Analysis of empirical dependencies to calculate the crater diameter produced by the collision of a spacecraft with a space debris fragment

The intensive use of near-Earth space and the lack of disposal measures for space objects of various purposes (spacecraft, launch vehicle stages, upper stages, upper stages, etc.) resulted in the formation of what is called debris, in this case space debris. Part of the space debris is observed and registered, these are objects over 100 mm in size and currently there are more than 18,000 objects registered. The bulk of space debris is small, unobserved fragments ranging in size from 100 mm to several microns. This fraction of space debris, which poses a serious risk, is the result of explosions left in orbit by space objects or the intentional destruction of a space object, but the bulk of the minor space debris is generated by collisions of existing debris with each other. If, from a collision with an observed fragment whose trajectory is known, an operational space object can manoeuvre and evade the collision, the trajectory of the small fragment is unknown and its collision cannot be predicted. It is not possible to assess the damage caused by space debris to operational space objects, as all of them remain in orbit and it is not possible to record the angle and impact velocity of the fragment with the object in a laboratory environment using spherical (usually) percussion launchers up to the velocities of hypersonic collisions. On the basis of these experiments, empirical dependencies are developed that describe the results obtained and are appropriate to the conditions in which the experiment was carried out. This work is devoted to the analysis of empirical equations obtained by different authors.