To solve this problem, we need to consider the principles of physics in a gravitational free space.$\\$When two astronauts are floating in space, they are subject to the laws of conservation of momentum.$\\$Let's analyze the situation:$\\$• Both astronauts are initially at rest relative to each other.$\\$• There is no external force acting on them since they are in gravitational free space.$\\$According to Newton's Third Law of Motion:$\\$• If one astronaut exerts a force on the other, the other exerts an equal and opposite force back.$\\$Since they are in a closed system with no external forces, the total momentum of the system is conserved.$\\$If they push off each other:$\\$• They will move in opposite directions, but since the question implies no initial push,$\\$• The only force acting between them is their mutual gravitational attraction.$\\$Gravitational attraction, even though very weak in space, will cause them to move towards each other.$\\$Therefore, the correct answer is:$\\$Option 1: move towards each other.$\\$This is because the gravitational force, though minimal, is the only force acting between them,$\\$causing them to slowly drift towards each other over time.