In a Mensa forum recently, someone mentioned Schwarzchild radius, which reminded me of some notes buried deep from 24 years ago. Back then I used MathCad to document the calculations. I no longer have a license to MathCad. These 4 old pages show how I stumbled across the Schwarzchild radius by considering how massive an object must be to accelerate a small object to the speed of light.
Given: An unusual star of large mass M and radius r is alone in a system until an exterior agent deposits a small object with velocity zero at distance R.
Find: What is the relationship between M, r, and R if the velocity at impact is c, the velocity of light?
I came up with r <= 2GM/c^2. Imagine my surprise to discover that had a name, the Schwarzchild radius.