Let us consider a tidal disruption event of a star with mass and a radius by a black hole of mass . The tidal radius is defined as and the dimensionless impact parameter is defined as where is the periapse (i.e. the closest the star gets to the black hole). For very massive black holes the minimum periapse is given by the gravitational radius

and the maximum dimensionless impact parameter is given by

In the limit of a very small black hole, the minimal impact parameter is limited by the radius of the disrupted star

and the maximum dimensionless impact parameter in this case is given by

It is therefore clear that the maximum is attained when

The right hand side of the previous equation can be interpreted as the ratio between the actual radius of the star and the gravitational radius of the same mass. The corresponding maximal is