into a circle): that is why it eventually ends up “overshooting” the Earth on the other side.
