If you want to derive the Schwarzschild radius for a given body, without mastering linear algebra and tensor mathematics – don’t fear. There is a classical method, that gets to the right answer. No need to delve into the Schwarzschild metric, when you have trusty old Newton.
**Disclaimer- If you can always do this derivation the relativity way. It is better, and will
Using Newtons Laws, it is possible to derive an equation for the escape velocity for a given body. For example, on earth it is equal to around 11 kilometers per second. For a body equal in radius to it’s Schwarzschild radius this escape velocity is equal to the speed of light. This little fact ends up given quite a nice result.
Set the escape velocity to equal the speed of light in the equation derived before, and solving it for the radius will give an answer identical to the relativity method.
**Derivation via the Schwarzschild metric coming soon.