Isaac Physics Careless Astronauts

Four astronauts are fixing a satellite in deep space. They are attached to each other by four light, inextensible ropes of length l; each astronaut is attached to his two nearest neighbours. On the way back to their ship they form a perfect square formation which is rotating at some angular speed.
All the astronauts have the same mass with all of their tools. On the way back one of the astronauts drops all his equipment by mistake and the astronaut at the far corner of the square is laughing so hard that he does so too.
Assuming that the mass of an astronaut without tools is half of the mass with tools, how far from the centre of mass (ignoring the lost tools) will the astronauts who dropped their tools be when the rotation has stabilised?

The answer is 0 but I can't figure out how to get there mathematically for the life of me. The hint suggests using the tension in the ropes and centripetal force but then you have to introduce an angle as a variable I can't then get rid of. I tried using conservation of angular momentum but couldn't get anywhere, unless I also used conservation of rotational kinetic energy but then I just found that nothing changes so I assume it doesn't apply here but I'm not sure why. If someone could explain it would be much appreciated :smile: