United Federation Starship Excelsior drops two small robotic probes toward the surface of a neutron star for exploration. The mass of the star is the same as that of the Sun, but the star's diameter is only 10 km. The robotic probes are linked together by a 1.0-m-long steel cord (which includes communication lines between the two probes), and are dropped vertically (that is, one always above the other). The ship hovers at rest above the star's surface. As the Chief of Materials Engineering on the ship, you are concerned that the communication between the two probes, a crucial aspect of the mission, will not survive. Assume that the cord in use has a breaking tension of 27 kN and that the robots each have a mass of 0.9 kg. How close will the robots be to the surface of the star before the cord breaks?