I have lots of favorite mathematical formulas, but few offer as much fun and entertainment as the Schwarzchild Radius. Developed in 1916 by German physicist Karl Schwarzchild, the formula built on Einstein's discoveries around general relativity in 1915, and quantified the exact radius down to which an object would need to be compressed for it to become a black hole. In other words, the Schwarzchild Radius formula enables us to calculate the event horizon of anything with mass, ranging from a grape to the sun to the laptop on which I'm typing this.
As with Einstein's mass-energy equivalence formula, the Schwarzchild Radius formula is deceptively simple:
To identify the radius (Rs) for any object simply plug in the following values:
G is the gravitational constant (6.67 x 10-11m3 / kg x s2)
m is the mass of the object in question (for unit sanity, use kg)
c is the speed of light (9 x 1016 m2 / s2)
Working out the units is a bit tricky, but if you're careful you'll end up with a measurement in meters, which will give you the exact distance between the singularity and the event horizon for any object. Showing just how simple it can be, a video that recently became popular on Reddit walks you through a practical example, calculating the event horizon radius for the Earth.
So you obviously know what comes next, right?
For the sake of humanity, I have calculated and now offer below the Schwarzchild Radii* for the following objects. I, for one, would really, really, really like to see the world's largest cookie experience an event horizon:
A Ford Fiesta
The world's largest cookie
A blue whale
All the copies of World of Warcraft sold to-date (roughly 19 million, at 1lb each)
The Large Hadron Collider (specifically, its Compact Muon Solenoid, or giant detector / magnet)
All the houses in Capeside, MA (fictitious town in Dawson's Creek)
The Death Star (click for an epically nerdy, in-depth examination of the Death Star's est. dimensions)
13.9 microns (0.0139 mm)
My math is really rough and likely incorrect, so try the formula for yourself! Endless fun awaits! If the math gives you a headache, I'm also taking requests.
* Did you know that this was the plural of radius? I sure didn't.